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http://hdl.handle.net/10023/28
Tue, 01 Dec 2015 14:50:19 GMT
20151201T14:50:19Z
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http://hdl.handle.net/10023/28

The appearance, motion, and disappearance of threedimensional magnetic null points
http://hdl.handle.net/10023/7868
Abstract: While theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is colocated with a flow stagnation point, the introduction of asymmetry typically leads to nonideal flows across the null point. To understand this behavior, we present exact expressions for the motion of threedimensional linear null points. The most general expression shows that linear null points move in the direction along which the magnetic field and its time derivative are antiparallel. Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field, which allows nonideal flows across topological boundaries. Null point motion is described intrinsically by parameters evaluated locally; however, global dynamics help set the local conditions at the null point. During a bifurcation of a degenerate null point into a nullnull pair or the reverse, the instantaneous velocity of separation or convergence of the nullnull pair will typically be infinite along the null space of the Jacobian matrix of the magnetic field, but with finite components in the directions orthogonal to the null space. Not all bifurcating nullnull pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating nullnull pair. The motion of separators cannot be described using solely local parameters because the identification of a particular field line as a separator may change as a result of nonideal behavior elsewhere along the field line.
Description: N.A.M. acknowledges support from NASA grants NNX11AB61G, NNX12AB25G, and NNX15AF43G; NASA contract NNM07AB07C; and NSF SHINE grants AGS1156076 and AGS1358342 to SAO. C.E.P. acknowledges support from the St Andrews 2013 STFC Consolidated grant. Date of Acceptance: 19/10/2015
Fri, 30 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7868
20151030T00:00:00Z
A. Murphy, Nicholas
Parnell, Clare Elizabeth
Haynes, Andrew Lewis
While theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is colocated with a flow stagnation point, the introduction of asymmetry typically leads to nonideal flows across the null point. To understand this behavior, we present exact expressions for the motion of threedimensional linear null points. The most general expression shows that linear null points move in the direction along which the magnetic field and its time derivative are antiparallel. Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field, which allows nonideal flows across topological boundaries. Null point motion is described intrinsically by parameters evaluated locally; however, global dynamics help set the local conditions at the null point. During a bifurcation of a degenerate null point into a nullnull pair or the reverse, the instantaneous velocity of separation or convergence of the nullnull pair will typically be infinite along the null space of the Jacobian matrix of the magnetic field, but with finite components in the directions orthogonal to the null space. Not all bifurcating nullnull pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating nullnull pair. The motion of separators cannot be described using solely local parameters because the identification of a particular field line as a separator may change as a result of nonideal behavior elsewhere along the field line.

Dimension and measure theory of selfsimilar structures with no separation condition
http://hdl.handle.net/10023/7854
Abstract: We introduce methods to cope with selfsimilar sets when we do not assume any separation condition. For a selfsimilar set K ⊆ ℝᵈ we establish a similarity dimensionlike formula for Hausdorff dimension regardless of any separation condition. By the application of this result we deduce that the Hausdorff measure and Hausdorff content of K are equal, which implies that K is Ahlfors regular if and only if Hᵗ (K) > 0 where t = dim[sub]H K. We further show that if t = dim[sub]H K < 1 then Hᵗ (K) > 0 is also equivalent to the weak separation property. Regarding Hausdorff dimension, we give a dimension approximation method that provides a tool to generalise results on nonoverlapping selfsimilar sets to overlapping selfsimilar sets.
We investigate how the Hausdorff dimension and measure of a selfsimilar set
K ⊆ ℝᵈ behave under linear mappings. This depends on the nature of the group T generated by the orthogonal parts of the defining maps of K. We show that if T is finite then every linear image of K is a graph directed attractor and there exists at least one projection of K such that the dimension drops under projection. In general, with no restrictions on T we establish that Hᵗ (L ∘ O(K)) = Hᵗ (L(K)) for every element O of the closure of T , where L is a linear map and t = dim[sub]H K. We also prove that for disjoint subsets A and B of K we have that Hᵗ (L(A) ∩ L(B)) = 0. Hochman and Shmerkin showed that if T is dense in SO(d; ℝ) and the strong separation condition is satisfied then dim[sub]H (g(K)) = min {dim[sub]H K; l} for every continuously differentiable map g of rank l. We deduce the same result without any separation condition and we generalize a result of Eroğlu by obtaining that Hᵗ (g(K)) = 0.
We show that for the attractor (K1, … ,Kq) of a graph directed iterated function system, for each 1 ≤ j ≤ q and ε > 0 there exists a selfsimilar set K ⊆ Kj that satisfies the strong separation condition and dim[sub]H Kj  ε < dim[sub]H K. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of K. Using this property we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets.
We study the situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result here shows that this equality holds for any subset of a set corresponding to a nontrivial cylinder of an irreducible subshift of finite type, and thus also for any selfsimilar or graph directed selfsimilar set, regardless of separation conditions. The main tool in the proof is an exhaustion lemma for Hausdorff measure based on the Vitali's Covering Theorem. We also give several examples showing that one cannot hope for the equality to hold in general if one moves in a number of the natural directions away from `selfsimilar'. Finally we consider an analogous version of the problem for packing measure. In this case we need the strong separation condition and can only prove that the packing measure and δapproximate packing premeasure coincide for sufficiently small δ > 0.
Mon, 30 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7854
20151130T00:00:00Z
Farkas, Ábel
We introduce methods to cope with selfsimilar sets when we do not assume any separation condition. For a selfsimilar set K ⊆ ℝᵈ we establish a similarity dimensionlike formula for Hausdorff dimension regardless of any separation condition. By the application of this result we deduce that the Hausdorff measure and Hausdorff content of K are equal, which implies that K is Ahlfors regular if and only if Hᵗ (K) > 0 where t = dim[sub]H K. We further show that if t = dim[sub]H K < 1 then Hᵗ (K) > 0 is also equivalent to the weak separation property. Regarding Hausdorff dimension, we give a dimension approximation method that provides a tool to generalise results on nonoverlapping selfsimilar sets to overlapping selfsimilar sets.
We investigate how the Hausdorff dimension and measure of a selfsimilar set
K ⊆ ℝᵈ behave under linear mappings. This depends on the nature of the group T generated by the orthogonal parts of the defining maps of K. We show that if T is finite then every linear image of K is a graph directed attractor and there exists at least one projection of K such that the dimension drops under projection. In general, with no restrictions on T we establish that Hᵗ (L ∘ O(K)) = Hᵗ (L(K)) for every element O of the closure of T , where L is a linear map and t = dim[sub]H K. We also prove that for disjoint subsets A and B of K we have that Hᵗ (L(A) ∩ L(B)) = 0. Hochman and Shmerkin showed that if T is dense in SO(d; ℝ) and the strong separation condition is satisfied then dim[sub]H (g(K)) = min {dim[sub]H K; l} for every continuously differentiable map g of rank l. We deduce the same result without any separation condition and we generalize a result of Eroğlu by obtaining that Hᵗ (g(K)) = 0.
We show that for the attractor (K1, … ,Kq) of a graph directed iterated function system, for each 1 ≤ j ≤ q and ε > 0 there exists a selfsimilar set K ⊆ Kj that satisfies the strong separation condition and dim[sub]H Kj  ε < dim[sub]H K. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of K. Using this property we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets.
We study the situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result here shows that this equality holds for any subset of a set corresponding to a nontrivial cylinder of an irreducible subshift of finite type, and thus also for any selfsimilar or graph directed selfsimilar set, regardless of separation conditions. The main tool in the proof is an exhaustion lemma for Hausdorff measure based on the Vitali's Covering Theorem. We also give several examples showing that one cannot hope for the equality to hold in general if one moves in a number of the natural directions away from `selfsimilar'. Finally we consider an analogous version of the problem for packing measure. In this case we need the strong separation condition and can only prove that the packing measure and δapproximate packing premeasure coincide for sufficiently small δ > 0.

Acoustic sequences in nonhuman animals : a tutorial review and prospectus
http://hdl.handle.net/10023/7848
Abstract: Animal acoustic communication often takes the form of complex sequences, made up of multiple distinct acoustic units. Apart from the wellknown example of birdsong, other animals such as insects, amphibians,and mammals (including bats, rodents, primates, and cetaceans) also generate complex acoustic sequences. Occasionally, such as with birdsong, the adaptive role of these sequences seems clear (e.g. mate attraction and territorial defence). More often however, researchers have only begun to characterise – let alone understand – the significance and meaning of acoustic sequences. Hypotheses abound, but there is little agreement as to how sequences should be defined and analysed. Our review aims to outline suitable methods for testing these hypotheses, and to describe the major limitations to our current and nearfuture knowledge on questions of acoustic sequences. This review and prospectus is the result of a collaborative effort between 43 scientists from the fields of animal behaviour, ecology and evolution, signal processing, machine learning,quantitative linguistics, and information theory, who gathered for a 2013 workshop entitled, ‘Analysing vocal sequences in animals’. Our goal is to present not just a review of the state of the art, but to propose a methodological framework that summarises what we suggest are the best practices for research in this field,across taxa and across disciplines. We also provide a tutorialstyle introduction to some of the most promising algorithmic approaches for analysing sequences. We divide our review into three sections: identifying the distinct units of an acoustic sequence, describing the different ways that information can be contained within a sequence, and analysing the structure of that sequence. Each of these sections is further subdivided to address the key questions and approaches in that area. We propose a uniform, systematic, and comprehensive approach to studying sequences, with the goal of clarifying research terms used in different fields, and facilitating collaboration and comparative studies. Allowing greater interdisciplinary collaboration will facilitate the investigation of many important questions in the evolution of communication and sociality.
Description: Date of Acceptance: 15/10/2014
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/7848
20140101T00:00:00Z
Kershenbaum, Arik
Blumstein, Dan
Roch, Marie
Akçay, Çaglar
Backus, Gregory
Bee, Mark A.
Bohn, Kirsten
Cao, Yan
Carter, Gerald
Cäsar, Cristiane
Coen, Michael
De Ruiter, Stacy Lynn
Doyle, Laurance
Edelman, Shimon
FerreriCancho, Ramon
Freeberg, Todd M.
Garland, Ellen Clare
Gustison, Morgan
Harley, Heidi E.
Huetz, Chloé
Hughes, Melissa
Bruno, Julia Hyland
Ilany, Amiyaal
Jin, Dezhe Z.
Johnson, Michael
Ju, Chenghui
Karnowski, Jeremy
Lohr, Bernard
Manser, Marta
McCowan, Brenda
Mercado III, Eduardo
Narins, Peter M.
Piel, Alex
Rice, Megan
Salmi, Roberta
Sasahara, Kazutoshi
Sayigh, Laela
Shiu, Yu
Taylor, Charles
Vallejo, Edgar E.
Waller, Sara
ZamoraGutierrez, Veronica
Animal acoustic communication often takes the form of complex sequences, made up of multiple distinct acoustic units. Apart from the wellknown example of birdsong, other animals such as insects, amphibians,and mammals (including bats, rodents, primates, and cetaceans) also generate complex acoustic sequences. Occasionally, such as with birdsong, the adaptive role of these sequences seems clear (e.g. mate attraction and territorial defence). More often however, researchers have only begun to characterise – let alone understand – the significance and meaning of acoustic sequences. Hypotheses abound, but there is little agreement as to how sequences should be defined and analysed. Our review aims to outline suitable methods for testing these hypotheses, and to describe the major limitations to our current and nearfuture knowledge on questions of acoustic sequences. This review and prospectus is the result of a collaborative effort between 43 scientists from the fields of animal behaviour, ecology and evolution, signal processing, machine learning,quantitative linguistics, and information theory, who gathered for a 2013 workshop entitled, ‘Analysing vocal sequences in animals’. Our goal is to present not just a review of the state of the art, but to propose a methodological framework that summarises what we suggest are the best practices for research in this field,across taxa and across disciplines. We also provide a tutorialstyle introduction to some of the most promising algorithmic approaches for analysing sequences. We divide our review into three sections: identifying the distinct units of an acoustic sequence, describing the different ways that information can be contained within a sequence, and analysing the structure of that sequence. Each of these sections is further subdivided to address the key questions and approaches in that area. We propose a uniform, systematic, and comprehensive approach to studying sequences, with the goal of clarifying research terms used in different fields, and facilitating collaboration and comparative studies. Allowing greater interdisciplinary collaboration will facilitate the investigation of many important questions in the evolution of communication and sociality.

Dose response severity functions for acoustic disturbance in cetaceans using recurrent event survival analysis
http://hdl.handle.net/10023/7845
Abstract: Behavioral response studies (BRSs) aim to enhance our understanding of the behavior changes made by animals in response to specific exposure levels of different stimuli, often presented in an increasing dosage. Here, we focus on BRSs that aim to understand behavioral responses of freeranging whales and dolphins to manmade acoustic signals (although the methods are applicable more generally). One desired outcome of these studies is doseresponse functions relevant to different species, signals and contexts. We adapted and applied recurrent event survival analysis (Cox proportional hazard models) to data from the 3S BRS project, where multiple behavioral responses of different severities had been observed per experimental exposure and per individual based upon expert scoring. We included species, signal type, exposure number and behavioral state prior to exposure as potential covariates. The best model included all main effect terms, with the exception of exposure number, as well as two interaction terms. The interactions between signal and behavioral state, and between species and behavioral state highlighted that the sensitivity of animals to different signal types (a 6–7 kHz upsweep sonar signal [MFAS] or a 1–2 kHz upsweep sonar signal [LFAS]) depended on their behavioral state (feeding or nonfeeding), and this differed across species. Of the three species included in this analysis (sperm whale [Physeter macrocephalus], killer whale [Orcinus orca] and longfinned pilot whale [Globicephala melas]), killer whales were consistently the most likely to exhibit behavioral responses to naval sonar exposure. We conclude that recurrent event survival analysis provides an effective framework for fitting doseresponse severity functions to data from behavioral response studies. It can provide outputs that can help government and industry to evaluate the potential impacts of anthropogenic sound production in the ocean.
Description: Date of Acceptance: 08/06/2015
Fri, 20 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7845
20151120T00:00:00Z
Harris, Catriona M
Sadykova, Dinara
De Ruiter, Stacy Lynn
Tyack, Peter Lloyd
Miller, Patrick
Kvadsheim, Petter
Lam, FransPeter
Thomas, Len
Behavioral response studies (BRSs) aim to enhance our understanding of the behavior changes made by animals in response to specific exposure levels of different stimuli, often presented in an increasing dosage. Here, we focus on BRSs that aim to understand behavioral responses of freeranging whales and dolphins to manmade acoustic signals (although the methods are applicable more generally). One desired outcome of these studies is doseresponse functions relevant to different species, signals and contexts. We adapted and applied recurrent event survival analysis (Cox proportional hazard models) to data from the 3S BRS project, where multiple behavioral responses of different severities had been observed per experimental exposure and per individual based upon expert scoring. We included species, signal type, exposure number and behavioral state prior to exposure as potential covariates. The best model included all main effect terms, with the exception of exposure number, as well as two interaction terms. The interactions between signal and behavioral state, and between species and behavioral state highlighted that the sensitivity of animals to different signal types (a 6–7 kHz upsweep sonar signal [MFAS] or a 1–2 kHz upsweep sonar signal [LFAS]) depended on their behavioral state (feeding or nonfeeding), and this differed across species. Of the three species included in this analysis (sperm whale [Physeter macrocephalus], killer whale [Orcinus orca] and longfinned pilot whale [Globicephala melas]), killer whales were consistently the most likely to exhibit behavioral responses to naval sonar exposure. We conclude that recurrent event survival analysis provides an effective framework for fitting doseresponse severity functions to data from behavioral response studies. It can provide outputs that can help government and industry to evaluate the potential impacts of anthropogenic sound production in the ocean.

Speed of convergence for laws of rare events and escape rates
http://hdl.handle.net/10023/7837
Abstract: We obtain error terms on the rate of convergence to Extreme Value Laws, and to the asymptotic Hitting Time Statistics, for a general class of weakly dependent stochastic processes. The dependence of the error terms on the ‘time’ and ‘length’ scales is very explicit. Specialising to data derived from a class of dynamical systems we find even more detailed error terms, one application of which is to consider escape rates through small holes in these systems.
Description: MT was partially supported by NSF grant DMS 1109587. All authors are supported by FCT (Portugal) projects PTDC/MAT/099493/2008 and PTDC/MAT/120346/2010, which are financed by national and European structural funds through the programs FEDER and COMPETE. All three authors were also supported by CMUP, which is financed by FCT (Portugal) through the programs POCTI and POSI, with national and European structural funds, under the project PEstC/MAT/UI0144/2013. Date of Acceptance: 14/11/2014
Wed, 01 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/7837
20150401T00:00:00Z
Freitas, Ana
Freitas, Jorge
Todd, Michael John
We obtain error terms on the rate of convergence to Extreme Value Laws, and to the asymptotic Hitting Time Statistics, for a general class of weakly dependent stochastic processes. The dependence of the error terms on the ‘time’ and ‘length’ scales is very explicit. Specialising to data derived from a class of dynamical systems we find even more detailed error terms, one application of which is to consider escape rates through small holes in these systems.

A general framework for animal density estimation from acoustic detections across a fixed microphone array
http://hdl.handle.net/10023/7786
Abstract: Acoustic monitoring can be an efficient, cheap, noninvasive alternative to physical trapping of individuals. Spatially explicit capturerecapture (SECR) methods have been proposed to estimate calling animal abundance and density from data collected by a fixed array of microphones. However, these methods make some assumptions that are unlikely to hold in many situations, and the consequences of violating these are yet to be investigated. We generalize existing acoustic SECR methodology, enabling these methods to be used in a much wider variety of situations. We incorporate timeofarrival (TOA) data collected by the microphone array, increasing the precision of calling animal density estimates. We use our method to estimate calling male density of the Cape Peninsula Moss Frog Arthroleptella lightfooti. Our method gives rise to an estimator of calling animal density that has negligible bias, and 95% confidence intervals with appropriate coverage. We show that using TOA information can substantially improve estimate precision. Our analysis of the A. lightfooti data provides the first statistically rigorous estimate of calling male density for an anuran population using a microphone array. This method fills a methodological gap in the monitoring of frog populations and is applicable to acoustic monitoring of other species that call or vocalize.
Description: Funding for the frog survey was received from the National Geographic Society/Waitt Grants Program (No. W18411). The EPSRC and NERC helped to fund this research through a PhD grant (No. EP/I000917/1). Date of Acceptance: 07/10/2014
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7786
20150101T00:00:00Z
Stevenson, B.C.
Borchers, D.L.
Altwegg, R.
Swift, R.J.
Gillespie, D.M.
Measey, G.J.
Acoustic monitoring can be an efficient, cheap, noninvasive alternative to physical trapping of individuals. Spatially explicit capturerecapture (SECR) methods have been proposed to estimate calling animal abundance and density from data collected by a fixed array of microphones. However, these methods make some assumptions that are unlikely to hold in many situations, and the consequences of violating these are yet to be investigated. We generalize existing acoustic SECR methodology, enabling these methods to be used in a much wider variety of situations. We incorporate timeofarrival (TOA) data collected by the microphone array, increasing the precision of calling animal density estimates. We use our method to estimate calling male density of the Cape Peninsula Moss Frog Arthroleptella lightfooti. Our method gives rise to an estimator of calling animal density that has negligible bias, and 95% confidence intervals with appropriate coverage. We show that using TOA information can substantially improve estimate precision. Our analysis of the A. lightfooti data provides the first statistically rigorous estimate of calling male density for an anuran population using a microphone array. This method fills a methodological gap in the monitoring of frog populations and is applicable to acoustic monitoring of other species that call or vocalize.

Passive acoustic monitoring of beaked whale densities in the Gulf of Mexico
http://hdl.handle.net/10023/7779
Abstract: Beaked whales are deep diving elusive animals, difficult to census with conventional visual surveys. Methods are presented for the density estimation of beaked whales, using passive acoustic monitoring data collected at sites in the Gulf of Mexico (GOM) from the period during and following the Deepwater Horizon oil spill (2010–2013). Beaked whale species detected include: Gervais’ (Mesoplodon europaeus), Cuvier’s (Ziphius cavirostris), Blainville’s (Mesoplodon densirostris) and an unknown species of Mesoplodon sp. (designated as Beaked Whale Gulf — BWG). For Gervais’ and Cuvier’s beaked whales, we estimated weekly animal density using two methods, one based on the number of echolocation clicks, and another based on the detection of animal groups during 5 min timebins. Density estimates derived from these two methods were in good general agreement. At two sites in the western GOM, Gervais’ beaked whales were present throughout the monitoring period, but Cuvier’s beaked whales were present only seasonally, with periods of low density during the summer and higher density in the winter. At an eastern GOM site, both Gervais’ and Cuvier’s beaked whales had a high density throughout the monitoring period.
Description: Funding to support the tag data was also received from the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions. Date of Acceptance: 06/10/2015
Thu, 12 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7779
20151112T00:00:00Z
Hildebrand, John
BaumannPickering, Simone
Frasier, Kaitlin
Trickey, Jennifer
Merkens, Karlina
Wiggins, Sean
McDonald, Mark
Garrison, Lance
Harris, Danielle
Marques, Tiago A.
Thomas, Len
Beaked whales are deep diving elusive animals, difficult to census with conventional visual surveys. Methods are presented for the density estimation of beaked whales, using passive acoustic monitoring data collected at sites in the Gulf of Mexico (GOM) from the period during and following the Deepwater Horizon oil spill (2010–2013). Beaked whale species detected include: Gervais’ (Mesoplodon europaeus), Cuvier’s (Ziphius cavirostris), Blainville’s (Mesoplodon densirostris) and an unknown species of Mesoplodon sp. (designated as Beaked Whale Gulf — BWG). For Gervais’ and Cuvier’s beaked whales, we estimated weekly animal density using two methods, one based on the number of echolocation clicks, and another based on the detection of animal groups during 5 min timebins. Density estimates derived from these two methods were in good general agreement. At two sites in the western GOM, Gervais’ beaked whales were present throughout the monitoring period, but Cuvier’s beaked whales were present only seasonally, with periods of low density during the summer and higher density in the winter. At an eastern GOM site, both Gervais’ and Cuvier’s beaked whales had a high density throughout the monitoring period.

On simultaneous local dimension functions of subsets of Rd
http://hdl.handle.net/10023/7778
Abstract: For a subset E ⊑ Rd and x ∈ Rd, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by (Formula presented.) where dimH and dimP denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions f,g: Rd → [0, d] with f ≤ g, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.
Description: Date of Acceptance: 04/05/2015
Wed, 30 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/7778
20150930T00:00:00Z
Olsen, Lars Ole Ronnow
For a subset E ⊑ Rd and x ∈ Rd, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by (Formula presented.) where dimH and dimP denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions f,g: Rd → [0, d] with f ≤ g, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.

Occurrence, distribution and abundance of cetaceans in Onslow Bay, North Carolina, USA
http://hdl.handle.net/10023/7772
Abstract: In this paper the occurrence, distribution and abundance of cetaceans in offshore waters of Onslow Bay, North Carolina, USA is described. Between June 2007 and June 2010 monthly aerial and shipboard linetransect surveys were conducted along ten 74km transects placed perpendicular to the shelf break. In total 42,676km of aerial trackline (218 sightings) and 5,209km of vessel trackline (100 sightings) were observed. Seven species of cetaceans were observed, but the fauna was dominated strongly by common bottlenose and Atlantic spotted dolphins. Both species were present yearround in the study area. Using photoidentification techniques, five bottlenose dolphins and one spotted dolphin were resighted during the threeyear period. In general, the abundance of cetaceans in Onslow Bay was low and too few sightings were made to estimate monthly abundances for species other than bottlenose and spotted dolphins. Maximum monthly abundances of bottlenose and spotted dolphins were 4,100 (95% CI: 1,300–9,400) in May 2010 and 6,000 (95% CI: 2,500–17,400) in March 2009, respectively. Bottlenose dolphins were found throughout the study area, although they were encountered most frequently just off the shelf break. In contrast, spotted dolphins exhibited a strong preference for waters over the continental shelf and were not encountered beyond the shelf break.
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/7772
20140101T00:00:00Z
Read, Andrew, J.
Barco, S.
Bell, J.
Borchers, David Louis
Burt, M Louise
Cummings, E.W.
Dunn, J.
Fougeres, J.
Hazen, L.
WilliamsHodge, L.E.
Laura, AM.
McAlarney, R.J.
Nilsson, P.
Pabst, D.A.
Paxton, Charles G. M.
Schneider, S.Z.
Urian, Kim
Waples, D.M.
McLellan, W.A.
In this paper the occurrence, distribution and abundance of cetaceans in offshore waters of Onslow Bay, North Carolina, USA is described. Between June 2007 and June 2010 monthly aerial and shipboard linetransect surveys were conducted along ten 74km transects placed perpendicular to the shelf break. In total 42,676km of aerial trackline (218 sightings) and 5,209km of vessel trackline (100 sightings) were observed. Seven species of cetaceans were observed, but the fauna was dominated strongly by common bottlenose and Atlantic spotted dolphins. Both species were present yearround in the study area. Using photoidentification techniques, five bottlenose dolphins and one spotted dolphin were resighted during the threeyear period. In general, the abundance of cetaceans in Onslow Bay was low and too few sightings were made to estimate monthly abundances for species other than bottlenose and spotted dolphins. Maximum monthly abundances of bottlenose and spotted dolphins were 4,100 (95% CI: 1,300–9,400) in May 2010 and 6,000 (95% CI: 2,500–17,400) in March 2009, respectively. Bottlenose dolphins were found throughout the study area, although they were encountered most frequently just off the shelf break. In contrast, spotted dolphins exhibited a strong preference for waters over the continental shelf and were not encountered beyond the shelf break.

Nearthreshold electron injection in the laserplasma wakefield accelerator leading to femtosecond bunches
http://hdl.handle.net/10023/7750
Abstract: The laserplasma wakefield accelerator is a compact source of high brightness, ultrashort duration electron bunches. Selfinjection occurs when electrons from the background plasma gain sufficient momentum at the back of the bubbleshaped accelerating structure to experience sustained acceleration. The shortest duration and highest brightness electron bunches result from selfinjection close to the threshold for injection. Here we show that in this case injection is due to the localized charge density buildup in the sheath crossing region at the rear of the bubble, which has the effect of increasing the accelerating potential to above a critical value. Bunch duration is determined by the dwell time above this critical value, which explains why single or multiple ultrashort electron bunches with little dark current are formed in the first bubble. We confirm experimentally, using coherent optical transition radiation measurements, that single or multiple bunches with femtosecond duration and peak currents of several kiloAmpere, and femtosecond intervals between bunches, emerge from the accelerator.
Description: We gratefully acknowledge the support of the UK EPSRC (grant no. EP/J018171/1), the EU FP7 programmes: the Extreme Light Infrastructure (ELI) project, the LaserlabEurope (no. 284464), and the EUCARD2 project (no. 312453). Date of Acceptance: 24/08/2015
Thu, 17 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/7750
20150917T00:00:00Z
Islam, M.R.
Brunetti, E.
Shanks, R.P.
Ersfeld, B.
Issac, R.C.
Cipiccia, S.
Anania, M.P.
Welsh, G.H.
Wiggins, S.M.
Noble, A.
Cairns, R Alan
Raj, G.
Jaroszynski, D.A.
The laserplasma wakefield accelerator is a compact source of high brightness, ultrashort duration electron bunches. Selfinjection occurs when electrons from the background plasma gain sufficient momentum at the back of the bubbleshaped accelerating structure to experience sustained acceleration. The shortest duration and highest brightness electron bunches result from selfinjection close to the threshold for injection. Here we show that in this case injection is due to the localized charge density buildup in the sheath crossing region at the rear of the bubble, which has the effect of increasing the accelerating potential to above a critical value. Bunch duration is determined by the dwell time above this critical value, which explains why single or multiple ultrashort electron bunches with little dark current are formed in the first bubble. We confirm experimentally, using coherent optical transition radiation measurements, that single or multiple bunches with femtosecond duration and peak currents of several kiloAmpere, and femtosecond intervals between bunches, emerge from the accelerator.

Future capabilities of CME polarimetric 3D reconstructions with the METIS instrument : a numerical test
http://hdl.handle.net/10023/7748
Abstract: Context. Understanding the 3D structure of coronal mass ejections (CMEs) is crucial for understanding the nature and origin of solar eruptions. However, owing to the optical thinness of the solar corona we can only observe the line of sight integrated emission. As a consequence the resulting projection effects hide the true 3D structure of CMEs. To derive information on the 3D structure of CMEs from whitelight (total and polarized brightness) images, the polarization ratio technique is widely used. The soontobelaunched METIS coronagraph on board Solar Orbiter will use this technique to produce new polarimetric images. Aims. This work considers the application of the polarization ratio technique to synthetic CME observations from METIS. In particular we determine the accuracy at which the position of the centre of mass, direction and speed of propagation, and the column density of the CME can be determined along the line of sight. Methods. We perform a 3D MHD simulation of a flux rope ejection where a CME is produced. From the simulation we (i) synthesize the corresponding METIS whitelight (total and polarized brightness) images and (ii) apply the polarization ratio technique to these synthesized images and compare the results with the known density distribution from the MHD simulation. In addition, we use recent results that consider how the position of a single blob of plasma is measured depending on its projected position in the plane of the sky. From this we can interpret the results of the polarization ratio technique and give an estimation of the error associated with derived parameters. Results. We find that the polarization ratio technique reproduces with high accuracy the position of the centre of mass along the line of sight. However, some errors are inherently associated with this determination. The polarization ratio technique also allows information to be derived on the real 3D direction of propagation of the CME. The determination of this is of fundamental importance for future space weather forecasting. In addition, we find that the column density derived from whitelight images is accurate and we propose an improved technique where the combined use of the polarization ratio technique and whitelight images minimizes the error in the estimation of column densities. Moreover, by applying the comparison to a set of snapshots of the simulation we can also assess the errors related to the trajectory and the expansion of the CME. Conclusions. Our method allows us to thoroughly test the performance of the polarization ratio technique and allows a determination of the errors associated with it, which means that it can be used to quantify the results from the analysis of the forthcoming METIS observations in white light (total and polarized brightness). Finally, we describe a satellite observing configuration relative to the Earth that can allow the technique to be efficiently used for space weather predictions.
Description: D.H.M. would like to thank STFC and the Leverhulme Trust for their financial support. P.P. would like to thank STFC and the Leverhulme Trust. The computational work for this paper was carried out on the joint STFC and SFC (SRIF) funded cluster at the University of St Andrews (Scotland, UK). Date of Acceptance: 08/08/2015
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7748
20151001T00:00:00Z
Pagano, Paolo
Bemporad, A
Mackay, Duncan Hendry
Context. Understanding the 3D structure of coronal mass ejections (CMEs) is crucial for understanding the nature and origin of solar eruptions. However, owing to the optical thinness of the solar corona we can only observe the line of sight integrated emission. As a consequence the resulting projection effects hide the true 3D structure of CMEs. To derive information on the 3D structure of CMEs from whitelight (total and polarized brightness) images, the polarization ratio technique is widely used. The soontobelaunched METIS coronagraph on board Solar Orbiter will use this technique to produce new polarimetric images. Aims. This work considers the application of the polarization ratio technique to synthetic CME observations from METIS. In particular we determine the accuracy at which the position of the centre of mass, direction and speed of propagation, and the column density of the CME can be determined along the line of sight. Methods. We perform a 3D MHD simulation of a flux rope ejection where a CME is produced. From the simulation we (i) synthesize the corresponding METIS whitelight (total and polarized brightness) images and (ii) apply the polarization ratio technique to these synthesized images and compare the results with the known density distribution from the MHD simulation. In addition, we use recent results that consider how the position of a single blob of plasma is measured depending on its projected position in the plane of the sky. From this we can interpret the results of the polarization ratio technique and give an estimation of the error associated with derived parameters. Results. We find that the polarization ratio technique reproduces with high accuracy the position of the centre of mass along the line of sight. However, some errors are inherently associated with this determination. The polarization ratio technique also allows information to be derived on the real 3D direction of propagation of the CME. The determination of this is of fundamental importance for future space weather forecasting. In addition, we find that the column density derived from whitelight images is accurate and we propose an improved technique where the combined use of the polarization ratio technique and whitelight images minimizes the error in the estimation of column densities. Moreover, by applying the comparison to a set of snapshots of the simulation we can also assess the errors related to the trajectory and the expansion of the CME. Conclusions. Our method allows us to thoroughly test the performance of the polarization ratio technique and allows a determination of the errors associated with it, which means that it can be used to quantify the results from the analysis of the forthcoming METIS observations in white light (total and polarized brightness). Finally, we describe a satellite observing configuration relative to the Earth that can allow the technique to be efficiently used for space weather predictions.

Corotating interaction regions as seen by the STEREO Heliospheric Imagers 2007 – 2010
http://hdl.handle.net/10023/7746
Abstract: NASA’s Solar Terrestrial Relations Observatory (STEREO) mission has coincided with a pronounced solar minimum. This allowed for easier detection of corotating interaction regions (CIRs). CIRs are formed by the interaction between fast and slow solarwind streams ejected from source regions on the solar surface that rotate with the Sun. Highdensity plasma blobs that have become entrained at the stream interface can be tracked out to large elongations in data from the Heliospheric Imager (HI) instruments onboard STEREO. These blobs act as tracers of the CIR itself such that their HI signatures can be used to estimate CIR source location and radial speed. We estimate the kinematic properties of solarwind transients associated with 40 CIRs detected by the HI instrument onboard the STEREOA spacecraft between 2007 and 2010. We identify insitu signatures of these transients at L1 using the Advanced Composition Explorer (ACE) and compare the insitu parameters with the HI results. We note that solarwind transients associated with CIRs appear to travel at or close to the slow solarwind speed preceding the event as measured in situ. We also highlight limitations in the commonly used analysis techniques of solarwind transients by considering variability in the solar wind.
Description: T.M. Conlon and A.O. Williams were supported by an STFC, UK studentship and S.E. Milan was supported by STFC grant ST/K001000/1. Date of Acceptance: 08/08/2015
Sat, 01 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/7746
20150801T00:00:00Z
Conlon, Thomas Michael
Milan, S.E.
Davies, J.A.
Williams, A.O.
NASA’s Solar Terrestrial Relations Observatory (STEREO) mission has coincided with a pronounced solar minimum. This allowed for easier detection of corotating interaction regions (CIRs). CIRs are formed by the interaction between fast and slow solarwind streams ejected from source regions on the solar surface that rotate with the Sun. Highdensity plasma blobs that have become entrained at the stream interface can be tracked out to large elongations in data from the Heliospheric Imager (HI) instruments onboard STEREO. These blobs act as tracers of the CIR itself such that their HI signatures can be used to estimate CIR source location and radial speed. We estimate the kinematic properties of solarwind transients associated with 40 CIRs detected by the HI instrument onboard the STEREOA spacecraft between 2007 and 2010. We identify insitu signatures of these transients at L1 using the Advanced Composition Explorer (ACE) and compare the insitu parameters with the HI results. We note that solarwind transients associated with CIRs appear to travel at or close to the slow solarwind speed preceding the event as measured in situ. We also highlight limitations in the commonly used analysis techniques of solarwind transients by considering variability in the solar wind.

Status and future of research on the behavioural responses of marine mammals to U.S. Navy sonar
http://hdl.handle.net/10023/7741
Abstract: A review of the status and future of research into behavioral responses of marine mammals to naval sonar exposure was undertaken to evaluate the return on investment of current US Navy funded programs, identify the data needs and the contributions of current research programs to meeting data needs, and determine the ability to meet outstanding data needs given the current state of technology. As part of this review, a workshop was held from 2122 April 2015 in Monterey, California. Workshop attendees were key representatives of Navyfunded behavioral response studies, as well as three external reviewers who were selected because of their expertise in animal behavior and behavioral responses to anthropogenic stimuli in the aquatic and terrestrial environments. Prior to the workshop, a questionnaire was circulated to canvass the opinions of members of the scientific community (primarily workshop attendees exclusive of external reviewers) on each of the research approaches taken to address this topic. The workshop was then structured around the questionnaire and responses received, via a series of discussion sessions. Afterwards, each research approach was evaluated independently by the external reviewers. This report presents a synthesis of the evaluations and recommendations of the external reviewers on current and future behavioral response research relevant to naval sonar. All reviewers agreed that excellent progress has been made on this topic and that each of the research approaches has contributed to our understanding of cetacean responses to naval sonar. The report includes specific comments and recommendations of the reviewers relevant to each approach, but also includes suggestions for priority species and a comprehensive list of recommendations for the future of BRS research in general (Tables 1 and 2). In summary it was recommended that BRS research be continued and extended to increase sample sizes and experimental replication, and temporal duration and spatial scale including more research in areas where the animals are presumably more naïve than on the naval ranges. It was noted that future investigations would benefit from combining experimentation and observation to enable linkage of shortterm behavioral response to longterm fitness consequences of repeated exposure. Beaked whales were the species group ranked highest in terms of research priority. The importance of baseline studies and longerterm monitoring of animals before and after exposure is emphasized throughout.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7741
20150101T00:00:00Z
Harris, Catriona M
Thomas, Len
A review of the status and future of research into behavioral responses of marine mammals to naval sonar exposure was undertaken to evaluate the return on investment of current US Navy funded programs, identify the data needs and the contributions of current research programs to meeting data needs, and determine the ability to meet outstanding data needs given the current state of technology. As part of this review, a workshop was held from 2122 April 2015 in Monterey, California. Workshop attendees were key representatives of Navyfunded behavioral response studies, as well as three external reviewers who were selected because of their expertise in animal behavior and behavioral responses to anthropogenic stimuli in the aquatic and terrestrial environments. Prior to the workshop, a questionnaire was circulated to canvass the opinions of members of the scientific community (primarily workshop attendees exclusive of external reviewers) on each of the research approaches taken to address this topic. The workshop was then structured around the questionnaire and responses received, via a series of discussion sessions. Afterwards, each research approach was evaluated independently by the external reviewers. This report presents a synthesis of the evaluations and recommendations of the external reviewers on current and future behavioral response research relevant to naval sonar. All reviewers agreed that excellent progress has been made on this topic and that each of the research approaches has contributed to our understanding of cetacean responses to naval sonar. The report includes specific comments and recommendations of the reviewers relevant to each approach, but also includes suggestions for priority species and a comprehensive list of recommendations for the future of BRS research in general (Tables 1 and 2). In summary it was recommended that BRS research be continued and extended to increase sample sizes and experimental replication, and temporal duration and spatial scale including more research in areas where the animals are presumably more naïve than on the naval ranges. It was noted that future investigations would benefit from combining experimentation and observation to enable linkage of shortterm behavioral response to longterm fitness consequences of repeated exposure. Beaked whales were the species group ranked highest in terms of research priority. The importance of baseline studies and longerterm monitoring of animals before and after exposure is emphasized throughout.

Observational signatures of waves and flows in the solar corona
http://hdl.handle.net/10023/7722
Abstract: Propagating perturbations have been observed in extended coronal loop structures for a number of years, but the interpretation in terms of slow (propagating) magnetoacoustic waves and/or as quasiperiodic upflows remains unresolved. We used forwardmodelling to construct observational signatures associated with a simple slow magnetoacoustic wave or periodic flow model. Observational signatures were computed for the 171 Å Fe ix and the 193 Å Fe xii spectral lines. Although there are many differences between the flow and wave models, we did not find any clear, robust observational characteristics that can be used in isolation (i.e. that do not rely on a comparison between the models). For the waves model, a relatively rapid change of the average line widths as a function of (shallow) lineofsight angles was found, whereas the ratio of the line width amplitudes to the Doppler velocity amplitudes is relatively high for the flow model. The most robust observational signature found is that the ratio of the mean to the amplitudes of the Doppler velocity is always higher than one for the flow model. This ratio is substantially higher for flows than for waves, and for the flows model used in the study is exactly the same in the 171 Å Fe ix and the 193 Å Fe xii spectral lines. However, these potential observational signatures need to be treated cautiously because they are likely to be modeldependent.
Description: DM acknowledges support of a Royal Society University Research Fellowship and a KU Leuven Research Council senior research fellowship (SF/12/008). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/20072013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/solspanet ). TVD has been sponsored by an Odysseus grant of the FWO Vlaanderen. The research was performed in the context of the IAP P7/08 CHARM (Belspo) and the GOA2015014 (KU Leuven). TVD acknowledges the funding from the FP7 ERG grant with number 276808. Date of Acceptance: 08/10/2014
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/7722
20150201T00:00:00Z
De Moortel, I.
Antolin, P.
Van Doorsselaere, T.
Propagating perturbations have been observed in extended coronal loop structures for a number of years, but the interpretation in terms of slow (propagating) magnetoacoustic waves and/or as quasiperiodic upflows remains unresolved. We used forwardmodelling to construct observational signatures associated with a simple slow magnetoacoustic wave or periodic flow model. Observational signatures were computed for the 171 Å Fe ix and the 193 Å Fe xii spectral lines. Although there are many differences between the flow and wave models, we did not find any clear, robust observational characteristics that can be used in isolation (i.e. that do not rely on a comparison between the models). For the waves model, a relatively rapid change of the average line widths as a function of (shallow) lineofsight angles was found, whereas the ratio of the line width amplitudes to the Doppler velocity amplitudes is relatively high for the flow model. The most robust observational signature found is that the ratio of the mean to the amplitudes of the Doppler velocity is always higher than one for the flow model. This ratio is substantially higher for flows than for waves, and for the flows model used in the study is exactly the same in the 171 Å Fe ix and the 193 Å Fe xii spectral lines. However, these potential observational signatures need to be treated cautiously because they are likely to be modeldependent.

A description of LATTE outputs
http://hdl.handle.net/10023/7720
Fri, 30 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7720
20151030T00:00:00Z
Marques, Tiago A.
Thomas, Len

Digit frequencies and Bernoulli convolutions
http://hdl.handle.net/10023/7719
Abstract: It is well known that when β is a Pisot number, the corresponding Bernoulli convolution ν(β) has Hausdorff dimension less than 1, i.e. that there exists a set A(β) with (ν(β))(A(β))=1 and dim_H(A(β))<1. We show explicitly how to construct for each Pisot number β such a set A(β).
Description: This work was supported partly by the Dutch Organisation for Scientific Research (NWO) grant number 613.001.022 and partly by the Engineering and Physical Sciences Research Council grant number EP/K029061/1. Date of Acceptance: 05/2014
Fri, 27 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/7719
20140627T00:00:00Z
Kempton, Thomas Michael William
It is well known that when β is a Pisot number, the corresponding Bernoulli convolution ν(β) has Hausdorff dimension less than 1, i.e. that there exists a set A(β) with (ν(β))(A(β))=1 and dim_H(A(β))<1. We show explicitly how to construct for each Pisot number β such a set A(β).

Selfaffine sets with positive Lebesgue measure
http://hdl.handle.net/10023/7718
Abstract: Using techniques introduced by C. Gunturk, we prove that the attractors of a family of overlapping selfaffine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous βexpansion’ of different numbers in different bases.
Description: Date of Acceptance: 05/2015
Fri, 27 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/7718
20140627T00:00:00Z
Dajani, Karma
Jiang, Kan
Kempton, Thomas Michael William
Using techniques introduced by C. Gunturk, we prove that the attractors of a family of overlapping selfaffine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous βexpansion’ of different numbers in different bases.

Multiscale modelling of cancer progression and treatment control : the role of intracellular heterogeneities in chemotherapy treatment
http://hdl.handle.net/10023/7714
Abstract: Cancer is a complex, multiscale process involving interactions at intracellular, intercellular and tissue scales that are in turn susceptible to microenvironmental changes. Each individual cancer cell within a cancer cell mass is unique, with its own internal cellular pathways and biochemical interactions. These interactions contribute to the functional changes at the cellular and tissue scale, creating a heterogenous cancer cell population. Anticancer drugs are effective in controlling cancer growth by inflicting damage to various target molecules and thereby triggering multiple cellular and intracellular pathways, leading to cell death or cellcycle arrest. One of the major impediments in the chemotherapy treatment of cancer is drug resistance driven by multiple mechanisms, including multidrug and cellcycle mediated resistance to chemotherapy drugs. In this article, we discuss two hybrid multiscale modelling approaches, incorporating multiple interactions involved in the subcellular, cellular and microenvironmental levels to study the effects of cellcycle, phasespecific chemotherapy on the growth and progression of cancer cells.
Description: Date of Acceptance: 03/11/2014
Mon, 01 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7714
20150601T00:00:00Z
Chaplain, Mark Andrew Joseph
Powathil, Gibin
Cancer is a complex, multiscale process involving interactions at intracellular, intercellular and tissue scales that are in turn susceptible to microenvironmental changes. Each individual cancer cell within a cancer cell mass is unique, with its own internal cellular pathways and biochemical interactions. These interactions contribute to the functional changes at the cellular and tissue scale, creating a heterogenous cancer cell population. Anticancer drugs are effective in controlling cancer growth by inflicting damage to various target molecules and thereby triggering multiple cellular and intracellular pathways, leading to cell death or cellcycle arrest. One of the major impediments in the chemotherapy treatment of cancer is drug resistance driven by multiple mechanisms, including multidrug and cellcycle mediated resistance to chemotherapy drugs. In this article, we discuss two hybrid multiscale modelling approaches, incorporating multiple interactions involved in the subcellular, cellular and microenvironmental levels to study the effects of cellcycle, phasespecific chemotherapy on the growth and progression of cancer cells.

Systems oncology : towards patientspecific treatment regimes informed by multiscale mathematical modelling
http://hdl.handle.net/10023/7713
Abstract: The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially suboptimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patientspecific multimodality treatment protocols that may increase patients quality of life.
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/7713
20150201T00:00:00Z
Powathil, Gibin G.
Swat, Maciej
Chaplain, Mark A. J.
The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially suboptimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patientspecific multimodality treatment protocols that may increase patients quality of life.

Mathematical modelling of cancer invasion : implications of cell adhesion variability for tumour infiltrative growth patterns
http://hdl.handle.net/10023/7712
Abstract: Cancer invasion, recognised as one of the hallmarks of cancer, is a complex, multiscale phenomenon involving many interrelated genetic, biochemical, cellular and tissue processes at different spatial and temporal scales. Central to invasion is the ability of cancer cells to alter and degrade an extracellular matrix. Combined with abnormal excessive proliferation and migration which is enabled and enhanced by altered cellcell and cellmatrix adhesion, the cancerous mass can invade the neighbouring tissue. Along with tumourinduced angiogenesis, invasion is a key component of metastatic spread, ultimately leading to the formation of secondary tumours in other parts of the host body. In this paper we explore the spatiotemporal dynamics of a model of cancer invasion, where cellcell and cellmatrix adhesion is accounted for through nonlocal interaction terms in a system of partial integrodifferential equations. The change of adhesion properties during cancer growth and development is investigated here through timedependent adhesion characteristics within the cell population as well as those between the cells and the components of the extracellular matrix. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as tumour infiltrative growth patterns (INF).
Description: Date of Acceptance: 07/07/2014
Fri, 21 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/7712
20141121T00:00:00Z
Domschke, Pia
Trucu, Dumitru
Gerisch, Alf
Chaplain, Mark A. J.
Cancer invasion, recognised as one of the hallmarks of cancer, is a complex, multiscale phenomenon involving many interrelated genetic, biochemical, cellular and tissue processes at different spatial and temporal scales. Central to invasion is the ability of cancer cells to alter and degrade an extracellular matrix. Combined with abnormal excessive proliferation and migration which is enabled and enhanced by altered cellcell and cellmatrix adhesion, the cancerous mass can invade the neighbouring tissue. Along with tumourinduced angiogenesis, invasion is a key component of metastatic spread, ultimately leading to the formation of secondary tumours in other parts of the host body. In this paper we explore the spatiotemporal dynamics of a model of cancer invasion, where cellcell and cellmatrix adhesion is accounted for through nonlocal interaction terms in a system of partial integrodifferential equations. The change of adhesion properties during cancer growth and development is investigated here through timedependent adhesion characteristics within the cell population as well as those between the cells and the components of the extracellular matrix. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as tumour infiltrative growth patterns (INF).

Stochastic modelling of chromosomal segregation : errors can introduce correction
http://hdl.handle.net/10023/7711
Abstract: Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochoremicrotubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.
Description: Date of Acceptance: 17/04/2014
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/7711
20140701T00:00:00Z
Matzavinos, Anastasios
Roitershtein, Alexander
Shtylla, Blerta
Voller, Zachary
Liu, Sijia
Chaplain, Mark A.J.
Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochoremicrotubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.

Mathematical modeling of tumor growth and treatment
http://hdl.handle.net/10023/7710
Abstract: Using mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative approaches have also made their way into cancer research. An increasing number of mathematical, physical, computational and engineering techniques have been applied to various aspects of tumor growth, with the ultimate goal of understanding the response of the cancer population to clinical intervention. Socalled in silico trials that predict patientspecific response to various dose schedules or treatment combinations and sequencing are on the way to becoming an invaluable tool to optimize patient care. Herein we describe fundamentals of mathematical modeling of tumor growth and tumorhost interactions, and summarize some of the seminal and most prominent approaches.
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/7710
20140101T00:00:00Z
Enderling, Heiko
Chaplain, Mark A. J.
Using mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative approaches have also made their way into cancer research. An increasing number of mathematical, physical, computational and engineering techniques have been applied to various aspects of tumor growth, with the ultimate goal of understanding the response of the cancer population to clinical intervention. Socalled in silico trials that predict patientspecific response to various dose schedules or treatment combinations and sequencing are on the way to becoming an invaluable tool to optimize patient care. Herein we describe fundamentals of mathematical modeling of tumor growth and tumorhost interactions, and summarize some of the seminal and most prominent approaches.

Mean field analysis of a spatial stochastic model of a gene regulatory network
http://hdl.handle.net/10023/7709
Abstract: A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatiotemporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatiotemporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steadystate analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatiotemporal and spatiallyhomogeneous models.
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7709
20151001T00:00:00Z
Sturrock, M.
Murray, P. J.
Matzavinos, A.
Chaplain, M. A. J.
A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatiotemporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatiotemporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steadystate analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatiotemporal and spatiallyhomogeneous models.

An exact collisionless equilibrium for the ForceFree Harris Sheet with low plasma beta
http://hdl.handle.net/10023/7691
Abstract: We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a onedimensional nonlinear forcefree magnetic field, namely, the forcefree Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear forcefree collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and nonnegativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.
Description: Funding: STFC Consolidated Grant [ST/K000950/1] (OA, TN & FW) and a Doctoral Training Grant [ST/K502327/1] (OA). EPSRC Doctoral Training Grant [EP/K503162/1] (ST). Date of Acceptance: 14/10/2015
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7691
20151001T00:00:00Z
Allanson, Oliver Douglas
Neukirch, Thomas
Wilson, Fiona
Troscheit, Sascha
We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a onedimensional nonlinear forcefree magnetic field, namely, the forcefree Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear forcefree collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and nonnegativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.

3D wholeprominence fine structure modeling. II. Prominence evolution
http://hdl.handle.net/10023/7683
Abstract: We use the new threedimensional (3D) wholeprominence fine structure model to study the evolution of prominences and their fine structures in response to changes in the underlying photospheric magnetic flux distribution. The applied model combines a detailed 3D prominence magnetic field configuration with a realistic description of the prominence plasma distributed along multiple fine structures. In addition, we utilize an approximate Hα visualization technique to study the evolution of the visible cool prominence plasma both in emission (prominence) and absorption (filament). We show that the initial magnetic field configuration of the modeled prominence is significantly disturbed by the changing position of a single polarity of a magnetic bipole as the bipole is advected toward the main body of the filament. This leads to the creation of a barb, which becomes the dominant feature visible in the synthetic Hα images of both the prominence and filament views. The evolution of the bipole also creates conditions that lead to the disappearance and reappearance of large portions of the main body. We also show that an archlike region containing a dark void (a bubble) can be naturally produced in the synthetic prominence Hα images. While not visible in terms of the magnetic field lines, it is due to a lack of Hα emission from lowpressure, lowdensity plasma located in shallow magnetic dips lying along the lines of sight intersecting the dark void. In addition, a quasivertical smallscale feature consisting of short and deep dips, piled one above the other, is produced.
Description: Date of Acceptance: 08/09/2015
Tue, 20 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7683
20151020T00:00:00Z
Gunar, Stanislav
Mackay, Duncan Hendry
We use the new threedimensional (3D) wholeprominence fine structure model to study the evolution of prominences and their fine structures in response to changes in the underlying photospheric magnetic flux distribution. The applied model combines a detailed 3D prominence magnetic field configuration with a realistic description of the prominence plasma distributed along multiple fine structures. In addition, we utilize an approximate Hα visualization technique to study the evolution of the visible cool prominence plasma both in emission (prominence) and absorption (filament). We show that the initial magnetic field configuration of the modeled prominence is significantly disturbed by the changing position of a single polarity of a magnetic bipole as the bipole is advected toward the main body of the filament. This leads to the creation of a barb, which becomes the dominant feature visible in the synthetic Hα images of both the prominence and filament views. The evolution of the bipole also creates conditions that lead to the disappearance and reappearance of large portions of the main body. We also show that an archlike region containing a dark void (a bubble) can be naturally produced in the synthetic prominence Hα images. While not visible in terms of the magnetic field lines, it is due to a lack of Hα emission from lowpressure, lowdensity plasma located in shallow magnetic dips lying along the lines of sight intersecting the dark void. In addition, a quasivertical smallscale feature consisting of short and deep dips, piled one above the other, is produced.

A spatially explicit capturerecapture estimator for singlecatch traps
http://hdl.handle.net/10023/7680
Abstract: 1. Singlecatch traps are frequently used in livetrapping studies of small mammals. Thus far a likelihood for singlecatch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capturerecapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. 2. We build on a recently developed continuoustime model for SECR to derive a likelihood for singlecatch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. 3. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height (but not range) of the detection function. By contrast, the single catch estimators of density, distribution and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance, so that despite the lower bias of the singlecatch estimator of the density surface over space, its root mean squared error is similar to that of the multicatch estimator. 4. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constantover the survey region, then the multicatch estimator performs well with singlecatch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the singlecatch estimator when trap saturation is above about 60%. The estimator’s performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a singlecatch likelihood with unknown capture times remains intractable for now, researchers using singlecatch traps should aim to incorporate timing devices with their traps.
Description: This work was partfunded by EPSRC grant EP/I000917/1. Date of Acceptance: 24/08/2015
Sun, 01 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7680
20151101T00:00:00Z
Distiller, Greg
Borchers, David Louis
1. Singlecatch traps are frequently used in livetrapping studies of small mammals. Thus far a likelihood for singlecatch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capturerecapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. 2. We build on a recently developed continuoustime model for SECR to derive a likelihood for singlecatch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. 3. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height (but not range) of the detection function. By contrast, the single catch estimators of density, distribution and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance, so that despite the lower bias of the singlecatch estimator of the density surface over space, its root mean squared error is similar to that of the multicatch estimator. 4. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constantover the survey region, then the multicatch estimator performs well with singlecatch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the singlecatch estimator when trap saturation is above about 60%. The estimator’s performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a singlecatch likelihood with unknown capture times remains intractable for now, researchers using singlecatch traps should aim to incorporate timing devices with their traps.

Homomorphic image orders on combinatorial structures
http://hdl.handle.net/10023/7679
Abstract: Combinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a surjective homomorphism between two structures. We distinguish between strong and induced forms of the order and explore how they behave in the context of different common combinatorial structures. We focus on three aspects: antichains and partial wellorder, the joint preimage property and the dual amalgamation property. The two latter properties are natural analogues of the wellknown joint embedding property and amalgamation property, and are investigated here for the first time.
Description: Date of Acceptance: 03/04/2014
Wed, 01 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/7679
20150701T00:00:00Z
Huczynska, Sophie
Ruskuc, Nik
Combinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a surjective homomorphism between two structures. We distinguish between strong and induced forms of the order and explore how they behave in the context of different common combinatorial structures. We focus on three aspects: antichains and partial wellorder, the joint preimage property and the dual amalgamation property. The two latter properties are natural analogues of the wellknown joint embedding property and amalgamation property, and are investigated here for the first time.

Formation and largescale patterns of filament channels and filaments
http://hdl.handle.net/10023/7673
Abstract: The properties and largescale patterns of filament channels and filaments are considered. Initially, the global formation locations of filament channels and filaments are discussed, along with their hemispheric pattern. Next, observations of the formation of filament channels and filaments are described where two opposing views are considered. Finally, the wide range of models that have been constructed to consider the formation of filament channels and filaments over long timescales are described, along with the origin of the hemispheric pattern of filaments.
Description: 2015ASSL..415..355M Date of Acceptance: 21/10/14
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7673
20150101T00:00:00Z
Mackay, Duncan Hendry
The properties and largescale patterns of filament channels and filaments are considered. Initially, the global formation locations of filament channels and filaments are discussed, along with their hemispheric pattern. Next, observations of the formation of filament channels and filaments are described where two opposing views are considered. Finally, the wide range of models that have been constructed to consider the formation of filament channels and filaments over long timescales are described, along with the origin of the hemispheric pattern of filaments.

A Höldertype inequality on a regular rooted tree
http://hdl.handle.net/10023/7658
Abstract: We establish an inequality which involves a nonnegative function defined on the vertices of a finite mary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree summed over automorphisms of the tree, to a product of sums of powers of the function over vertices at certain levels of the tree. Conjugate powers arise naturally in the inequality, indeed, Hölder's inequality is a key tool in the proof which uses induction on subgroups of the automorphism group of the tree.
Sun, 15 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/7658
20150315T00:00:00Z
Falconer, Kenneth John
We establish an inequality which involves a nonnegative function defined on the vertices of a finite mary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree summed over automorphisms of the tree, to a product of sums of powers of the function over vertices at certain levels of the tree. Conjugate powers arise naturally in the inequality, indeed, Hölder's inequality is a key tool in the proof which uses induction on subgroups of the automorphism group of the tree.

The modelling and assessment of whalewatching impacts
http://hdl.handle.net/10023/7642
Abstract: In recent years there has been significant interest in modelling cumulative effects and the population consequences of individual changes in cetacean behaviour and physiology due to disturbance. One potential source of disturbance that has garnered particular interest is whalewatching. Though perceived as 'green' or ecofriendly tourism, there is evidence that whalewatching can result in statistically significant and biologically meaningful changes in cetacean behaviour, raising the question whether whalewatching is in fact a long term sustainable activity. However, an assessment of the impacts of whalewatching on cetaceans requires an understanding of the potential behavioural and physiological effects, data to effectively address the question and suitable modelling techniques. Here, we review the current state of knowledge on the viability of longterm whalewatching, as well as logistical limitations and potential opportunities. We conclude that an integrated, coordinated approach will be needed to further understanding of the possible effects of whalewatching on cetaceans.
Description: Date of Acceptance: 03/04/2015
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7642
20151001T00:00:00Z
New, Leslie Frances
Hall, Ailsa Jane
Harcourt, R.
Kaufman, G.
Parsons, E.C.M.
Pearson, H.C.
Cosentino, A.M.
Schick, Robert Schilling
In recent years there has been significant interest in modelling cumulative effects and the population consequences of individual changes in cetacean behaviour and physiology due to disturbance. One potential source of disturbance that has garnered particular interest is whalewatching. Though perceived as 'green' or ecofriendly tourism, there is evidence that whalewatching can result in statistically significant and biologically meaningful changes in cetacean behaviour, raising the question whether whalewatching is in fact a long term sustainable activity. However, an assessment of the impacts of whalewatching on cetaceans requires an understanding of the potential behavioural and physiological effects, data to effectively address the question and suitable modelling techniques. Here, we review the current state of knowledge on the viability of longterm whalewatching, as well as logistical limitations and potential opportunities. We conclude that an integrated, coordinated approach will be needed to further understanding of the possible effects of whalewatching on cetaceans.

Impacts of anthropogenic noise on marine life : publication patterns, new discoveries, and future directions in research and management
http://hdl.handle.net/10023/7640
Abstract: Anthropogenic underwater noise is now recognized as a worldwide problem, and recent studies have shown a broad range of negative effects in a variety of taxa. Underwater noise from shipping is increasingly recognized as a significant and pervasive pollutant with the potential to impact marine ecosystems on a global scale. We reviewed six regional case studies as examples of recent research and management activities relating to ocean noise in a variety of taxonomic groups, locations, and approaches. However, as no six projects could ever cover all taxa, sites and noise sources, a brief bibliometric analysis places these case studies into the broader historical and topical context of the peerreviewed ocean noise literature as a whole. The case studies highlighted emerging knowledge of impacts, including the ways that noninjurious effects can still accumulate at the population level, and detailed approaches to guide ocean noise management. They build a compelling case that a number of anthropogenic noise types can affect a variety of marine taxa. Meanwhile, the bibliometric analyses revealed an increasing diversity of ocean noise topics covered and journal outlets since the 1940s. This could be seen in terms of both the expansion of the literature from more physical interests to ecological impacts of noise, management and policy, and consideration of a widening range of taxa. However, if our scientific knowledge base is ever to get ahead of the curve of rapid industrialization of the ocean, we are going to have to identify naïve populations and relatively pristine seas, and construct mechanistic models, so that we can predict impacts before they occur, and guide effective mitigation for the most vulnerable populations.
Description: Funding for R. Bruintjes, J. Purser, A. N. Radford, S. D, Simpson and M. A. Wale was provided by the UK Department for Environment Food and Rural Affairs (Defra). N.D. Merchant received travel funding from Ocean Networks Canada. RW was supported by a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme (Project CONCEAL, FP7, PIIFGA2009253407), and received travel funding to attend IMCC3 from the Society for Conservation Biology (SCB) Marine Section and the International Whaling Commission’s Climate Change steering group (with thanks to Mark Simmonds). A.J. Wright also received travel funding to attend IMCC3 from the SCB Marine Section. Date of Acceptance: 28/05/2015 Date of Acceptance: 28/05/2015
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7640
20151001T00:00:00Z
Williams, Robert
Wright, Andrew J
Ashe, Erin
Blight, LK
Bruintjes, R
Canessa, R
Clark, CW
CullisSuzuki, S
Dakin, DT
Erbe, C
Hammond, Philip Steven
Merchant, MD
O'Hara, PD
Purser, J
Radford, AN
Simpson, SD
Thomas, Len
Wale, MA
Anthropogenic underwater noise is now recognized as a worldwide problem, and recent studies have shown a broad range of negative effects in a variety of taxa. Underwater noise from shipping is increasingly recognized as a significant and pervasive pollutant with the potential to impact marine ecosystems on a global scale. We reviewed six regional case studies as examples of recent research and management activities relating to ocean noise in a variety of taxonomic groups, locations, and approaches. However, as no six projects could ever cover all taxa, sites and noise sources, a brief bibliometric analysis places these case studies into the broader historical and topical context of the peerreviewed ocean noise literature as a whole. The case studies highlighted emerging knowledge of impacts, including the ways that noninjurious effects can still accumulate at the population level, and detailed approaches to guide ocean noise management. They build a compelling case that a number of anthropogenic noise types can affect a variety of marine taxa. Meanwhile, the bibliometric analyses revealed an increasing diversity of ocean noise topics covered and journal outlets since the 1940s. This could be seen in terms of both the expansion of the literature from more physical interests to ecological impacts of noise, management and policy, and consideration of a widening range of taxa. However, if our scientific knowledge base is ever to get ahead of the curve of rapid industrialization of the ocean, we are going to have to identify naïve populations and relatively pristine seas, and construct mechanistic models, so that we can predict impacts before they occur, and guide effective mitigation for the most vulnerable populations.

On generators, relations and Dsimplicity of direct products, Byleen extensions, and other semigroup constructions
http://hdl.handle.net/10023/7629
Abstract: In this thesis we study two different topics, both in the context of semigroup constructions. The first is the investigation of an embedding problem, specifically the problem of whether it is possible to embed any given finitely presentable semigroup into a Dsimple finitely presentable semigroup. We consider some wellknown semigroup constructions, investigating their properties to determine whether they might prove useful for finding a solution to our problem. We carry out a more detailed study into a more complicated semigroup construction, the Byleen extension, which has been used to solve several other embedding problems. We prove several results regarding the structure of this extension, finding necessary and sufficient conditions for an extension to be Dsimple and a very strong necessary condition for an extension to be finitely presentable.
The second topic covered in this thesis is relative rank, specifically the sequence obtained by taking the rank of incremental direct powers of a given semigroup modulo the diagonal subsemigroup. We investigate the relative rank sequences of infinite Cartesian products of groups and of semigroups. We characterise all semigroups for which the relative rank sequence of an infinite Cartesian product is finite, and show that if the sequence is finite then it is bounded above by a logarithmic function. We will find sufficient conditions for the relative rank sequence of an infinite Cartesian product to be logarithmic, and sufficient conditions for it to be constant. Chapter 4 ends with the introduction of a new topic, relative presentability, which follows naturally from the topic of relative rank.
Mon, 30 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7629
20151130T00:00:00Z
Baynes, Samuel
In this thesis we study two different topics, both in the context of semigroup constructions. The first is the investigation of an embedding problem, specifically the problem of whether it is possible to embed any given finitely presentable semigroup into a Dsimple finitely presentable semigroup. We consider some wellknown semigroup constructions, investigating their properties to determine whether they might prove useful for finding a solution to our problem. We carry out a more detailed study into a more complicated semigroup construction, the Byleen extension, which has been used to solve several other embedding problems. We prove several results regarding the structure of this extension, finding necessary and sufficient conditions for an extension to be Dsimple and a very strong necessary condition for an extension to be finitely presentable.
The second topic covered in this thesis is relative rank, specifically the sequence obtained by taking the rank of incremental direct powers of a given semigroup modulo the diagonal subsemigroup. We investigate the relative rank sequences of infinite Cartesian products of groups and of semigroups. We characterise all semigroups for which the relative rank sequence of an infinite Cartesian product is finite, and show that if the sequence is finite then it is bounded above by a logarithmic function. We will find sufficient conditions for the relative rank sequence of an infinite Cartesian product to be logarithmic, and sufficient conditions for it to be constant. Chapter 4 ends with the introduction of a new topic, relative presentability, which follows naturally from the topic of relative rank.

Genetic censusing identifies an unexpectedly sizeable population of an endangered large mammal in a fragmented forest landscape
http://hdl.handle.net/10023/7614
Abstract: Background: As habitat degradation and fragmentation continue to impact wildlife populations around the world, it is critical to understand the behavioral flexibility of species in these environments. In Uganda, the mostly unprotected forest fragment landscape between the Budongo and Bugoma Forests is a potential corridor for chimpanzees, yet little is known about the status of chimpanzee populations in these fragments. Results: From 2011 through 2013, we noninvasively collected 865 chimpanzee fecal samples across 633 km2 and successfully genotyped 662 (77%) at up to 14 microsatellite loci. These genotypes corresponded to 182 chimpanzees, with a mean of 3.5 captures per individual. We obtained population size estimates of 256 (95% confidence interval 246321) and 319 (288357) chimpanzees using capturewithreplacement and spatially explicit capturerecapture models, respectively. The spatial clustering of associated genotypes suggests the presence of at least nine communities containing a minimum of 833 individuals each. Putative community distributions defined by the locations of associated genotypes correspond well with the distribution of 14 Ychromosome haplotypes. Conclusions: These census figures are more than three times greater than a previous estimate based on an extrapolation from smallscale nest count surveys that tend to underestimate population size. The distribution of genotype clusters and Ychromosome haplotypes together indicate the presence of numerous male philopatric chimpanzee communities throughout the corridor habitat. Our findings demonstrate that, despite extensive habitat loss and fragmentation, chimpanzees remain widely distributed and exhibit distinct community home ranges. Our results further imply that elusive and rare species may adapt to degraded habitats more successfully than previously believed. Their longterm persistence is unlikely, however, if protection is not afforded to them and habitat loss continues unabated.
Description: This study was funded by the American Society of Primatologists, the German Academic Exchange Service (DAAD), the Max Planck Society, the University of Southern California Jane Goodall Research Center and Dornsife College of Letters, Arts, and Sciences, the Nacey Maggioncalda Foundation, and Primate Conservation, Inc. Date of Acceptance: 15/07/2015
Tue, 25 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/7614
20150825T00:00:00Z
McCarthy, M.S.
Lester, J.D.
Howe, Eric John
Arandjelovic, M.
Stanford, C.B.
Vigilant, L.
Background: As habitat degradation and fragmentation continue to impact wildlife populations around the world, it is critical to understand the behavioral flexibility of species in these environments. In Uganda, the mostly unprotected forest fragment landscape between the Budongo and Bugoma Forests is a potential corridor for chimpanzees, yet little is known about the status of chimpanzee populations in these fragments. Results: From 2011 through 2013, we noninvasively collected 865 chimpanzee fecal samples across 633 km2 and successfully genotyped 662 (77%) at up to 14 microsatellite loci. These genotypes corresponded to 182 chimpanzees, with a mean of 3.5 captures per individual. We obtained population size estimates of 256 (95% confidence interval 246321) and 319 (288357) chimpanzees using capturewithreplacement and spatially explicit capturerecapture models, respectively. The spatial clustering of associated genotypes suggests the presence of at least nine communities containing a minimum of 833 individuals each. Putative community distributions defined by the locations of associated genotypes correspond well with the distribution of 14 Ychromosome haplotypes. Conclusions: These census figures are more than three times greater than a previous estimate based on an extrapolation from smallscale nest count surveys that tend to underestimate population size. The distribution of genotype clusters and Ychromosome haplotypes together indicate the presence of numerous male philopatric chimpanzee communities throughout the corridor habitat. Our findings demonstrate that, despite extensive habitat loss and fragmentation, chimpanzees remain widely distributed and exhibit distinct community home ranges. Our results further imply that elusive and rare species may adapt to degraded habitats more successfully than previously believed. Their longterm persistence is unlikely, however, if protection is not afforded to them and habitat loss continues unabated.

Particle energisation in a collapsing magnetic trap model : the relativistic regime
http://hdl.handle.net/10023/7603
Abstract: Context. In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the rapidly relaxing magnetic field can form a collapsing magnetic trap (CMT) and that this trap may contribute to particle energisation. Aims. In this Research Note we focus on a particular analytical CMT model based on kinematic magnetohydrodynamics. Previous investigations of particle acceleration for this CMT model focused on the nonrelativistic energy regime. It is the specific aim of this Research Note to extend the previous work to relativistic particle energies. Methods. Particle orbits were calculated numerically using the relativistic guiding centre equations. We also calculated particle orbits using the nonrelativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and nonrelativistic particle orbits mainly agree well, but clear deviations are seen for higher energies. In particular, the final particle energies obtained from the relativistic calculations are systematically lower than the energies reached from the corresponding nonrelativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding nonrelativistic orbits. Conclusions. While the overall behaviour of particle orbits in CMTs does not differ qualitatively when using the relativistic guiding centre equations, there are a few systematic quantitative differences between relativistic and nonrelativistic particle dynamics.
Description: The authors acknowledge financial support by the UK’s Science and Technology Facilities Council through a Doctoral Training Grant (SEO) and Consolidated Grant ST/K000950/1 (SEO and TN). Date of Acceptance: 18/06/2014
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/7603
20140701T00:00:00Z
Eradat Oskoui, S.
Neukirch, T.
Context. In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the rapidly relaxing magnetic field can form a collapsing magnetic trap (CMT) and that this trap may contribute to particle energisation. Aims. In this Research Note we focus on a particular analytical CMT model based on kinematic magnetohydrodynamics. Previous investigations of particle acceleration for this CMT model focused on the nonrelativistic energy regime. It is the specific aim of this Research Note to extend the previous work to relativistic particle energies. Methods. Particle orbits were calculated numerically using the relativistic guiding centre equations. We also calculated particle orbits using the nonrelativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and nonrelativistic particle orbits mainly agree well, but clear deviations are seen for higher energies. In particular, the final particle energies obtained from the relativistic calculations are systematically lower than the energies reached from the corresponding nonrelativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding nonrelativistic orbits. Conclusions. While the overall behaviour of particle orbits in CMTs does not differ qualitatively when using the relativistic guiding centre equations, there are a few systematic quantitative differences between relativistic and nonrelativistic particle dynamics.

Pairwise interaction point processes for modelling bivariate spatial point patterns in the presence of interaction uncertainty
http://hdl.handle.net/10023/7583
Abstract: Current ecological research seeks to understand the mechanisms that sustain biodiversity and allow a large number of species to coexist. Coexistence concerns interindividual interactions. Consequently, there is an interest in identifying and quantifying interactions within and between species as reflected in the spatial pattern formed by the individuals. This study analyses the spatial pattern formed by the locations of plants in a community with high biodiversity from Western Australia. We fit a pairwise interaction Gibbs marked point process to the data using a Bayesian approach and quantify the inhibitory interactions within and between the two species. We quantitatively discriminate between competing models corresponding to different interspecific and intraspecific interactions via posterior model probabilities. The analysis provides evidence that the intraspecific interactions for the two species of the genus Banksia are generally similar to those between the two species providing some evidence for mechanisms that sustain biodiversity.
Description: Date of Acceptance: 01/09/2015
Tue, 01 Sep 2015 00:00:00 GMT
http://hdl.handle.net/10023/7583
20150901T00:00:00Z
Nightingale, Glenna Faith
Illian, Janine Baerbel
King, Ruth
Current ecological research seeks to understand the mechanisms that sustain biodiversity and allow a large number of species to coexist. Coexistence concerns interindividual interactions. Consequently, there is an interest in identifying and quantifying interactions within and between species as reflected in the spatial pattern formed by the individuals. This study analyses the spatial pattern formed by the locations of plants in a community with high biodiversity from Western Australia. We fit a pairwise interaction Gibbs marked point process to the data using a Bayesian approach and quantify the inhibitory interactions within and between the two species. We quantitatively discriminate between competing models corresponding to different interspecific and intraspecific interactions via posterior model probabilities. The analysis provides evidence that the intraspecific interactions for the two species of the genus Banksia are generally similar to those between the two species providing some evidence for mechanisms that sustain biodiversity.

Multiscale modelling of the dynamics of cell colonies : insights into celladhesion forces and cancer invasion from in silico simulations
http://hdl.handle.net/10023/7571
Abstract: Studying the biophysical interactions between cells is crucial to understanding how normal tissue develops, how it is structured and also when malfunctions occur. Traditional experiments try to infer events at the tissue level after observing the behaviour of and interactions between individual cells. This approach assumes that cells behave in the same biophysical manner in isolated experiments as they do within colonies and tissues. In this paper, we develop a multiscale multicompartment mathematical model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell?cell level but also at the level of cell colonies (in contrast to the traditional approach). Our results suggest that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated singlecell experiments infer. As a consequence, isolated singlecell experiments may be insufficient to deduce important biological processes such as singlecell invasion after detachment from a solid tumour. The simulations further show that kinetic rates and cell biophysical characteristics such as pressurerelated cellcycle arrest have a major influence on cell colony patterns and can allow for the development of protrusive cellular structures as seen in invasive cancer cell lines independent of expression levels of proinvasion molecules.
Description: Date of Acceptance: 25/11/2014
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/7571
20150201T00:00:00Z
Schluter, Daniela K.
RamisConde, Ignacio
Chaplain, Mark A. J.
Studying the biophysical interactions between cells is crucial to understanding how normal tissue develops, how it is structured and also when malfunctions occur. Traditional experiments try to infer events at the tissue level after observing the behaviour of and interactions between individual cells. This approach assumes that cells behave in the same biophysical manner in isolated experiments as they do within colonies and tissues. In this paper, we develop a multiscale multicompartment mathematical model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell?cell level but also at the level of cell colonies (in contrast to the traditional approach). Our results suggest that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated singlecell experiments infer. As a consequence, isolated singlecell experiments may be insufficient to deduce important biological processes such as singlecell invasion after detachment from a solid tumour. The simulations further show that kinetic rates and cell biophysical characteristics such as pressurerelated cellcycle arrest have a major influence on cell colony patterns and can allow for the development of protrusive cellular structures as seen in invasive cancer cell lines independent of expression levels of proinvasion molecules.

Hopf bifurcation in a gene regulatory network model : molecular movement causes oscillations
http://hdl.handle.net/10023/7564
Abstract: Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper, we analyze a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatiotemporal inter actions between the protein and its mRNA in a 1dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behavior and this is the case for our model, shown initially via computational simulations. In order to investigate this behavior more deeply, we undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. Our result has implications for transcription factors such as p53, NFκB and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer.
Description: M.A.J.C. and M.S. gratefully acknowledge the support of the ERC Advanced Investigator Grant 227619, “M5CGS — From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread”. M.S. would also like to thank the support from the Mathematical Biosciences Institute at the Ohio State University and NSF Grant DMS0931642. Date of Acceptance: 16/11/2014
Mon, 15 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7564
20150615T00:00:00Z
Chaplain, Mark
Ptashnyk, Mariya
Sturrock, Marc
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper, we analyze a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatiotemporal inter actions between the protein and its mRNA in a 1dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behavior and this is the case for our model, shown initially via computational simulations. In order to investigate this behavior more deeply, we undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. Our result has implications for transcription factors such as p53, NFκB and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer.

Procedure description : using AUTEC’s hydrophones surrounding a DTAGed whale to obtain localizations
http://hdl.handle.net/10023/7523
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7523
20150101T00:00:00Z
Marques, Tiago A.
Shaeffer, Jessica
Moretti, David
Thomas, Len

Magnetospheric signatures of ionospheric density cavities observed by Cluster
http://hdl.handle.net/10023/7509
Abstract: We present Cluster measurements of large amplitude electric fields corre lated with intense downward fieldaligned currents, observed during a nightside crossing of the auroral zone. The data are reproduced by a simple model of magnetosphereionosphere coupling which, under different conditions, can also produce a divergent electric field signature in the downward current region, or correlation between the electric and perturbed magnetic fields. We conclude that strong electric field associated with intense downward fieldaligned current, such as this observation, is a signature of ionospheric plasma depletion caused by the downward current. It is also shown that the electric field in the downward current region correlates with downward current density if a background field is present, e.g. due to magnetospheric convection.
Description: AJBR ackowledges support from STFC under consolidated grant ST/K000993/1. Date of Acceptance: 17/02/2015
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/7509
20150301T00:00:00Z
Russell, Alexander John Barkway
Karlsson, Tomas
Wright, Andrew Nicholas
We present Cluster measurements of large amplitude electric fields corre lated with intense downward fieldaligned currents, observed during a nightside crossing of the auroral zone. The data are reproduced by a simple model of magnetosphereionosphere coupling which, under different conditions, can also produce a divergent electric field signature in the downward current region, or correlation between the electric and perturbed magnetic fields. We conclude that strong electric field associated with intense downward fieldaligned current, such as this observation, is a signature of ionospheric plasma depletion caused by the downward current. It is also shown that the electric field in the downward current region correlates with downward current density if a background field is present, e.g. due to magnetospheric convection.

Strategies of eradicating glioma cells : a multiscale mathematical model with miR451AMPKmTOR control
http://hdl.handle.net/10023/7503
Abstract: The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical and biomechanical cues in the microenvironment. Recent studies have shown that a particular microRNA, miR451, regulates downstream molecules including AMPK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this multiscale nature of glioblastoma proliferation and invasion and its response to conventional treatment, we propose a hybrid model of glioblastoma that analyses spatiotemporal dynamics at the cellular level, linking individual tumor cells with the macroscopic behaviour of cell organization and the microenvironment, and with the intracellular dynamics of miR451AMPKmTOR signaling within a tumour cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress and biophysical interaction between cells in response to fluctuating glucose levels in the presence of blood vessels (BVs). The model predicts that cell migration, therefore efficacy of the treatment, not only depends on oxygen and glucose availability but also on the relative balance between random motility and strength of chemoattractants. Effective control of growing cells near BV sites in addition to relocalization of invisible migratory cells back to the resection site was suggested as a way of eradicating these migratory cells.
Description: Date of Acceptance: 06/11/2014
Wed, 28 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7503
20150128T00:00:00Z
Kim, Yangjin
Powathil, Gibin
Kang, Hyunji
Trucu, Dumitru
Kim, Hyeongi
Lawler, Sean
Chaplain, Mark
The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical and biomechanical cues in the microenvironment. Recent studies have shown that a particular microRNA, miR451, regulates downstream molecules including AMPK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this multiscale nature of glioblastoma proliferation and invasion and its response to conventional treatment, we propose a hybrid model of glioblastoma that analyses spatiotemporal dynamics at the cellular level, linking individual tumor cells with the macroscopic behaviour of cell organization and the microenvironment, and with the intracellular dynamics of miR451AMPKmTOR signaling within a tumour cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress and biophysical interaction between cells in response to fluctuating glucose levels in the presence of blood vessels (BVs). The model predicts that cell migration, therefore efficacy of the treatment, not only depends on oxygen and glucose availability but also on the relative balance between random motility and strength of chemoattractants. Effective control of growing cells near BV sites in addition to relocalization of invisible migratory cells back to the resection site was suggested as a way of eradicating these migratory cells.

Sunspot rotation. I : a consequence of flux emergence
http://hdl.handle.net/10023/7497
Abstract: Context. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release. Aims. We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the subphotospheric twist stored in the interior is injected into the solar atmosphere by means of a definitive rotation of the sunspots. Methods. A numerical experiment is performed to solve the 3D resistive magnetohydrodynamic (MHD) equations using a LagrangianRemap code. We track the emergence of a toroidal flux tube as it rises through the solar interior and emerges into the atmosphere investigating various quantities related to both the magnetic field and plasma. Results. Through detailed analysis of the numerical experiment, we find clear evidence that the photospheric footprints or sunspots of the flux tube undergo a rotation. Significant vertical vortical motions are found to develop within the two polarity sources after the field emerges. These rotational motions are found to leave the interior portion of the field untwisted and twist up the atmospheric portion of the field. This is shown by our analysis of the relative magnetic helicity as a significant portion of the interior helicity is transported to the atmosphere. In addition, there is a substantial transport of magnetic energy to the atmosphere. Rotation angles are also calculated by tracing selected fieldlines; the fieldlines threading through the sunspot are found to rotate through angles of up to 353º over the course of the experiment. We explain the rotation by an unbalanced torque produced by the magnetic tension force, rather than an apparent effect.
Description: ZS acknowledges the financial support of the Carnegie Trust for Scotland and CMM the support of the Royal Society of Edinburgh. This work used the DIRAC 1, UKMHD Consortium machine at the University of St Andrews and the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National Einfrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National EInfrastructure. Date of Acceptance: 02/08/2015
Mon, 12 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/7497
20151012T00:00:00Z
Sturrock, Zoe
Hood, Alan William
Archontis, Vasilis
McNeill, Craig
Context. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release. Aims. We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the subphotospheric twist stored in the interior is injected into the solar atmosphere by means of a definitive rotation of the sunspots. Methods. A numerical experiment is performed to solve the 3D resistive magnetohydrodynamic (MHD) equations using a LagrangianRemap code. We track the emergence of a toroidal flux tube as it rises through the solar interior and emerges into the atmosphere investigating various quantities related to both the magnetic field and plasma. Results. Through detailed analysis of the numerical experiment, we find clear evidence that the photospheric footprints or sunspots of the flux tube undergo a rotation. Significant vertical vortical motions are found to develop within the two polarity sources after the field emerges. These rotational motions are found to leave the interior portion of the field untwisted and twist up the atmospheric portion of the field. This is shown by our analysis of the relative magnetic helicity as a significant portion of the interior helicity is transported to the atmosphere. In addition, there is a substantial transport of magnetic energy to the atmosphere. Rotation angles are also calculated by tracing selected fieldlines; the fieldlines threading through the sunspot are found to rotate through angles of up to 353º over the course of the experiment. We explain the rotation by an unbalanced torque produced by the magnetic tension force, rather than an apparent effect.

Evolution of field line helicity during magnetic reconnection
http://hdl.handle.net/10023/7485
Abstract: We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finiteB magnetic reconnection. Total ( relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a worklike term that is evaluated at the field line endpoints, namely, the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a wellorganized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity.
Description: This work was supported by the Science and Technology Facilities Council (UK) through consortium Grant Nos. ST/K000993/1 and ST/K001043 to the University of Dundee and Durham University. Date of Acceptance: 12/02/2015
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/7485
20150301T00:00:00Z
Russell, A. J. B.
Yeates, A. R.
Hornig, G.
WilmotSmith, A. L.
We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finiteB magnetic reconnection. Total ( relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a worklike term that is evaluated at the field line endpoints, namely, the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a wellorganized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity.

On the theory of translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear
http://hdl.handle.net/10023/7484
Abstract: We present an improved formalism for translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component. The derivation of a GradShafranov type equation is given along with a constraint which links the shear field to the parallel pressure. The difficulties of the formalism are discussed and various methods of circumventing these difficulties are given. A simple example is then used to highlight the methods and difficulties involved.
Description: Funding: STFC Doctoral Training Grant ST/K502327/1 (Jonathan Hodgson) and STFC Consolidated Grant ST/K000950/1 (Thomas Neukirch) Date of Acceptance: 05/08/2015
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7484
20150101T00:00:00Z
Hodgson, Jonathan David Brockie
Neukirch, Thomas
We present an improved formalism for translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component. The derivation of a GradShafranov type equation is given along with a constraint which links the shear field to the parallel pressure. The difficulties of the formalism are discussed and various methods of circumventing these difficulties are given. A simple example is then used to highlight the methods and difficulties involved.

Higher moments for random multiplicative measures
http://hdl.handle.net/10023/7474
Abstract: We obtain a condition for the Lqconvergence of martingales generated by random multiplicative cascade measures for q>1 without any selfsimilarity requirements on the cascades.
Description: Date of Acceptance: 06/05/2014
Sat, 01 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/7474
20150801T00:00:00Z
Falconer, Kenneth John
We obtain a condition for the Lqconvergence of martingales generated by random multiplicative cascade measures for q>1 without any selfsimilarity requirements on the cascades.

Circular designs balanced for neighbours at distances one and two
http://hdl.handle.net/10023/7454
Abstract: We define three types of neighbourbalanced designs for experiments where the units are arranged in a circle or single line in space or time. The designs are balanced with respect to neighbours at distance one and at distance two. The variants come from allowing or forbidding selfneighbours, and from considering neighbours to be directed or undirected. For two of the variants, we give a method of constructing a design for all values of the number of treatments, except for some small values where it is impossible. In the third case, we give a partial solution that covers all sizes likely to be used in practice.
Description: Date of Acceptance: 23/05/2014
Mon, 01 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/7454
20141201T00:00:00Z
Aldred, R. E. L.
Bailey, R. A.
Mckay, Brendan D.
Wanless, Ian M.
We define three types of neighbourbalanced designs for experiments where the units are arranged in a circle or single line in space or time. The designs are balanced with respect to neighbours at distance one and at distance two. The variants come from allowing or forbidding selfneighbours, and from considering neighbours to be directed or undirected. For two of the variants, we give a method of constructing a design for all values of the number of treatments, except for some small values where it is impossible. In the third case, we give a partial solution that covers all sizes likely to be used in practice.

Modelbased distance sampling
http://hdl.handle.net/10023/7410
Abstract: Conventional distance sampling adopts a mixed approach, using modelbased methods for the detection process, and designbased methods to estimate animal abundance in the study region, given estimated probabilities of detection. In recent years, there has been increasing interest in fully modelbased methods. Modelbased methods are less robust for estimating animal abundance than conventional methods, but offer several advantages: they allow the analyst to explore how animal density varies by habitat or topography; abundance can be estimated for any subregion of interest; they provide tools for analysing data from designed distance sampling experiments, to assess treatment effects. We develop a common framework for modelbased distance sampling, and show how the various modelbased methods that have been proposed fit within this framework.
Description: CSO was partfunded by EPSRC/NERC Grant EP/1000917/1. Date of acceptance: 20/08/2015
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7410
20150101T00:00:00Z
Buckland, Stephen Terrence
Oedekoven, Cornelia Sabrina
Borchers, David Louis
Conventional distance sampling adopts a mixed approach, using modelbased methods for the detection process, and designbased methods to estimate animal abundance in the study region, given estimated probabilities of detection. In recent years, there has been increasing interest in fully modelbased methods. Modelbased methods are less robust for estimating animal abundance than conventional methods, but offer several advantages: they allow the analyst to explore how animal density varies by habitat or topography; abundance can be estimated for any subregion of interest; they provide tools for analysing data from designed distance sampling experiments, to assess treatment effects. We develop a common framework for modelbased distance sampling, and show how the various modelbased methods that have been proposed fit within this framework.

The statistical analysis of point events associated with a fixed point
http://hdl.handle.net/10023/7294
Abstract: This work concerns the analysis of point events which are distributed on a planar region and are thought to be related to a fixed point. Data examples are considered from Epidemiology, where morbidity events are thought to be related to a pollution source, and Ecology and Geology where events associated with a central point are to be modelled. We have developed a variety of Heterogeneous Poisson Process (HEPP) models for the above examples. In particular, I have developed interaction and 8dependence models for angularlinear correlation, with their ML estimation and associated score/W aId tests. In the Epidemiological case we have developed casecontrol models and tests. The possibility of secondorder effects being important has also led to the development of Bayesian Spatial Prior (BSP) models. In addition, we have developed a new deviance residual for HEPP models and explored the use of GLIM for modelling purposes. A variety of results were found in data analysis. In some cases HEPP models provide adequate descriptions of the process. In others, BSP models yield better fits. In general, the discrete case admits a simple spatial Poisson model for counts and does not require BSP model extensions.
Tue, 01 Jan 1991 00:00:00 GMT
http://hdl.handle.net/10023/7294
19910101T00:00:00Z
Lawson, Andrew B.
This work concerns the analysis of point events which are distributed on a planar region and are thought to be related to a fixed point. Data examples are considered from Epidemiology, where morbidity events are thought to be related to a pollution source, and Ecology and Geology where events associated with a central point are to be modelled. We have developed a variety of Heterogeneous Poisson Process (HEPP) models for the above examples. In particular, I have developed interaction and 8dependence models for angularlinear correlation, with their ML estimation and associated score/W aId tests. In the Epidemiological case we have developed casecontrol models and tests. The possibility of secondorder effects being important has also led to the development of Bayesian Spatial Prior (BSP) models. In addition, we have developed a new deviance residual for HEPP models and explored the use of GLIM for modelling purposes. A variety of results were found in data analysis. In some cases HEPP models provide adequate descriptions of the process. In others, BSP models yield better fits. In general, the discrete case admits a simple spatial Poisson model for counts and does not require BSP model extensions.

Coronal heating in multiple magnetic threads
http://hdl.handle.net/10023/7259
Abstract: Context. Heating the solar corona to several million degrees requires the conversion of magnetic energy into thermal energy. In this paper, we investigate whether an unstable magnetic thread within a coronal loop can destabilise a neighbouring magnetic thread. Aims. By running a series of simulations, we aim to understand under what conditions the destabilisation of a single magnetic thread can also trigger a release of energy in a nearby thread. Methods. The 3D magnetohydrodynamics code, Lare3d, is used to simulate the temporal evolution of coronal magnetic fields during a kink instability and the subsequent relaxation process. We assume that a coronal magnetic loop consists of nonpotential magnetic threads that are initially in an equilibrium state. Results. The nonlinear kink instability in one magnetic thread forms a helical current sheet and initiates magnetic reconnection. The current sheet fragments, and magnetic energy is released throughout that thread. We find that, under certain conditions, this event can destabilise a nearby thread, which is a necessary requirement for starting an avalanche of energy release in magnetic threads. Conclusions. It is possible to initiate an energy release in a nearby, nonpotential magnetic thread, because the energy released from one unstable magnetic thread can trigger energy release in nearby threads, provided that the nearby structures are close to marginal stability.
Description: We acknowledge the financial support of STFC through the Consolidated grant to the University of St Andrews. Date of Acceptance: 24/06/2015
Sat, 01 Aug 2015 00:00:00 GMT
http://hdl.handle.net/10023/7259
20150801T00:00:00Z
Tam, Kuan Vai
Hood, Alan William
Browning, Philippa
Cargill, Peter
Context. Heating the solar corona to several million degrees requires the conversion of magnetic energy into thermal energy. In this paper, we investigate whether an unstable magnetic thread within a coronal loop can destabilise a neighbouring magnetic thread. Aims. By running a series of simulations, we aim to understand under what conditions the destabilisation of a single magnetic thread can also trigger a release of energy in a nearby thread. Methods. The 3D magnetohydrodynamics code, Lare3d, is used to simulate the temporal evolution of coronal magnetic fields during a kink instability and the subsequent relaxation process. We assume that a coronal magnetic loop consists of nonpotential magnetic threads that are initially in an equilibrium state. Results. The nonlinear kink instability in one magnetic thread forms a helical current sheet and initiates magnetic reconnection. The current sheet fragments, and magnetic energy is released throughout that thread. We find that, under certain conditions, this event can destabilise a nearby thread, which is a necessary requirement for starting an avalanche of energy release in magnetic threads. Conclusions. It is possible to initiate an energy release in a nearby, nonpotential magnetic thread, because the energy released from one unstable magnetic thread can trigger energy release in nearby threads, provided that the nearby structures are close to marginal stability.

Are tornadolike magnetic structures able to support solar prominence plasma?
http://hdl.handle.net/10023/7202
Abstract: Recent highresolution and highcadence observations have surprisingly suggested that prominence barbs exhibit apparent rotating motions suggestive of a tornadolike structure. Additional evidence has been provided by Doppler measurements. The observations reveal opposite velocities for both hot and cool plasma on the two sides of a prominence barb. This motion is persistent for several hours and has been interpreted in terms of rotational motion of prominence feet. Several authors suggest that such barb motions are rotating helical structures around a vertical axis similar to tornadoes on Earth. One of the difficulties of such a proposal is how to support cool prominence plasma in almostvertical structures against gravity. In this work we model analytically a tornadolike structure and try to determine possible mechanisms to support the prominence plasma. We have found that the Lorentz force can indeed support the barb plasma provided the magnetic structure is sufficiently twisted and/or significant poloidal flows are present.
Description: M. Luna and F. MorenoInsertis acknowledge support by the Spanish Ministry of Economy and Competitiveness through projects AYA201124808 and AYA201455078P. M.L. is also grateful to ERC2011StG 277829SPIA. E.R.P. is grateful to the UK STFC and the Leverhulme Trust for financial support. Date of Acceptance: 30/06/2015
Mon, 20 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/7202
20150720T00:00:00Z
Luna, M.
MorenoInsertis, F.
Priest, E.
Recent highresolution and highcadence observations have surprisingly suggested that prominence barbs exhibit apparent rotating motions suggestive of a tornadolike structure. Additional evidence has been provided by Doppler measurements. The observations reveal opposite velocities for both hot and cool plasma on the two sides of a prominence barb. This motion is persistent for several hours and has been interpreted in terms of rotational motion of prominence feet. Several authors suggest that such barb motions are rotating helical structures around a vertical axis similar to tornadoes on Earth. One of the difficulties of such a proposal is how to support cool prominence plasma in almostvertical structures against gravity. In this work we model analytically a tornadolike structure and try to determine possible mechanisms to support the prominence plasma. We have found that the Lorentz force can indeed support the barb plasma provided the magnetic structure is sufficiently twisted and/or significant poloidal flows are present.

Effect of Prandtl's ration on balance in geophysical turbulence
http://hdl.handle.net/10023/7201
Abstract: The fluid dynamics of the atmosphere and oceans are to a large extent controlled by the slow evolution of a scalar field called ‘potential vorticity’, with relatively fast motions such as inertiagravity waves playing only a minor role. This state of affairs is commonly referred to as ‘balance’. Potential vorticity (PV) is a special scalar field which is materially conserved in the absence of diabatic effects and dissipation, effects which are generally weak in the atmosphere and oceans. Moreover, in a balanced flow, PV induces the entire fluid motion and its thermodynamic structure (Hoskins et al. 1985). While exact balance is generally not achievable, it is now well established that balance holds to a high degree of accuracy in rapidly rotating and strongly stratified flows. Such flows are characterised by both a small Rossby number, Ro ≡ ζmax/f, and a small Froude number, Fr ≡ .hmax/N, where ζ and .h are the relative vertical and horizontal vorticity components, while f and N are the Coriolis and buoyancy frequencies. In fact, balance can even be a good approximation when Fr < ∼ Ro ∼ O(1). In this study, we examine how balance depends specifically on Prandtl’s ratio, f/N, in unforced freelyevolving turbulence. We examine a wide variety of turbulent flows, at a mature and complex stage of their evolution, making use of the fully nonhydrostatic equations under the Boussinesq and incompressible approximations. We perform numerical simulations at exceptionally high resolution in order to carefully assess the degree to which balance holds, and to determine when it breaks down. For this purpose, it proves most useful to employ an invariant, PVbased Rossby number ε, together with f/N. For a given ε, our key finding is that — for at least tens of characteristic vortex rotation periods — the flow is insensitive to f/N for all values for which the flow remains statically stable (typically f/N < ∼1). Only the vertical velocity varies in proportion to f/N, in line with quasigeostrophic scaling for which Fr2 ≪ Ro ≪ 1. We also find that as ε increases toward unity, the maximum f/N attainable decreases toward 0. No statically stable flows occur for ε > ∼ 1. For all stable flows, balance is found to hold to a remarkably high degree: as measured by an energy norm, imbalance never exceeds more than a few percent of the balance, even in flows where Ro > 1. The vertical velocity w remains a tiny fraction of the horizontal velocity uh, even when w is dominantly balanced. Finally, typical vertical to horizontal scale ratios H/L remain close to f/N, as found previously in quasigeostrophic turbulence for which Fr ∼ Ro ≪ 1.
Description: Support for this research has come from the UK Engineering and Physical Sciences Research Council (grant no. EP/H001794/1). Date of Acceptance: 18/06/2015
Tue, 21 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/7201
20150721T00:00:00Z
Dritschel, David Gerard
McKiver, William Joseph
The fluid dynamics of the atmosphere and oceans are to a large extent controlled by the slow evolution of a scalar field called ‘potential vorticity’, with relatively fast motions such as inertiagravity waves playing only a minor role. This state of affairs is commonly referred to as ‘balance’. Potential vorticity (PV) is a special scalar field which is materially conserved in the absence of diabatic effects and dissipation, effects which are generally weak in the atmosphere and oceans. Moreover, in a balanced flow, PV induces the entire fluid motion and its thermodynamic structure (Hoskins et al. 1985). While exact balance is generally not achievable, it is now well established that balance holds to a high degree of accuracy in rapidly rotating and strongly stratified flows. Such flows are characterised by both a small Rossby number, Ro ≡ ζmax/f, and a small Froude number, Fr ≡ .hmax/N, where ζ and .h are the relative vertical and horizontal vorticity components, while f and N are the Coriolis and buoyancy frequencies. In fact, balance can even be a good approximation when Fr < ∼ Ro ∼ O(1). In this study, we examine how balance depends specifically on Prandtl’s ratio, f/N, in unforced freelyevolving turbulence. We examine a wide variety of turbulent flows, at a mature and complex stage of their evolution, making use of the fully nonhydrostatic equations under the Boussinesq and incompressible approximations. We perform numerical simulations at exceptionally high resolution in order to carefully assess the degree to which balance holds, and to determine when it breaks down. For this purpose, it proves most useful to employ an invariant, PVbased Rossby number ε, together with f/N. For a given ε, our key finding is that — for at least tens of characteristic vortex rotation periods — the flow is insensitive to f/N for all values for which the flow remains statically stable (typically f/N < ∼1). Only the vertical velocity varies in proportion to f/N, in line with quasigeostrophic scaling for which Fr2 ≪ Ro ≪ 1. We also find that as ε increases toward unity, the maximum f/N attainable decreases toward 0. No statically stable flows occur for ε > ∼ 1. For all stable flows, balance is found to hold to a remarkably high degree: as measured by an energy norm, imbalance never exceeds more than a few percent of the balance, even in flows where Ro > 1. The vertical velocity w remains a tiny fraction of the horizontal velocity uh, even when w is dominantly balanced. Finally, typical vertical to horizontal scale ratios H/L remain close to f/N, as found previously in quasigeostrophic turbulence for which Fr ∼ Ro ≪ 1.

On the parallel and perpendicular propagating motions visible in polar plumes : an incubator for (fast) solar wind acceleration?
http://hdl.handle.net/10023/7190
Abstract: We combine observations of the Coronal Multichannel Polarimeter and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the characteristic properties of (propagating) Alfvenic motions and quasiperiodic intensity disturbances in polar plumes. This unique combination of instruments highlights the physical richness of the processes taking place at the base of the (fast) solar wind. The (parallel) intensity perturbations with intensity enhancements around 1% have an apparent speed of 120 km s(1) (in both the 171 and 193 angstrom passbands) and a periodicity of 15 minutes, while the (perpendicular) Alfvenic wave motions have a velocity amplitude of 0.5 km s(1), a phase speed of 830 km s(1), and a shorter period of 5 minutes on the same structures. These observations illustrate a scenario where the excited Alfvenic motions are propagating along an inhomogeneously loaded magnetic field structure such that the combination could be a potential progenitor of the magnetohydrodynamic turbulence required to accelerate the fast solar wind.
Description: J.L. was a student visitor at HAO. J.L. acknowledges the financial support for his visit to HAO from the Chinese Scholarship Council (CSC). The authors acknowledge support from NSFC 41131065, 41121003, 973 Key Project 2011CB811403, and CAS Key Research Program KZZDEW014. We also acknowledge support from NASA contracts NNX08BA99G, NNX11AN98G, NNM12AB40P, NNG09FA40C (IRIS), and NNM07AA01C (Hinode). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/ 20072013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/solspanet) Date of Acceptance: 25/05/2015
Sat, 20 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7190
20150620T00:00:00Z
Liu, Jiajia
McIntosh, Scott W.
De Moortel, Ineke
Wang, Yuming
We combine observations of the Coronal Multichannel Polarimeter and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the characteristic properties of (propagating) Alfvenic motions and quasiperiodic intensity disturbances in polar plumes. This unique combination of instruments highlights the physical richness of the processes taking place at the base of the (fast) solar wind. The (parallel) intensity perturbations with intensity enhancements around 1% have an apparent speed of 120 km s(1) (in both the 171 and 193 angstrom passbands) and a periodicity of 15 minutes, while the (perpendicular) Alfvenic wave motions have a velocity amplitude of 0.5 km s(1), a phase speed of 830 km s(1), and a shorter period of 5 minutes on the same structures. These observations illustrate a scenario where the excited Alfvenic motions are propagating along an inhomogeneously loaded magnetic field structure such that the combination could be a potential progenitor of the magnetohydrodynamic turbulence required to accelerate the fast solar wind.

Uncertainties in polarimetric 3D reconstructions of coronal mass ejections
http://hdl.handle.net/10023/7178
Abstract: Aims. The aim of this work is to quantify the uncertainties in the threedimensional (3D) reconstruction of the location of coronal mass ejections (CMEs) obtained with the socalled polarization ratio technique. The method takes advantage of the different distributions along the line of sight of total (tB) and polarized (pB) brightnesses emitted by Thomson scattering to estimate the average location of the emitting plasma. This is particularly important to correctly identify of CME propagation angles and unprojected velocities, thus allowing better capabilities for space weather forecastings. Methods. To this end, we assumed two simple electron density distributions along the line of sight (a constant density and Gaussian density profiles) for a plasma blob and synthesized the expected tB and pB for different distances z of the blob from the plane of the sky and different projected altitudes.. Reconstructed locations of the blob along the line of sight were thus compared with the real ones, allowing a precise determination of uncertainties in the method. Results. Results show that, independently of the analytical density profile, when the blob is centered at a small distance from the plane of the sky (i. e. for limb CMEs) the distance from the plane of the sky starts to be significantly overestimated. Polarization ratio technique provides the lineofsight position of the center of mass of what we call folded density distribution, given by reflecting and summing in front of the plane of the sky the fraction of density profile located behind that plane. On the other hand, when the blob is far from the plane of the sky, but with very small projected altitudes (i. e. for halo CMEs, rho< 1.4 Rcircle dot), the inferred distance from that plane is significantly underestimated. Better determination of the real blob position along the line of sight is given for intermediate locations, and in particular when the blob is centered at an angle of 20 degrees from the plane of the sky. Conclusions. These result have important consequences not only for future 3D reconstruction of CMEs with polarization ratio technique, but also for the design of future coronagraphs aimed at providing a continuous monitoring of haloCMEs for space weather prediction purposes.
Description: P.P. acknowledges STFC for financial support. Date of Acceptance: 21/01/2015
Mon, 06 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/7178
20150406T00:00:00Z
Bemporad, A.
Pagano, P.
Aims. The aim of this work is to quantify the uncertainties in the threedimensional (3D) reconstruction of the location of coronal mass ejections (CMEs) obtained with the socalled polarization ratio technique. The method takes advantage of the different distributions along the line of sight of total (tB) and polarized (pB) brightnesses emitted by Thomson scattering to estimate the average location of the emitting plasma. This is particularly important to correctly identify of CME propagation angles and unprojected velocities, thus allowing better capabilities for space weather forecastings. Methods. To this end, we assumed two simple electron density distributions along the line of sight (a constant density and Gaussian density profiles) for a plasma blob and synthesized the expected tB and pB for different distances z of the blob from the plane of the sky and different projected altitudes.. Reconstructed locations of the blob along the line of sight were thus compared with the real ones, allowing a precise determination of uncertainties in the method. Results. Results show that, independently of the analytical density profile, when the blob is centered at a small distance from the plane of the sky (i. e. for limb CMEs) the distance from the plane of the sky starts to be significantly overestimated. Polarization ratio technique provides the lineofsight position of the center of mass of what we call folded density distribution, given by reflecting and summing in front of the plane of the sky the fraction of density profile located behind that plane. On the other hand, when the blob is far from the plane of the sky, but with very small projected altitudes (i. e. for halo CMEs, rho< 1.4 Rcircle dot), the inferred distance from that plane is significantly underestimated. Better determination of the real blob position along the line of sight is given for intermediate locations, and in particular when the blob is centered at an angle of 20 degrees from the plane of the sky. Conclusions. These result have important consequences not only for future 3D reconstruction of CMEs with polarization ratio technique, but also for the design of future coronagraphs aimed at providing a continuous monitoring of haloCMEs for space weather prediction purposes.

NonLTE modelling of prominence fine structures using hydrogen Lymanline profiles
http://hdl.handle.net/10023/7177
Abstract: Aims. We perform a detailed statistical analysis of the spectral Lymanline observations of the quiescent prominence observed on May 18, 2005. Methods. We used a profiletoprofile comparison of the synthetic Lyman spectra obtained by 2D singlethread prominence finestructure model as a starting point for a full statistical analysis of the observed Lyman spectra. We employed 2D multithread finestructure models with random positions and lineofsight velocities of each thread to obtain a statistically significant set of synthetic Lymanline profiles. We used for the first time multithread models composed of nonidentical threads and viewed at lineofsight angles different from perpendicular to the magnetic field. Results. We investigated the plasma properties of the prominence observed with the SoHO/SUMER spectrograph on May 18, 2005 by comparing the histograms of three statistical parameters characterizing the properties of the synthetic and observed line profiles. In this way, the integrated intensity, Lyman decrement ratio, and the ratio of intensity at the central reversal to the average intensity of peaks provided insight into the column mass and the central temperature of the prominence fine structures.
Description: Date of Acceptance: 10/03/2015
Fri, 08 May 2015 00:00:00 GMT
http://hdl.handle.net/10023/7177
20150508T00:00:00Z
Schwartz, P.
Gunar, S.
Curdt, W.
Aims. We perform a detailed statistical analysis of the spectral Lymanline observations of the quiescent prominence observed on May 18, 2005. Methods. We used a profiletoprofile comparison of the synthetic Lyman spectra obtained by 2D singlethread prominence finestructure model as a starting point for a full statistical analysis of the observed Lyman spectra. We employed 2D multithread finestructure models with random positions and lineofsight velocities of each thread to obtain a statistically significant set of synthetic Lymanline profiles. We used for the first time multithread models composed of nonidentical threads and viewed at lineofsight angles different from perpendicular to the magnetic field. Results. We investigated the plasma properties of the prominence observed with the SoHO/SUMER spectrograph on May 18, 2005 by comparing the histograms of three statistical parameters characterizing the properties of the synthetic and observed line profiles. In this way, the integrated intensity, Lyman decrement ratio, and the ratio of intensity at the central reversal to the average intensity of peaks provided insight into the column mass and the central temperature of the prominence fine structures.

Large scale surveys for cetaceans : line transect assumptions, reliability of abundance estimates and improving survey efficiency – A response to MacLeod
http://hdl.handle.net/10023/7159
Description: Date of Acceptance: 11/01/2014
Sat, 01 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/7159
20140201T00:00:00Z
Hammond, Philip Steven
Gillespie, Douglas Michael
Lovell, Philip
Samarra, Filipa Isabel Pereira
Swift, Rene James
Macleod, Kelly
Tasker, Mark L
Berggren, Per
Borchers, David Louis
Burt, M Louise
Paxton, Charles G. M.
Canadas, Ana
Desportes, Genevieve
Donovan, Greg P
Gilles, Anita
Lehnert, Kristina
Siebert, Ursula
Gordon, Jonathan Charles David
Leaper, Russell
Leopold, Mardik
Scheidat, Meike
Oien, Nils
Ridoux, Vincent
Rogan, Emer
Skov, Henrik
Teilmann, Jonas
Van Canneyt, Olivier
Vazquez, Jose Antonio

Detectability in audiovisual surveys of tropical rainforest birds : the influence of species, weather and habitat characteristics
http://hdl.handle.net/10023/7147
Abstract: Indices of relative abundance do not control for variation in detectability, which can bias density estimates such that ecological processes are difficult to infer. Distance sampling methods can be used to correct for detectability, but in rainforest, where dense vegetation and diverse assemblages complicate sampling, information is lacking about factors affecting their application. Rare species present an additional challenge, as data may be too sparse to fit detection functions. We present analyses of distance sampling data collected for a diverse tropical rainforest bird assemblage across broad elevational and latitudinal gradients in North Queensland, Australia. Using audio and visual detections, we assessed the influence of various factors on Effective Strip Width (ESW), an intuitively useful parameter, since it can be used to calculate an estimate of density from count data. Body size and species exerted the most important influence on ESW, with larger species detectable over greater distances than smaller species. Secondarily, wet weather and high shrub density decreased ESW for most species. ESW for several species also differed between summer and winter, possibly due to seasonal differences in calling behavior. Distance sampling proved logistically intensive in these environments, but large differences in ESW between species confirmed the need to correct for detection probability to obtain accurate density estimates. Our results suggest an evidencebased approach to controlling for factors influencing detectability, and avenues for further work including modeling detectability as a function of species characteristics such as body size and call characteristics. Such models may be useful in developing a calibration for nondistance sampling data and for estimating detectability of rare species.
Description: This research was funded by the Australian Government’s National Environmental Research Program, the Stuart Leslie Bird Research Award from Birds Australia (http://www.birdsaustralia.com.au/), the Earthwatch Institute (http://www.earthwatch.org/australia/), the Marine and Tropical Sciences Research Facility (MTSRF: http://www.rrrc.org.au/mtsrf). In addition, TAM was partially sponsored by national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal – FCT under the project (PEstOE/MAT/UI0006/2011). Date of Acceptance: 27/04/2015
Thu, 25 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7147
20150625T00:00:00Z
Anderson, Alexander S.
Marques, Tiago A.
Shoo, Luke P.
Williams, Stephen E.
Indices of relative abundance do not control for variation in detectability, which can bias density estimates such that ecological processes are difficult to infer. Distance sampling methods can be used to correct for detectability, but in rainforest, where dense vegetation and diverse assemblages complicate sampling, information is lacking about factors affecting their application. Rare species present an additional challenge, as data may be too sparse to fit detection functions. We present analyses of distance sampling data collected for a diverse tropical rainforest bird assemblage across broad elevational and latitudinal gradients in North Queensland, Australia. Using audio and visual detections, we assessed the influence of various factors on Effective Strip Width (ESW), an intuitively useful parameter, since it can be used to calculate an estimate of density from count data. Body size and species exerted the most important influence on ESW, with larger species detectable over greater distances than smaller species. Secondarily, wet weather and high shrub density decreased ESW for most species. ESW for several species also differed between summer and winter, possibly due to seasonal differences in calling behavior. Distance sampling proved logistically intensive in these environments, but large differences in ESW between species confirmed the need to correct for detection probability to obtain accurate density estimates. Our results suggest an evidencebased approach to controlling for factors influencing detectability, and avenues for further work including modeling detectability as a function of species characteristics such as body size and call characteristics. Such models may be useful in developing a calibration for nondistance sampling data and for estimating detectability of rare species.

Evaluating the utility of B/Ca ratios in planktic foraminifera as a proxy for the carbonate system : a case study of Globigerinoides ruber
http://hdl.handle.net/10023/7133
Abstract: B/Ca ratios in foraminifera have attracted considerable scientific attention as a proxy for past ocean carbonate system. However, the carbonate system controls on B/Ca ratios are not straightforward, with Δ[ CO32] ([ CO32]in situ  [ CO32]at saturation) correlating best with B/Ca ratios in benthic foraminifera, rather than pH, B(OH)4/HCO3, or B(OH)4/DIC (as a simple model of boron speciation in seawater and incorporation into CaCO3 would predict). Furthermore, culture experiments have shown that in planktic foraminifera properties such as salinity and [B]SW can have profound effects on B/Ca ratios beyond those predicted by simple partition coefficients. Here, we investigate the controls on B/Ca ratios in G. ruber via a combination of culture experiments and coretop measurements, and add to a growing body of evidence that suggests B/Ca ratios in symbiontbearing foraminiferal carbonate are not a straightforward proxy for past seawater carbonate system conditions. We find that while B/Ca ratios in culture experiments covary with pH, in open ocean sediments this relationship is not seen. In fact, our B/Ca data correlate best with [ PO43] (a previously undocumented association) and in most regions, salinity. These findings might suggest a precipitation rate or crystallographic control on boron incorporation into foraminiferal calcite. Regardless, our results underscore the need for caution when attempting to interpret B/Ca records in terms of the ocean carbonate system, at the very least in the case of mixedlayer planktic foraminifera.
Description: This research was funded by NERC, Grant Number: NE/D00876X/2. Date of Acceptance: 06/03/2015
Wed, 01 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/7133
20150401T00:00:00Z
Henehan, M.J.
Foster, G.L.
Rae, J.W.B.
Prentice, K.C.
Erez, J.
Bostock, H.C.
Marshall, B.J.
Wilson, P.A.
B/Ca ratios in foraminifera have attracted considerable scientific attention as a proxy for past ocean carbonate system. However, the carbonate system controls on B/Ca ratios are not straightforward, with Δ[ CO32] ([ CO32]in situ  [ CO32]at saturation) correlating best with B/Ca ratios in benthic foraminifera, rather than pH, B(OH)4/HCO3, or B(OH)4/DIC (as a simple model of boron speciation in seawater and incorporation into CaCO3 would predict). Furthermore, culture experiments have shown that in planktic foraminifera properties such as salinity and [B]SW can have profound effects on B/Ca ratios beyond those predicted by simple partition coefficients. Here, we investigate the controls on B/Ca ratios in G. ruber via a combination of culture experiments and coretop measurements, and add to a growing body of evidence that suggests B/Ca ratios in symbiontbearing foraminiferal carbonate are not a straightforward proxy for past seawater carbonate system conditions. We find that while B/Ca ratios in culture experiments covary with pH, in open ocean sediments this relationship is not seen. In fact, our B/Ca data correlate best with [ PO43] (a previously undocumented association) and in most regions, salinity. These findings might suggest a precipitation rate or crystallographic control on boron incorporation into foraminiferal calcite. Regardless, our results underscore the need for caution when attempting to interpret B/Ca records in terms of the ocean carbonate system, at the very least in the case of mixedlayer planktic foraminifera.

Generalized energy inequalities and higher multifractal moments
http://hdl.handle.net/10023/7095
Abstract: We present a class of generalized energy inequalities and indicate their use in investigating higher multifractal moments, in particular Lqdimensions of images of measures under Brownian processes, Lqdimensions of almost selfaﬃne measures, and moments of random cascade measures
Sat, 02 Aug 2014 00:00:00 GMT
http://hdl.handle.net/10023/7095
20140802T00:00:00Z
Falconer, Kenneth John
We present a class of generalized energy inequalities and indicate their use in investigating higher multifractal moments, in particular Lqdimensions of images of measures under Brownian processes, Lqdimensions of almost selfaﬃne measures, and moments of random cascade measures

Doubleobserver line transect surveys with Markovmodulated Poisson process models for overdispersed animal availability
http://hdl.handle.net/10023/7085
Abstract: We develop maximum likelihood methods for line transect surveys in which animals go undetected at distance zero, either because they are stochastically unavailable while within view or because they are missed when they are available. These incorporate a Markovmodulated Poisson process model for animal availability, allowing more clustered availability events than is possible with Poisson availability models. They include a markrecapture component arising from the independentobserver survey, leading to more accurate estimation of detection probability given availability. We develop models for situations in which (a) multiple detections of the same individual are possible and (b) some or all of the availability process parameters are estimated from the line transect survey itself, rather than from independent data. We investigate estimator performance by simulation, and compare the multipledetection estimators with estimators that use only initial detections of individuals, and with a singleobserver estimator. Simultaneous estimation of detection function parameters and availability model parameters is shown to be feasible from the line transect survey alone with multiple detections and doubleobserver data but not with singleobserver data. Recording multiple detections of individuals improves estimator precision substantially when estimating the availability model parameters from survey data, and we recommend that these data be gathered. We apply the methods to estimate detection probability from a doubleobserver survey of North Atlantic minke whales, and find that doubleobserver data greatly improve estimator precision here too.
Description: Date of Acceptance: 01/04/2015
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/7085
20150101T00:00:00Z
Borchers, David Louis
Langrock, Roland
We develop maximum likelihood methods for line transect surveys in which animals go undetected at distance zero, either because they are stochastically unavailable while within view or because they are missed when they are available. These incorporate a Markovmodulated Poisson process model for animal availability, allowing more clustered availability events than is possible with Poisson availability models. They include a markrecapture component arising from the independentobserver survey, leading to more accurate estimation of detection probability given availability. We develop models for situations in which (a) multiple detections of the same individual are possible and (b) some or all of the availability process parameters are estimated from the line transect survey itself, rather than from independent data. We investigate estimator performance by simulation, and compare the multipledetection estimators with estimators that use only initial detections of individuals, and with a singleobserver estimator. Simultaneous estimation of detection function parameters and availability model parameters is shown to be feasible from the line transect survey alone with multiple detections and doubleobserver data but not with singleobserver data. Recording multiple detections of individuals improves estimator precision substantially when estimating the availability model parameters from survey data, and we recommend that these data be gathered. We apply the methods to estimate detection probability from a doubleobserver survey of North Atlantic minke whales, and find that doubleobserver data greatly improve estimator precision here too.

The formation and eruption of magnetic flux ropes in solar and stellar coronae
http://hdl.handle.net/10023/7069
Abstract: Flux ropes are magnetic structures commonly found in the solar corona. They are thought to play an important role in solar flares and coronal mass ejections. Understanding their formation and eruption is of paramount importance for our understanding of space weather. In this thesis the magnetofrictional method is applied to simulate the formation of flux ropes and track their evolution up to eruption both in solar and stellar coronae.
Initially, the coronal magnetic field of a solar active region is simulated using observed magnetograms to drive the coronal evolution. From the sequence of magnetograms the formation of a flux rope is simulated, and compared with coronal observations.
Secondly a procedure to produce proxy SOLIS synoptic magnetograms from SDO/HMI and SOHO/MDI magnetograms is presented. This procedure allows SOLISlike synoptic magnetograms to be produced during times when SOLIS magnetograms are not available.
Thirdly, a series of scaling laws for the formation and lifetimes of flux ropes in stellar coronae are determined as a function of stellar differential rotation and surface diffusion. These scaling laws can be used to infer the response of stellar coronae to the transport of magnetic fields at their surface.
Finally, global longterm simulations of stellar corona are carried out to determine the coronal response to flux emergence and differential rotation. A bipole emergence model is developed and is used in conjunction with a surface flux transport model in order to drive the global coronal evolution. These global simulations allow the flux, energy and flux rope distributions to be studied as a function of a star’s differential rotation and flux emergence rate.
Mon, 30 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7069
20151130T00:00:00Z
Gibb, Gordon P. S.
Flux ropes are magnetic structures commonly found in the solar corona. They are thought to play an important role in solar flares and coronal mass ejections. Understanding their formation and eruption is of paramount importance for our understanding of space weather. In this thesis the magnetofrictional method is applied to simulate the formation of flux ropes and track their evolution up to eruption both in solar and stellar coronae.
Initially, the coronal magnetic field of a solar active region is simulated using observed magnetograms to drive the coronal evolution. From the sequence of magnetograms the formation of a flux rope is simulated, and compared with coronal observations.
Secondly a procedure to produce proxy SOLIS synoptic magnetograms from SDO/HMI and SOHO/MDI magnetograms is presented. This procedure allows SOLISlike synoptic magnetograms to be produced during times when SOLIS magnetograms are not available.
Thirdly, a series of scaling laws for the formation and lifetimes of flux ropes in stellar coronae are determined as a function of stellar differential rotation and surface diffusion. These scaling laws can be used to infer the response of stellar coronae to the transport of magnetic fields at their surface.
Finally, global longterm simulations of stellar corona are carried out to determine the coronal response to flux emergence and differential rotation. A bipole emergence model is developed and is used in conjunction with a surface flux transport model in order to drive the global coronal evolution. These global simulations allow the flux, energy and flux rope distributions to be studied as a function of a star’s differential rotation and flux emergence rate.

The maximal subgroups of the classical groups in dimension 13, 14 and 15
http://hdl.handle.net/10023/7067
Abstract: One might easily argue that the Classification of Finite Simple Groups is
one of the most important theorems of group theory. Given that any finite
group can be deconstructed into its simple composition factors, it is of great
importance to have a detailed knowledge of the structure of finite simple
groups.
One of the classes of finite groups that appear in the classification theorem
are the simple classical groups, which are matrix groups preserving
some form. This thesis will shed some new light on almost simple classical
groups in dimension 13, 14 and 15. In particular we will determine their
maximal subgroups.
We will build on the results by Bray, Holt, and RoneyDougal who
calculated the maximal subgroups of all almost simple finite classical groups
in dimension less than 12. Furthermore, Aschbacher proved that the maximal
subgroups of almost simple classical groups lie in nine classes. The maximal
subgroups in the first eight classes, i.e. the subgroups of geometric type,
were determined by Kleidman and Liebeck for
dimension greater than 13.
Therefore this thesis concentrates on the ninth class of Aschbacher’s
Theorem. This class roughly consists of subgroups which are almost simple
modulo scalars and do not preserve a geometric structure. As our final
result we will give tables containing all maximal subgroups of almost simple
classical groups in dimension 13, 14 and 15.
Mon, 30 Nov 2015 00:00:00 GMT
http://hdl.handle.net/10023/7067
20151130T00:00:00Z
Schröder, Anna Katharina
One might easily argue that the Classification of Finite Simple Groups is
one of the most important theorems of group theory. Given that any finite
group can be deconstructed into its simple composition factors, it is of great
importance to have a detailed knowledge of the structure of finite simple
groups.
One of the classes of finite groups that appear in the classification theorem
are the simple classical groups, which are matrix groups preserving
some form. This thesis will shed some new light on almost simple classical
groups in dimension 13, 14 and 15. In particular we will determine their
maximal subgroups.
We will build on the results by Bray, Holt, and RoneyDougal who
calculated the maximal subgroups of all almost simple finite classical groups
in dimension less than 12. Furthermore, Aschbacher proved that the maximal
subgroups of almost simple classical groups lie in nine classes. The maximal
subgroups in the first eight classes, i.e. the subgroups of geometric type,
were determined by Kleidman and Liebeck for
dimension greater than 13.
Therefore this thesis concentrates on the ninth class of Aschbacher’s
Theorem. This class roughly consists of subgroups which are almost simple
modulo scalars and do not preserve a geometric structure. As our final
result we will give tables containing all maximal subgroups of almost simple
classical groups in dimension 13, 14 and 15.

Propagation and damping of MHD waves in the solar atmosphere
http://hdl.handle.net/10023/7054
Abstract: Quasiperiodic disturbances have been observed in the outer solar atmosphere for many years. Although first interpreted as upflows (Schrijver et al. (1999)), they have been widely regarded as slow magnetoacoustic waves, due to their observed velocities and periods. Here we conduct a detailed analysis of the velocities of these disturbances across several wavelengths using the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). We analysed 41 examples, including both sunspot and nonsunspot regions of the Sun. We found that the velocities of propagating disturbances (PDs) located at sunspots are more likely to be temperature dependent, whereas the velocities of PDs at nonsunspot locations do not show a clear temperature dependence. This suggests an interpretation in terms of slow magnetoacoustic waves in sunspots but the nature of PDs in nonsunspot (plage) regions remains unclear. Finally, we found that removing the contribution due to the cooler ions in the 193 wavelength suggests that a substantial part of the 193 emission of sunspot PDs can be attributed to the cool component of 193. Phase mixing is a well known and studied phenomenon in the solar corona, to enhance the dissipation of Alfvén waves (Heyvaerts and Priest (1982)). In this study we run numerical simulations of a continuously driven Alfvén wave in a low beta plasma along a uniform magnetic field. We model phase mixing by introducing a density inhomogeneity. Thermal conduction is then added into the model in the form of Braginskii thermal conduction. This acts to transport heat along the magnetic field. A parameter study will be carried out to investigate how changing the density structure and other parameters changes the results. We go on to consider the effect of wave reflection on phase mixing. We found that wave reflection has no effect on the damping of Alfvén waves but increases the heat in the system. We also consider a more realistic experiment where we drive both boundaries and study how the loop is heated in this situation. We also study what effect changing the frequency of one of the drivers so there is a small difference between the frequencies (10%) and a large difference (50%). We find the general behaviour is similar, but the heat is tilted.
We have investigated basic phase mixing model which incorporates the mass exchange between the corona and the chromosphere. Chromospheric evaporation is approximated by using a non dimensional version of the RTV (Rosner et al. (1978)) scaling laws, relating heating (by phase mixing of Alfvén waves), density and temperature. By combining this scaling law with our numerical MHD model for phase mixing of Alfvén waves, we investigate the modification of the density profile through the mass up flow. We find a rapid modification of the density profile, leading to drifting of the heating layers. We also find that similar results are own seen in the propagating Alfvén wave case when we incorporate the effects of reflection.
Fri, 27 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/7054
20140627T00:00:00Z
Kiddie, Greg
Quasiperiodic disturbances have been observed in the outer solar atmosphere for many years. Although first interpreted as upflows (Schrijver et al. (1999)), they have been widely regarded as slow magnetoacoustic waves, due to their observed velocities and periods. Here we conduct a detailed analysis of the velocities of these disturbances across several wavelengths using the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). We analysed 41 examples, including both sunspot and nonsunspot regions of the Sun. We found that the velocities of propagating disturbances (PDs) located at sunspots are more likely to be temperature dependent, whereas the velocities of PDs at nonsunspot locations do not show a clear temperature dependence. This suggests an interpretation in terms of slow magnetoacoustic waves in sunspots but the nature of PDs in nonsunspot (plage) regions remains unclear. Finally, we found that removing the contribution due to the cooler ions in the 193 wavelength suggests that a substantial part of the 193 emission of sunspot PDs can be attributed to the cool component of 193. Phase mixing is a well known and studied phenomenon in the solar corona, to enhance the dissipation of Alfvén waves (Heyvaerts and Priest (1982)). In this study we run numerical simulations of a continuously driven Alfvén wave in a low beta plasma along a uniform magnetic field. We model phase mixing by introducing a density inhomogeneity. Thermal conduction is then added into the model in the form of Braginskii thermal conduction. This acts to transport heat along the magnetic field. A parameter study will be carried out to investigate how changing the density structure and other parameters changes the results. We go on to consider the effect of wave reflection on phase mixing. We found that wave reflection has no effect on the damping of Alfvén waves but increases the heat in the system. We also consider a more realistic experiment where we drive both boundaries and study how the loop is heated in this situation. We also study what effect changing the frequency of one of the drivers so there is a small difference between the frequencies (10%) and a large difference (50%). We find the general behaviour is similar, but the heat is tilted.
We have investigated basic phase mixing model which incorporates the mass exchange between the corona and the chromosphere. Chromospheric evaporation is approximated by using a non dimensional version of the RTV (Rosner et al. (1978)) scaling laws, relating heating (by phase mixing of Alfvén waves), density and temperature. By combining this scaling law with our numerical MHD model for phase mixing of Alfvén waves, we investigate the modification of the density profile through the mass up flow. We find a rapid modification of the density profile, leading to drifting of the heating layers. We also find that similar results are own seen in the propagating Alfvén wave case when we incorporate the effects of reflection.

Extreme ultraviolet imaging of threedimensional magnetic reconnection in a solar eruption
http://hdl.handle.net/10023/7025
Abstract: Magnetic reconnection, a change of magnetic field connectivity, is a fundamental physical process in which magnetic energy is released explosively, and it is responsible for various eruptive phenomena in the universe. However, this process is difficult to observe directly. Here, the magnetic topology associated with a solar reconnection event is studied in three dimensions using the combined perspectives of two spacecraft. The sequence of extreme ultraviolet images clearly shows that two groups of oppositely directed and noncoplanar magnetic loops gradually approach each other, forming a separator or quasiseparator and then reconnecting. The plasma near the reconnection site is subsequently heated from ∼ 1 to ≥ 5MK. Shortly afterwards, warm flare loops (∼3MK) appear underneath the hot plasma. Other observational signatures of reconnection, including plasma inflows and downflows, are unambiguously revealed and quantitatively measured. These observations provide direct evidence of magnetic reconnection in a threedimensional configuration and reveal its origin.
Description: X.C., J.Q.S., M.D.D., Y.G., P.F.C. and C.F. are supported by NSFC through grants 11303016, 11373023, 11203014 and 11025314, and by NKBRSF through grants 2011CB811402 and 2014CB744203. C.E.P. and S.J.E. are supported by the UK STFC. J.Z. is supported by US NSF AGS1249270 and AGS1156120. Date of Acceptance: 22/05/2015
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7025
20150626T00:00:00Z
Sun, J.Q.
Cheng, X.
Ding, M.D.
Guo, Y.
Priest, E.R.
Parnell, C.E.
Edwards, S.J.
Zhang, J.
Chen, P.F.
Fang, C.
Magnetic reconnection, a change of magnetic field connectivity, is a fundamental physical process in which magnetic energy is released explosively, and it is responsible for various eruptive phenomena in the universe. However, this process is difficult to observe directly. Here, the magnetic topology associated with a solar reconnection event is studied in three dimensions using the combined perspectives of two spacecraft. The sequence of extreme ultraviolet images clearly shows that two groups of oppositely directed and noncoplanar magnetic loops gradually approach each other, forming a separator or quasiseparator and then reconnecting. The plasma near the reconnection site is subsequently heated from ∼ 1 to ≥ 5MK. Shortly afterwards, warm flare loops (∼3MK) appear underneath the hot plasma. Other observational signatures of reconnection, including plasma inflows and downflows, are unambiguously revealed and quantitatively measured. These observations provide direct evidence of magnetic reconnection in a threedimensional configuration and reveal its origin.

Ergodicity and spectral cascades in point vortex flows on the sphere
http://hdl.handle.net/10023/7024
Abstract: We present results for the equilibrium statistics and dynamic evolution of moderately large [n=O(102103)] numbers of interacting point vortices on the sphere under the constraint of zero mean angular momentum. For systems with equal numbers of positive and negative identical circulations, the density of rescaled energies, p(E), converges rapidly with n to a function with a single maximum with maximum entropy. Ensembleaveraged wavenumber spectra of the nonsingular velocity field induced by the vortices exhibit the expected k1 behavior at small scales for all energies. Spectra at the largest scales vary continuously with the inverse temperature of the system. For positive temperatures, spectra peak at finite intermediate wave numbers; for negative temperatures, spectra decrease everywhere. Comparisons of time and ensemble averages, over a large range of energies, strongly support ergodicity in the dynamics even for highly atypical initial vortex configurations. Crucially, rapid relaxation of spectra toward the microcanonical average implies that the direction of any spectral cascade process depends only on the relative difference between the initial spectrum and the ensemble mean spectrum at that energy, not on the energy, or temperature, of the system.
Description: A.C.P. was supported under DOD (MURI) Grant No. N000141110087 ONR. The computations were supported by the CUNY HPCC under NSF Grants No. CNS0855217 and No. CNS0958379.
Mon, 29 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/7024
20150629T00:00:00Z
Dritschel, D.G.
Lucia, M.
Poje, A.C.
We present results for the equilibrium statistics and dynamic evolution of moderately large [n=O(102103)] numbers of interacting point vortices on the sphere under the constraint of zero mean angular momentum. For systems with equal numbers of positive and negative identical circulations, the density of rescaled energies, p(E), converges rapidly with n to a function with a single maximum with maximum entropy. Ensembleaveraged wavenumber spectra of the nonsingular velocity field induced by the vortices exhibit the expected k1 behavior at small scales for all energies. Spectra at the largest scales vary continuously with the inverse temperature of the system. For positive temperatures, spectra peak at finite intermediate wave numbers; for negative temperatures, spectra decrease everywhere. Comparisons of time and ensemble averages, over a large range of energies, strongly support ergodicity in the dynamics even for highly atypical initial vortex configurations. Crucially, rapid relaxation of spectra toward the microcanonical average implies that the direction of any spectral cascade process depends only on the relative difference between the initial spectrum and the ensemble mean spectrum at that energy, not on the energy, or temperature, of the system.

Fast approximate radiative transfer method for visualizing the fine structure of prominences in the hydrogen Hα line
http://hdl.handle.net/10023/7020
Abstract: Aims. We present a novel approximate radiative transfer method developed to visualize 3D wholeprominence models with multiple fine structures using the hydrogen Hα spectral line. Methods. This method employs a fast lineofsight synthesis of the Hα line profiles through the whole 3D prominence volume and realistically reflects the basic properties of the Hα line formation in the cool and lowdensity prominence medium. The method can be applied both to prominences seen above the limb and filaments seen against the disk. Results. We provide recipes for the use of this method for visualizing the prominence or filament models that have multiple fine structures. We also perform tests of the method that demonstrate its accuracy under prominence conditions. Conclusions. We demonstrate that this fast approximate radiative transfer method provides realistic synthetic Hα intensities useful for a reliable visualization of prominences and filaments. Such synthetic highresolution images of modeled prominences/filaments can be used for a direct comparison with highresolution observations.
Description: P.H. acknowledges the support from grant 209/12/0906 of the Grant Agency of the Czech Republic. S.G. acknowledges support from the European Commission via the Marie Curie Actions – IntraEuropean Fellowships Project No. 328138. P.H. and S.G. acknowledge support from project RVO:67985815 of the Astronomical Institute of the Czech Academy of Sciences and from the MPA Garching. U.A. thanks for the support from the Astronomical Institute of the Czech Academy of Sciences. Date of Acceptance: 09/04/2015
Wed, 01 Jul 2015 00:00:00 GMT
http://hdl.handle.net/10023/7020
20150701T00:00:00Z
Heinzel, P.
Gunár, S.
Anzer, U.
Aims. We present a novel approximate radiative transfer method developed to visualize 3D wholeprominence models with multiple fine structures using the hydrogen Hα spectral line. Methods. This method employs a fast lineofsight synthesis of the Hα line profiles through the whole 3D prominence volume and realistically reflects the basic properties of the Hα line formation in the cool and lowdensity prominence medium. The method can be applied both to prominences seen above the limb and filaments seen against the disk. Results. We provide recipes for the use of this method for visualizing the prominence or filament models that have multiple fine structures. We also perform tests of the method that demonstrate its accuracy under prominence conditions. Conclusions. We demonstrate that this fast approximate radiative transfer method provides realistic synthetic Hα intensities useful for a reliable visualization of prominences and filaments. Such synthetic highresolution images of modeled prominences/filaments can be used for a direct comparison with highresolution observations.

Chronic exposure to imidacloprid increases neuronal vulnerability to mitochondrial dysfunction in the bumblebee (Bombus terrestris)
http://hdl.handle.net/10023/6986
Abstract: The global decline in the abundance and diversity of insect pollinators could result from habitat loss, disease, and pesticide exposure. The contribution of the neonicotinoid insecticides (e.g., clothianidin and imidacloprid) to this decline is controversial, and key to understanding their risk is whether the astonishingly low levels found in the nectar and pollen of plants is sufficient to deliver neuroactive levels to their site of action: the bee brain. Here we show that bumblebees (Bombusterrestris audax) fed field levels [10 nM, 2.1 ppb (w/w)] of neonicotinoid accumulate between 4 and 10 nM in their brains within 3 days. Acute (minutes) exposure of cultured neurons to 10 nM clothianidin, but not imidacloprid, causes a nicotinic acetylcholine receptordependent rapid mitochondrial depolarization. However, a chronic (2 days) exposure to 1 nM imidacloprid leads to a receptordependent increased sensitivity to a normally innocuous level of acetylcholine, which now also causes rapid mitochondrial depolarization in neurons. Finally, colonies exposed to this level of imidacloprid show deficits in colony growth and nest condition compared with untreated colonies. These findings provide a mechanistic explanation for the poor navigation and foraging observed in neonicotinoid treated bumblebee colonies.
Description: This work was funded jointly by the Biotechnology and Biological Sciences Research Council, the Department for Environment, Food and Rural Affairs, the Natural Environment Research Council, the Scottish Government, and The Wellcome Trust, under the Insect Pollinators Initiative (United Kingdom) Grant BB/ 1000313/1 (to C.N.C.). Date of Acceptance: 07/01/2015
Fri, 01 May 2015 00:00:00 GMT
http://hdl.handle.net/10023/6986
20150501T00:00:00Z
Moffat, C.
Goncalves Pacheco, J.
Sharpe, S.
Samson, A.J.
Bollan, K.A.
Huang, J.
Buckland, Stephen Terrence
Connolly, C.N.
The global decline in the abundance and diversity of insect pollinators could result from habitat loss, disease, and pesticide exposure. The contribution of the neonicotinoid insecticides (e.g., clothianidin and imidacloprid) to this decline is controversial, and key to understanding their risk is whether the astonishingly low levels found in the nectar and pollen of plants is sufficient to deliver neuroactive levels to their site of action: the bee brain. Here we show that bumblebees (Bombusterrestris audax) fed field levels [10 nM, 2.1 ppb (w/w)] of neonicotinoid accumulate between 4 and 10 nM in their brains within 3 days. Acute (minutes) exposure of cultured neurons to 10 nM clothianidin, but not imidacloprid, causes a nicotinic acetylcholine receptordependent rapid mitochondrial depolarization. However, a chronic (2 days) exposure to 1 nM imidacloprid leads to a receptordependent increased sensitivity to a normally innocuous level of acetylcholine, which now also causes rapid mitochondrial depolarization in neurons. Finally, colonies exposed to this level of imidacloprid show deficits in colony growth and nest condition compared with untreated colonies. These findings provide a mechanistic explanation for the poor navigation and foraging observed in neonicotinoid treated bumblebee colonies.

The use of the Poynting vector in interpreting ULF waves in magnetospheric waveguides
http://hdl.handle.net/10023/6976
Abstract: We numerically model ultralow frequency (ULF) waves in the magnetosphere assuming an ideal, lowbeta inhomogeneous plasma waveguide. The waveguide is based on the hydromagnetic box model. We develop a novel boundary condition that drives the magnetospheric boundary by pressure perturbations, in order to simulate solar wind dynamic pressure uctuations disturbing the magnetopause. The model is applied to observations from Cluster and THEMIS. Our model is able to reproduce similar wave signatures to those in the data, such as a unidirectional azimuthal Poynting vector, by interpreting the observations in terms of fast waveguide modes. Despite the simplicity of the model, we can shed light on the nature of these modes and the location of the energy source relative to the spacecraft. This is achieved by demonstrating that important information, such as phase shifts between components of the electric and magnetic fields and the balance of radial to azimuthal propagation of energy, may be extracted from a careful analysis of the components of the Poynting vector.
Description: T.E. would like to thank STFC for financial support for a doctoral training grant. Date of Acceptance: 04/12/2014
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/6976
20150101T00:00:00Z
Elsden, Tom
Wright, Andrew Nicholas
We numerically model ultralow frequency (ULF) waves in the magnetosphere assuming an ideal, lowbeta inhomogeneous plasma waveguide. The waveguide is based on the hydromagnetic box model. We develop a novel boundary condition that drives the magnetospheric boundary by pressure perturbations, in order to simulate solar wind dynamic pressure uctuations disturbing the magnetopause. The model is applied to observations from Cluster and THEMIS. Our model is able to reproduce similar wave signatures to those in the data, such as a unidirectional azimuthal Poynting vector, by interpreting the observations in terms of fast waveguide modes. Despite the simplicity of the model, we can shed light on the nature of these modes and the location of the energy source relative to the spacecraft. This is achieved by demonstrating that important information, such as phase shifts between components of the electric and magnetic fields and the balance of radial to azimuthal propagation of energy, may be extracted from a careful analysis of the components of the Poynting vector.

Dots and lines : geometric semigroup theory and finite presentability
http://hdl.handle.net/10023/6923
Abstract: Geometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure.
One such property is finite presentability. In geometric group theory, the geometric structure of choice is the Cayley graph of the group. It is known that in group theory finite presentability is an invariant under quasiisometry of Cayley graphs.
We choose to associate a metric space to a semigroup based on a Cayley graph of that semigroup. This metric space is constructed by removing directions, multiple edges and loops from the Cayley graph. We call this a skeleton of the semigroup.
We show that finite presentability of certain types of direct products, completely (0)simple, and Clifford semigroups is preserved under isomorphism of skeletons. A major tool employed in this is the ŠvarcMilnor Lemma.
We present an example that shows that in general, finite presentability is not an invariant property under isomorphism of skeletons of semigroups, and in fact is not an invariant property under quasiisometry of Cayley graphs for semigroups.
We give several skeletons and describe fully the semigroups that can be associated to these.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6923
20150626T00:00:00Z
Awang, Jennifer S.
Geometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure.
One such property is finite presentability. In geometric group theory, the geometric structure of choice is the Cayley graph of the group. It is known that in group theory finite presentability is an invariant under quasiisometry of Cayley graphs.
We choose to associate a metric space to a semigroup based on a Cayley graph of that semigroup. This metric space is constructed by removing directions, multiple edges and loops from the Cayley graph. We call this a skeleton of the semigroup.
We show that finite presentability of certain types of direct products, completely (0)simple, and Clifford semigroups is preserved under isomorphism of skeletons. A major tool employed in this is the ŠvarcMilnor Lemma.
We present an example that shows that in general, finite presentability is not an invariant property under isomorphism of skeletons of semigroups, and in fact is not an invariant property under quasiisometry of Cayley graphs for semigroups.
We give several skeletons and describe fully the semigroups that can be associated to these.

Ellipsoidal vortices in rotating stratified fluids : beyond the quasigeostrophic approximation
http://hdl.handle.net/10023/6889
Abstract: We examine the basic properties and stability of isolated vortices having uniform potential vorticity (PV) in a nonhydrostatic rotating stratified fluid, under the Boussinesq approximation. For simplicity, we consider a uniform background rotation and a linear basicstate stratification for which both the Coriolis and buoyancy frequencies, f and N, are constant. Moreover, we take ƒ/N≪1, as typically observed in the Earth’s atmosphere and oceans. In the small Rossby number ‘quasigeostrophic’ (QG) limit, when the flow is weak compared to the background rotation, there exist exact solutions for steadily rotating ellipsoidal volumes of uniform PV in an unbounded flow (Zhmur & Shchepetkin, Izv. Akad. Nauk SSSR Atmos. Ocean. Phys., vol. 27, 1991, pp. 492–503; Meacham, Dyn. Atmos. Oceans, vol. 16, 1992, pp. 189–223). Furthermore, a wide range of these solutions are stable as long as the horizontal and vertical aspect ratios λ and μ do not depart greatly from unity (Dritschel et al.,J. Fluid Mech., vol. 536, 2005, pp. 401–421). In the present study, we examine the behaviour of ellipsoidal vortices at Rossby numbers up to near unity in magnitude. We find that there is a monotonic increase in stability as one varies the Rossby number from nearly −1 (anticyclone) to nearly +1 (cyclone). That is, QG vortices are more stable than anticyclones at finite negative Rossby number, and generally less stable than cyclones at finite positive Rossby number. Ageostrophic effects strengthen both the rotation and the stratification within a cyclone, enhancing its stability. The converse is true for an anticyclone. For all Rossby numbers, stability is reinforced by increasing λ towards unity or decreasing μ. An unstable vortex often restabilises by developing a nearcircular crosssection, typically resulting in a roughly ellipsoidal vortex, but occasionally a binary system is formed. Throughout the nonlinear evolution of a vortex, the emission of inertia–gravity waves (IGWs) is negligible across the entire parameter space investigated. Thus, vortices at small to moderate Rossby numbers, and any associated instabilities, are (ageostrophically) balanced. A manifestation of this balance is that, at finite Rossby number, an anticyclone rotates faster than a cyclone.
Description: Support for this research has come from the UK Engineering and Physical Sciences Research Council (grant number EP/H001794/1). Date of Acceptance: 27/10/2014
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/6889
20150101T00:00:00Z
Tsang, YueKin
Dritschel, David G.
We examine the basic properties and stability of isolated vortices having uniform potential vorticity (PV) in a nonhydrostatic rotating stratified fluid, under the Boussinesq approximation. For simplicity, we consider a uniform background rotation and a linear basicstate stratification for which both the Coriolis and buoyancy frequencies, f and N, are constant. Moreover, we take ƒ/N≪1, as typically observed in the Earth’s atmosphere and oceans. In the small Rossby number ‘quasigeostrophic’ (QG) limit, when the flow is weak compared to the background rotation, there exist exact solutions for steadily rotating ellipsoidal volumes of uniform PV in an unbounded flow (Zhmur & Shchepetkin, Izv. Akad. Nauk SSSR Atmos. Ocean. Phys., vol. 27, 1991, pp. 492–503; Meacham, Dyn. Atmos. Oceans, vol. 16, 1992, pp. 189–223). Furthermore, a wide range of these solutions are stable as long as the horizontal and vertical aspect ratios λ and μ do not depart greatly from unity (Dritschel et al.,J. Fluid Mech., vol. 536, 2005, pp. 401–421). In the present study, we examine the behaviour of ellipsoidal vortices at Rossby numbers up to near unity in magnitude. We find that there is a monotonic increase in stability as one varies the Rossby number from nearly −1 (anticyclone) to nearly +1 (cyclone). That is, QG vortices are more stable than anticyclones at finite negative Rossby number, and generally less stable than cyclones at finite positive Rossby number. Ageostrophic effects strengthen both the rotation and the stratification within a cyclone, enhancing its stability. The converse is true for an anticyclone. For all Rossby numbers, stability is reinforced by increasing λ towards unity or decreasing μ. An unstable vortex often restabilises by developing a nearcircular crosssection, typically resulting in a roughly ellipsoidal vortex, but occasionally a binary system is formed. Throughout the nonlinear evolution of a vortex, the emission of inertia–gravity waves (IGWs) is negligible across the entire parameter space investigated. Thus, vortices at small to moderate Rossby numbers, and any associated instabilities, are (ageostrophically) balanced. A manifestation of this balance is that, at finite Rossby number, an anticyclone rotates faster than a cyclone.

Spatial variation in maximum dive depth in gray seals in relation to foraging.
http://hdl.handle.net/10023/6886
Abstract: Habitat preference maps are a way of representing animals’ space use in two dimensions. For marine animals, the third dimension is an important aspect of spatial ecology. We used dive data from seven gray seals Halichoerus grypus (a primarily benthic forager) collected with GPS phone tags (Sea Mammal Research Unit) to investigate the distribution of the maximum depth visited in each dive. We modeled maximum dive depth as a function of spatiotemporal covariates using a generalized additive mixed model (GAMM) with individual as a random effect. Bathymetry, horizontal displacement, latitude and longitude, Julian day, sediment type, and light conditions accounted for 37% of the variability in the data. Persistent patterns of autocorrelation in the raw data suggest that individual intrinsic rhythm might be an important factor, not captured by external covariates. The strength of using this statistical method to generate spatial predictions of the distribution of maximum dive depth is its applicability to other plunge and pursuit divers. Despite being predictions of a point estimate, these maps provide some insight into the third dimension of habitat use in marine animals. The capacity to predict this aspect of vertical habitat use may help avoid conflict between animal habitat and coastal or offshore developments
Description: Theoni Photopoulou was funded by SMRU Ltd in the form of a Ph.D. studentship, 2008–2012.
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/6886
20140701T00:00:00Z
Photopoulou, Theoni
Fedak, Mike
Thomas, Len
Matthiopoulos, Jason
Habitat preference maps are a way of representing animals’ space use in two dimensions. For marine animals, the third dimension is an important aspect of spatial ecology. We used dive data from seven gray seals Halichoerus grypus (a primarily benthic forager) collected with GPS phone tags (Sea Mammal Research Unit) to investigate the distribution of the maximum depth visited in each dive. We modeled maximum dive depth as a function of spatiotemporal covariates using a generalized additive mixed model (GAMM) with individual as a random effect. Bathymetry, horizontal displacement, latitude and longitude, Julian day, sediment type, and light conditions accounted for 37% of the variability in the data. Persistent patterns of autocorrelation in the raw data suggest that individual intrinsic rhythm might be an important factor, not captured by external covariates. The strength of using this statistical method to generate spatial predictions of the distribution of maximum dive depth is its applicability to other plunge and pursuit divers. Despite being predictions of a point estimate, these maps provide some insight into the third dimension of habitat use in marine animals. The capacity to predict this aspect of vertical habitat use may help avoid conflict between animal habitat and coastal or offshore developments

Estimating population sizes of lions Panthera leo and spotted hyaenas Crocuta crocuta in Uganda’s savannah parks, using lure count methods
http://hdl.handle.net/10023/6885
Abstract: Despite > 60 years of conservation in Uganda’s national parks the populations of lions and spotted hyaenas in these areas have never been estimated using a census method. Estimates for some sites have been extrapolated to other protected areas and educated guesses have been made but there has been nothing more definitive. We used a lure count analysis method of callup counts to estimate populations of the lion Panthera leo and spotted hyaena Crocuta crocuta in the parks where reasonable numbers of these species exist: Queen Elizabeth Protected Area, Murchison Falls Conservation Area and Kidepo Valley National Park. We estimated a total of 408 lions and 324 hyaenas for these three conservation areas. It is unlikely that other conservation areas in Uganda host >10 lions or > 40 hyaenas. The Queen Elizabeth Protected Area had the largest populations of lions and hyaenas: 140 and 211, respectively. It is estimated that lion numbers have declined by 30% in this protected area since the late 1990s and there are increasing concerns for the longterm viability of both species in Uganda.
Description: Funding: United States Agency for International Development
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/6885
20140701T00:00:00Z
Omoya, Edward Okot
Mudumba, Tutilo
Buckland, Stephen T
Mulondo, Paul
Plumptre, Andrew J
Despite > 60 years of conservation in Uganda’s national parks the populations of lions and spotted hyaenas in these areas have never been estimated using a census method. Estimates for some sites have been extrapolated to other protected areas and educated guesses have been made but there has been nothing more definitive. We used a lure count analysis method of callup counts to estimate populations of the lion Panthera leo and spotted hyaena Crocuta crocuta in the parks where reasonable numbers of these species exist: Queen Elizabeth Protected Area, Murchison Falls Conservation Area and Kidepo Valley National Park. We estimated a total of 408 lions and 324 hyaenas for these three conservation areas. It is unlikely that other conservation areas in Uganda host >10 lions or > 40 hyaenas. The Queen Elizabeth Protected Area had the largest populations of lions and hyaenas: 140 and 211, respectively. It is estimated that lion numbers have declined by 30% in this protected area since the late 1990s and there are increasing concerns for the longterm viability of both species in Uganda.

Inflations of geometric grid classes of permutations
http://hdl.handle.net/10023/6862
Abstract: Geometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes. In particular, these are the two main tools in the recent classification of permutation classes of growth rate less than κ ≈ 2.20557 (a specific algebraic integer at which infinite antichains first appear). Using language and ordertheoretic methods, we prove that the substitution closures of geometric grid classes are well partially ordered, finitely based, and that all their subclasses have algebraic generating functions. We go on to show that the inflation of a geometric grid class by a strongly rational class is well partially ordered, and that all its subclasses have rational generating functions. This latter fact allows us to conclude that every permutation class with growth rate less than κ has a rational generating function. This bound is tight as there are permutation classes with growth rate κ which have nonrational generating functions.
Description: All three authors were partially supported by EPSRC via the grant EP/J006440/1.
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/6862
20150201T00:00:00Z
Albert, M.D.
Ruskuc, Nik
Vatter, V.
Geometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes. In particular, these are the two main tools in the recent classification of permutation classes of growth rate less than κ ≈ 2.20557 (a specific algebraic integer at which infinite antichains first appear). Using language and ordertheoretic methods, we prove that the substitution closures of geometric grid classes are well partially ordered, finitely based, and that all their subclasses have algebraic generating functions. We go on to show that the inflation of a geometric grid class by a strongly rational class is well partially ordered, and that all its subclasses have rational generating functions. This latter fact allows us to conclude that every permutation class with growth rate less than κ has a rational generating function. This bound is tight as there are permutation classes with growth rate κ which have nonrational generating functions.

Annual report on the implementation of Council Regulation (EC) No 812/2004 during 2014
http://hdl.handle.net/10023/6855
Mon, 01 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6855
20150601T00:00:00Z
Northridge, Simon
Kingston, Al
Thomas, Len

Subalgebras of FApresentable algebras
http://hdl.handle.net/10023/6852
Abstract: Automatic presentations, also called FApresentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FApresentable algebras. First, an example is given to show that the class of finitely generated FApresentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FApresentable algebra with a single unary operation is itself FApresentable. Furthermore, it is proven that the class of unary FApresentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable.
Sun, 01 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/6852
20140601T00:00:00Z
Cain, A.J.
Ruskuc, Nik
Automatic presentations, also called FApresentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FApresentable algebras. First, an example is given to show that the class of finitely generated FApresentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FApresentable algebra with a single unary operation is itself FApresentable. Furthermore, it is proven that the class of unary FApresentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable.

Excitation and damping of broadband kink waves in the solar corona
http://hdl.handle.net/10023/6839
Abstract: Context. Observations such as those by the Coronal MultiChannel Polarimeter (CoMP) have revealed that broadband kink oscillations are ubiquitous in the solar corona. Aims. We consider footpointdriven kink waves propagating in a low β coronal plasma with a cylindrical density structure. We investigate the excitation and damping of propagating kink waves by a broadband driver, including the effects of different spatial profiles for the driver. Methods. We employ a general spatial damping profile in which the initial stage of the damping envelope is approximated by a Gaussian profile and the asymptotic state by an exponential one. We develop a method of accounting for the presence of these different damping regimes and test it using data from numerical simulations. Results. Strongly damped oscillations in low density coronal loops are more accurately described by a Gaussian spatial damping profile than an exponential profile. The consequences for coronal seismology are investigated and applied to observational data for the ubiquitous broadband waves observed by CoMP. Current data cannot distinguish between the exponential and Gaussian profiles because of the levels of noise. We demonstrate the importance of the spatial profile of the driver on the resulting damping profile. Furthermore, we show that a smallscale turbulent driver is inefficient at exciting propagating kink waves
Description: D.J.P. acknowledges financial support from STFC. I.D.M. acknowledges support of a Royal Society University Research Fellowship. The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/ 2007−2013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/solspanet). Date of Acceptance: 09/04/2015
Mon, 01 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6839
20150601T00:00:00Z
Pascoe, David James
Wright, Andrew Nicholas
De Moortel, Ineke
Hood, Alan William
Context. Observations such as those by the Coronal MultiChannel Polarimeter (CoMP) have revealed that broadband kink oscillations are ubiquitous in the solar corona. Aims. We consider footpointdriven kink waves propagating in a low β coronal plasma with a cylindrical density structure. We investigate the excitation and damping of propagating kink waves by a broadband driver, including the effects of different spatial profiles for the driver. Methods. We employ a general spatial damping profile in which the initial stage of the damping envelope is approximated by a Gaussian profile and the asymptotic state by an exponential one. We develop a method of accounting for the presence of these different damping regimes and test it using data from numerical simulations. Results. Strongly damped oscillations in low density coronal loops are more accurately described by a Gaussian spatial damping profile than an exponential profile. The consequences for coronal seismology are investigated and applied to observational data for the ubiquitous broadband waves observed by CoMP. Current data cannot distinguish between the exponential and Gaussian profiles because of the levels of noise. We demonstrate the importance of the spatial profile of the driver on the resulting damping profile. Furthermore, we show that a smallscale turbulent driver is inefficient at exciting propagating kink waves

Developing and enhancing biodiversity monitoring programmes : a collaborative assessment of priorities
http://hdl.handle.net/10023/6756
Abstract: Biodiversity is changing at unprecedented rates, and it is increasingly important that these changes are quantified through monitoring programmes. Previous recommendations for developing or enhancing these programmes focus either on the end goals, that is the intended use of the data, or on how these goals are achieved, for example through volunteer involvement in citizen science, but not both. These recommendations are rarely prioritized. We used a collaborative approach, involving 52 experts in biodiversity monitoring in the UK, to develop a list of attributes of relevance to any biodiversity monitoring programme and to order these attributes by their priority. We also ranked the attributes according to their importance in monitoring biodiversity in the UK. Experts involved included data users, funders, programme organizers and participants in data collection. They covered expertise in a wide range of taxa. We developed a final list of 25 attributes of biodiversity monitoring schemes, ordered from the most elemental (those essential for monitoring schemes; e.g. articulate the objectives and gain sufficient participants) to the most aspirational (e.g. electronic data capture in the field, reporting change annually). This ordered list is a practical framework which can be used to support the development of monitoring programmes. People's ranking of attributes revealed a difference between those who considered attributes with benefits to end users to be most important (e.g. people from governmental organizations) and those who considered attributes with greatest benefit to participants to be most important (e.g. people involved with volunteer biological recording schemes). This reveals a distinction between focussing on aims and the pragmatism in achieving those aims. Synthesis and applications. The ordered list of attributes developed in this study will assist in prioritizing resources to develop biodiversity monitoring programmes (including citizen science). The potential conflict between end users of data and participants in data collection that we discovered should be addressed by involving the diversity of stakeholders at all stages of programme development. This will maximize the chance of successfully achieving the goals of biodiversity monitoring programmes.
Description: This work was supported by the UK Department for Environment, Food and Rural Affairs (Defra) [grant number WC1014] and the Natural Environment Research Council through National Capability funding to the Centre for Ecology and Hydrology. Date of Acceptance: 05/03/2015
Mon, 01 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6756
20150601T00:00:00Z
Pocock, Michael J. O.
Newson, Stuart E.
Henderson, Ian G.
Peyton, Jodey
Sutherland, William J.
Noble, David G.
Ball, Stuart G.
Beckmann, Björn C.
Biggs, Jeremy
Brereton, Tom
Bullock, David J.
Buckland, Stephen T.
Edwards, Mike
Eaton, Mark A.
Harvey, Martin C.
Hill, Mark O.
Horlock, Martin
Hubble, David S.
Julian, Angela M.
Mackey, Edward C.
Mann, Darren J.
Marshall, Matthew J.
Medlock, Jolyon M.
O'Mahony, Elaine M.
Pacheco, Marina
Porter, Keith
Prentice, Steve
Procter, Deborah A.
Roy, Helen E.
Southway, Sue E.
Shortall, Chris R.
Stewart, Alan J. A.
Wembridge, David E.
Wright, Mark A.
Roy, David B.
Biodiversity is changing at unprecedented rates, and it is increasingly important that these changes are quantified through monitoring programmes. Previous recommendations for developing or enhancing these programmes focus either on the end goals, that is the intended use of the data, or on how these goals are achieved, for example through volunteer involvement in citizen science, but not both. These recommendations are rarely prioritized. We used a collaborative approach, involving 52 experts in biodiversity monitoring in the UK, to develop a list of attributes of relevance to any biodiversity monitoring programme and to order these attributes by their priority. We also ranked the attributes according to their importance in monitoring biodiversity in the UK. Experts involved included data users, funders, programme organizers and participants in data collection. They covered expertise in a wide range of taxa. We developed a final list of 25 attributes of biodiversity monitoring schemes, ordered from the most elemental (those essential for monitoring schemes; e.g. articulate the objectives and gain sufficient participants) to the most aspirational (e.g. electronic data capture in the field, reporting change annually). This ordered list is a practical framework which can be used to support the development of monitoring programmes. People's ranking of attributes revealed a difference between those who considered attributes with benefits to end users to be most important (e.g. people from governmental organizations) and those who considered attributes with greatest benefit to participants to be most important (e.g. people involved with volunteer biological recording schemes). This reveals a distinction between focussing on aims and the pragmatism in achieving those aims. Synthesis and applications. The ordered list of attributes developed in this study will assist in prioritizing resources to develop biodiversity monitoring programmes (including citizen science). The potential conflict between end users of data and participants in data collection that we discovered should be addressed by involving the diversity of stakeholders at all stages of programme development. This will maximize the chance of successfully achieving the goals of biodiversity monitoring programmes.

Bayesian methods for hierarchical distance sampling models
http://hdl.handle.net/10023/6714
Abstract: The few distance sampling studies that use Bayesian methods typically consider only line transect sampling with a halfnormal detection function. We present a Bayesian approach to analyse distance sampling data applicable to line and point transects, exact and interval distance data and any detection function possibly including covariates affecting detection probabilities. We use an integrated likelihood which combines the detection and count models. For the latter, counts are related to covariates in a loglinear mixed effect Poisson model which accommodates correlated counts. We use a MetropolisHastings algorithm for updating parameters and a reversible jump algorithm to include model selection for both the detection function and count models. The approach is applied to a largescale experimental design study of northern bobwhite coveys where the interest was to assess the effect of establishing herbaceous buffers around agricultural fields in several states in the US on bird densities. Results were compared with those from an existing maximum likelihood approach that analyses the detection and count models in two stages. Both methods revealed an increase of covey densities on buffered fields. Our approach gave estimates with higher precision even though it does not condition on a known detection function for the count model.
Description: Cornelia S. Oedekoven was supported by a studentship jointly funded by the University of St Andrews and EPSRC (EPSRC grant EP/C522702/1), through the National Centre for Statistical Ecology.
Sun, 01 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/6714
20140601T00:00:00Z
Oedekoven, Cornelia Sabrina
Buckland, Stephen Terrence
MacKenzie, Monique Lea
King, Ruth
Evans, Kristine
Burger, Wes
The few distance sampling studies that use Bayesian methods typically consider only line transect sampling with a halfnormal detection function. We present a Bayesian approach to analyse distance sampling data applicable to line and point transects, exact and interval distance data and any detection function possibly including covariates affecting detection probabilities. We use an integrated likelihood which combines the detection and count models. For the latter, counts are related to covariates in a loglinear mixed effect Poisson model which accommodates correlated counts. We use a MetropolisHastings algorithm for updating parameters and a reversible jump algorithm to include model selection for both the detection function and count models. The approach is applied to a largescale experimental design study of northern bobwhite coveys where the interest was to assess the effect of establishing herbaceous buffers around agricultural fields in several states in the US on bird densities. Results were compared with those from an existing maximum likelihood approach that analyses the detection and count models in two stages. Both methods revealed an increase of covey densities on buffered fields. Our approach gave estimates with higher precision even though it does not condition on a known detection function for the count model.

On the properties of singleseparator MHS equilibria and the nature of separator reconnection
http://hdl.handle.net/10023/6678
Abstract: This thesis considers the properties of MHS equilibria formed through nonresistive MHD relaxation of analytical nonpotential magnetic field models, which contain two null points connected by a generic separator. Four types of analytical magnetic fields are formulated, with different forms of current. The magnetic field model which has a uniform current directed along the separator, is used through the rest of this thesis to form MHS equilibria and to study reconnection.
This magnetic field, which is not forcefree, embedded in a highbeta plasma, relaxes nonresistively using a 3D MHD code. The relaxation causes the field about the separator to collapse leading to a twisted current layer forming along the separator. The MHS equilibrium current layer slowly becomes stronger, longer, wider and thinner with time. Its properties, and the properties of the plasma, are found to depend on the initial parameters of the magnetic field, which control the geometry of the magnetic configuration.
Such a MHS equilibria is used in a high plasmabeta reconnection experiment. An anomalous resistivity ensures that only the central strong current in the separator current layer is dissipated. The reconnection occurs in two phases characterised by fast and slow reconnection, respectively. Waves, launched from the diffusion site, communicate the loss of force balance at the current layer and set up flows in the system. The energy transport in this system is dominated by Ohmic dissipation.
Several methods are presented which allow a low plasmabeta value to be approached in the singleseparator model. One method is chosen and this model is relaxed nonresistively to form a MHS equilibrium. A twisted current layer grows along the separator, containing stronger current than in the high plasmabeta experiments, and has a local enhancement in pressure inside it. The growth rate of this current layer is similar to that found in the high plasmabeta experiments, however, the current layer becomes thinner and narrower over time.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6678
20150626T00:00:00Z
Stevenson, Julie E. H.
This thesis considers the properties of MHS equilibria formed through nonresistive MHD relaxation of analytical nonpotential magnetic field models, which contain two null points connected by a generic separator. Four types of analytical magnetic fields are formulated, with different forms of current. The magnetic field model which has a uniform current directed along the separator, is used through the rest of this thesis to form MHS equilibria and to study reconnection.
This magnetic field, which is not forcefree, embedded in a highbeta plasma, relaxes nonresistively using a 3D MHD code. The relaxation causes the field about the separator to collapse leading to a twisted current layer forming along the separator. The MHS equilibrium current layer slowly becomes stronger, longer, wider and thinner with time. Its properties, and the properties of the plasma, are found to depend on the initial parameters of the magnetic field, which control the geometry of the magnetic configuration.
Such a MHS equilibria is used in a high plasmabeta reconnection experiment. An anomalous resistivity ensures that only the central strong current in the separator current layer is dissipated. The reconnection occurs in two phases characterised by fast and slow reconnection, respectively. Waves, launched from the diffusion site, communicate the loss of force balance at the current layer and set up flows in the system. The energy transport in this system is dominated by Ohmic dissipation.
Several methods are presented which allow a low plasmabeta value to be approached in the singleseparator model. One method is chosen and this model is relaxed nonresistively to form a MHS equilibrium. A twisted current layer grows along the separator, containing stronger current than in the high plasmabeta experiments, and has a local enhancement in pressure inside it. The growth rate of this current layer is similar to that found in the high plasmabeta experiments, however, the current layer becomes thinner and narrower over time.

Numerical simulations of a flux rope ejection
http://hdl.handle.net/10023/6650
Abstract: Coronal mass ejections (CMEs) are the most violent phenomena observed on the Sun. One of the most successful models to explain CMEs is the flux rope ejection model, where a magnetic flux rope is expelled from the solar corona after a long phase along which the flux rope stays in equilibrium while magnetic energy is being accumulated. However, still many questions are outstanding on the detailed mechanism of the ejection and observations continuously provide new data to interpret and put in the context. Currently, extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. In particular, observations show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. However, these observations are difficult to interpret in terms of basic physical mechanisms and quantities, thus, we need to compare equivalent quantities to test and improve our models. In our work, we intend to bridge the gap between models and observations with our model of flux rope ejection where we consistently describe the full life span of a flux rope from its formation to ejection. This is done by coupling the global nonlinear forcefree model (GNLFFF) built to describe the slow low β formation phase, with a full MHD simulation run with the software MPIAMRVAC, suitable to describe the fast MHD evolution of the flux rope ejection that happens in a heterogeneous β regime. We also explore the parameter space to identify the conditions upon which the ejection is favoured (gravity stratification and magnetic field intensity) and we produce synthesised AIA observations (171 Å and 211 Å). To carry this out, we run 3D MHD simulation in spherical coordinates where we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. Our model of flux rope ejection is successful in realistically describing the entire life span of a flux rope and we also set some conditions for the backgroud solar corona to favour the escape of the flux rope, so that it turns into a CME. Furthermore, our MHD simulation reproduces many of the features found in the AIA observations.
Description: Date of acceptance: 10/01/2015
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/6650
20150301T00:00:00Z
Pagano, P.
Mackay, D.H.
Poedts, S.
Coronal mass ejections (CMEs) are the most violent phenomena observed on the Sun. One of the most successful models to explain CMEs is the flux rope ejection model, where a magnetic flux rope is expelled from the solar corona after a long phase along which the flux rope stays in equilibrium while magnetic energy is being accumulated. However, still many questions are outstanding on the detailed mechanism of the ejection and observations continuously provide new data to interpret and put in the context. Currently, extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. In particular, observations show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. However, these observations are difficult to interpret in terms of basic physical mechanisms and quantities, thus, we need to compare equivalent quantities to test and improve our models. In our work, we intend to bridge the gap between models and observations with our model of flux rope ejection where we consistently describe the full life span of a flux rope from its formation to ejection. This is done by coupling the global nonlinear forcefree model (GNLFFF) built to describe the slow low β formation phase, with a full MHD simulation run with the software MPIAMRVAC, suitable to describe the fast MHD evolution of the flux rope ejection that happens in a heterogeneous β regime. We also explore the parameter space to identify the conditions upon which the ejection is favoured (gravity stratification and magnetic field intensity) and we produce synthesised AIA observations (171 Å and 211 Å). To carry this out, we run 3D MHD simulation in spherical coordinates where we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. Our model of flux rope ejection is successful in realistically describing the entire life span of a flux rope and we also set some conditions for the backgroud solar corona to favour the escape of the flux rope, so that it turns into a CME. Furthermore, our MHD simulation reproduces many of the features found in the AIA observations.

Using accelerometers to determine the calling behavior of tagged baleen whales
http://hdl.handle.net/10023/6623
Abstract: Lowfrequency acoustic signals generated by baleen whales can propagate over vast distances, making the assignment of calls to specific individuals problematic. Here, we report the novel use of acoustic recording tags equipped with highresolution accelerometers to detect vibrations from the surface of two tagged fin whales that directly match the timing of recorded acoustic signals. A tag deployed on a buoy in the vicinity of calling fin whales and a recording from a tag that had just fallen off a whale were able to detect calls acoustically but did not record corresponding accelerometer signals that were measured on calling individuals. Across the hundreds of calls measured on two tagged fin whales, the accelerometer response was generally anisotropic across all three axes, appeared to depend on tag placement and increased with the level of received sound. These data demonstrate that highsample rate accelerometry can provide important insights into the acoustic behavior of baleen whales that communicate at low frequencies. This method helps identify vocalizing whales, which in turn enables the quantification of call rates, a fundamental component of models used to estimate baleen whale abundance and distribution from passive acoustic monitoring.
Tue, 15 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/6623
20140715T00:00:00Z
Goldbogen, Jeremy
De Ruiter, Stacy Lynn
Stimpert, Alison
Calambokidis, John
Friedlaender, Ari
Schorr, Greg
Moretti, David
Tyack, Peter Lloyd
Southall, Brandon
Lowfrequency acoustic signals generated by baleen whales can propagate over vast distances, making the assignment of calls to specific individuals problematic. Here, we report the novel use of acoustic recording tags equipped with highresolution accelerometers to detect vibrations from the surface of two tagged fin whales that directly match the timing of recorded acoustic signals. A tag deployed on a buoy in the vicinity of calling fin whales and a recording from a tag that had just fallen off a whale were able to detect calls acoustically but did not record corresponding accelerometer signals that were measured on calling individuals. Across the hundreds of calls measured on two tagged fin whales, the accelerometer response was generally anisotropic across all three axes, appeared to depend on tag placement and increased with the level of received sound. These data demonstrate that highsample rate accelerometry can provide important insights into the acoustic behavior of baleen whales that communicate at low frequencies. This method helps identify vocalizing whales, which in turn enables the quantification of call rates, a fundamental component of models used to estimate baleen whale abundance and distribution from passive acoustic monitoring.

Cayley automaton semigroups
http://hdl.handle.net/10023/6558
Abstract: Let S be a semigroup, C(S) the automaton constructed from the right Cayley
graph of S with respect to all of S as the generating set and ∑(C(S)) the
automaton semigroup constructed from C(S). Such semigroups are termed
Cayley automaton semigroups. For a given semigroup S we aim to establish
connections between S and ∑(C(S)).
For a finite monogenic semigroup S with a nontrivial cyclic subgroup C[sub]n we
show that ∑(C(S)) is a small extension of a free semigroup of rank n, and
that in the case of a trivial subgroup ∑(C(S)) is finite.
The notion of invariance is considered and we examine those semigroups S
satisfying S ≅ ∑(C(S)). We classify which bands satisfy this, showing that
they are those bands with faithful leftregular representations, but exhibit
examples outwith this classification. In doing so we answer an open problem
of Cain.
Following this, we consider iterations of the construction and show that for
any n there exists a semigroup where we can iterate the construction n times
before reaching a semigroup satisfying S ≅ ∑(C(S)). We also give an example of a semigroup where repeated iteration never produces a semigroup
satisfying S ≅ ∑(C(S)).
Cayley automaton semigroups of infinite semigroups are also considered and
we generalise and extend a result of Silva and Steinberg to cancellative semigroups. We also construct the Cayley automaton semigroup of the bicyclic
monoid, showing in particular that it is not finitely generated.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6558
20150626T00:00:00Z
McLeman, Alexander Lewis Andrew
Let S be a semigroup, C(S) the automaton constructed from the right Cayley
graph of S with respect to all of S as the generating set and ∑(C(S)) the
automaton semigroup constructed from C(S). Such semigroups are termed
Cayley automaton semigroups. For a given semigroup S we aim to establish
connections between S and ∑(C(S)).
For a finite monogenic semigroup S with a nontrivial cyclic subgroup C[sub]n we
show that ∑(C(S)) is a small extension of a free semigroup of rank n, and
that in the case of a trivial subgroup ∑(C(S)) is finite.
The notion of invariance is considered and we examine those semigroups S
satisfying S ≅ ∑(C(S)). We classify which bands satisfy this, showing that
they are those bands with faithful leftregular representations, but exhibit
examples outwith this classification. In doing so we answer an open problem
of Cain.
Following this, we consider iterations of the construction and show that for
any n there exists a semigroup where we can iterate the construction n times
before reaching a semigroup satisfying S ≅ ∑(C(S)). We also give an example of a semigroup where repeated iteration never produces a semigroup
satisfying S ≅ ∑(C(S)).
Cayley automaton semigroups of infinite semigroups are also considered and
we generalise and extend a result of Silva and Steinberg to cancellative semigroups. We also construct the Cayley automaton semigroup of the bicyclic
monoid, showing in particular that it is not finitely generated.

Nested rowcolumn designs for nearfactorial experiments with two treatment factors and one control treatment
http://hdl.handle.net/10023/6556
Abstract: This paper presents some methods of designing experiments in a block design with nested rows and columns. The treatments consist of all combinations of levels of two treatment factors, with an additional control treatment.
Description: The authors also thank Queen Mary, University of London, the University of St Andrews and the Poznan University of Life Sciences for financial support. The second author was also supported by the BritishPolish Young Scientists Programme, grant WAR/342/116. Date of Acceptance: 07/04/2015
Thu, 01 Oct 2015 00:00:00 GMT
http://hdl.handle.net/10023/6556
20151001T00:00:00Z
Bailey, Rosemary Anne
Lacka, Agnieszka
This paper presents some methods of designing experiments in a block design with nested rows and columns. The treatments consist of all combinations of levels of two treatment factors, with an additional control treatment.

3D wholeprominence fine structure modeling
http://hdl.handle.net/10023/6541
Abstract: We present the first 3D wholeprominence fine structure model. The model combines a 3D magnetic field configuration of an entire prominence obtained from nonlinear forcefree field simulations, with a detailed description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Through the use of a novel radiative transfer visualization technique for the Halpha line such plasmaloaded magnetic field model produces synthetic images of the modeled prominence comparable with highresolution observations. This allows us for the first time to use a single technique to consistently study, in both emission on the limb and absorption against the solar disk, the fine structures of prominences/filaments produced by a magnetic field model.
Description: Date of Acceptance: 17/02/2015
Mon, 20 Apr 2015 00:00:00 GMT
http://hdl.handle.net/10023/6541
20150420T00:00:00Z
Gunar, Stanislav
Mackay, Duncan Hendry
We present the first 3D wholeprominence fine structure model. The model combines a 3D magnetic field configuration of an entire prominence obtained from nonlinear forcefree field simulations, with a detailed description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Through the use of a novel radiative transfer visualization technique for the Halpha line such plasmaloaded magnetic field model produces synthetic images of the modeled prominence comparable with highresolution observations. This allows us for the first time to use a single technique to consistently study, in both emission on the limb and absorption against the solar disk, the fine structures of prominences/filaments produced by a magnetic field model.

Carl Friedrich Geiser and Ferdinand Rudio : the men behind the first International Congress of Mathematicians
http://hdl.handle.net/10023/6536
Abstract: The first International Congress of Mathematicians (ICM) was held in Zurich in 1897, setting the standards for all future ICMs. Whilst giving an overview of the congress itself, this thesis focuses on the Swiss organisers, who were predominantly university professors and secondary school teachers. As this thesis aims to offer some insight into their lives, it includes their biographies, highlighting their individual contributions to the congress. Furthermore, it explains why Zurich was chosen as the first host city and how the committee proceeded with the congress organisation.
Two of the main organisers were the Swiss geometers Carl Friedrich Geiser (18431934) and Ferdinand Rudio (18561929). In addition to the congress, they also made valuable contributions to mathematical education, and in Rudio’s case, the history of mathematics. Therefore, this thesis focuses primarily on these two mathematicians.
As for Geiser, the relationship to his greatuncle Jakob Steiner is explained in more detail. Furthermore, his contributions to the administration of the Swiss Federal Institute of Technology are summarised. Due to the overarching theme of mathematical education and collaborations in this thesis, Geiser’s schoolbook "Einleitung in die synthetische Geometrie" is considered in more detail and Geiser’s methods are highlighted.
A selection of Rudio’s contributions to the history of mathematics is studied as well. His book "Archimedes, Huygens, Lambert, Legendre" is analysed and compared to E W Hobson’s treatise "Squaring the Circle". Furthermore, Rudio’s papers relating to the commentary of Simplicius on quadratures by Antiphon and Hippocrates are considered, focusing on Rudio’s translation of the commentary and on "Die Möndchen des Hippokrates". The thesis concludes with an analysis of Rudio’s popular lectures "Leonhard Euler" and "Über den Antheil der mathematischen Wissenschaften an der Kultur der Renaissance", which are prime examples of his approach to the history of mathematics.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6536
20150626T00:00:00Z
Eminger, Stefanie Ursula
The first International Congress of Mathematicians (ICM) was held in Zurich in 1897, setting the standards for all future ICMs. Whilst giving an overview of the congress itself, this thesis focuses on the Swiss organisers, who were predominantly university professors and secondary school teachers. As this thesis aims to offer some insight into their lives, it includes their biographies, highlighting their individual contributions to the congress. Furthermore, it explains why Zurich was chosen as the first host city and how the committee proceeded with the congress organisation.
Two of the main organisers were the Swiss geometers Carl Friedrich Geiser (18431934) and Ferdinand Rudio (18561929). In addition to the congress, they also made valuable contributions to mathematical education, and in Rudio’s case, the history of mathematics. Therefore, this thesis focuses primarily on these two mathematicians.
As for Geiser, the relationship to his greatuncle Jakob Steiner is explained in more detail. Furthermore, his contributions to the administration of the Swiss Federal Institute of Technology are summarised. Due to the overarching theme of mathematical education and collaborations in this thesis, Geiser’s schoolbook "Einleitung in die synthetische Geometrie" is considered in more detail and Geiser’s methods are highlighted.
A selection of Rudio’s contributions to the history of mathematics is studied as well. His book "Archimedes, Huygens, Lambert, Legendre" is analysed and compared to E W Hobson’s treatise "Squaring the Circle". Furthermore, Rudio’s papers relating to the commentary of Simplicius on quadratures by Antiphon and Hippocrates are considered, focusing on Rudio’s translation of the commentary and on "Die Möndchen des Hippokrates". The thesis concludes with an analysis of Rudio’s popular lectures "Leonhard Euler" and "Über den Antheil der mathematischen Wissenschaften an der Kultur der Renaissance", which are prime examples of his approach to the history of mathematics.

Experiments on the structure and stability of mode2 internal solitarylike waves propagating on an offset pycnocline
http://hdl.handle.net/10023/6519
Abstract: The structure and stability of mode2 internal solitarylike waves is investigated experimentally. A rankordered train of mode2 internal solitary waves is generated using a lock release configuration. The pycnocline is centred either on the middepth of the water column (the 0% offset case) or it is offset in the positive vertical direction by a fraction of 5%, 10% or 20% of the total fluid depth. It is found that offsetting the pycnocline has little effect on the basic wave properties (e.g wave speed, wave amplitude and wave length) but it does significantly affect wave stability. Instability takes the form of small KHlike billows in the rear of the wave and small scale overturning in the core of the wave. In the 0% offset case, instability occurs on both the upper and lower interfaces of the pycnocline and is similar in extent and vigour over the two interfaces. As the offset percentage is increased, however, instability is more pronounced on the lower interface with little or no evidence of instability being observed on the upper interface. In the 20% offset case a mode1 tail is associated with the wave and the wave characteristics resemble qualitatively the recent field observations of Shroyer et al [E. L. Shroyer, J. N. Moum and J. D. Nash, J. Geophys. Res. 115, C07001 (2010)].
Description: Date of Acceptance: 23/03/2015
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/6519
20150101T00:00:00Z
Carr, Magda
Davies, Peter
Hoebers, Ruud
The structure and stability of mode2 internal solitarylike waves is investigated experimentally. A rankordered train of mode2 internal solitary waves is generated using a lock release configuration. The pycnocline is centred either on the middepth of the water column (the 0% offset case) or it is offset in the positive vertical direction by a fraction of 5%, 10% or 20% of the total fluid depth. It is found that offsetting the pycnocline has little effect on the basic wave properties (e.g wave speed, wave amplitude and wave length) but it does significantly affect wave stability. Instability takes the form of small KHlike billows in the rear of the wave and small scale overturning in the core of the wave. In the 0% offset case, instability occurs on both the upper and lower interfaces of the pycnocline and is similar in extent and vigour over the two interfaces. As the offset percentage is increased, however, instability is more pronounced on the lower interface with little or no evidence of instability being observed on the upper interface. In the 20% offset case a mode1 tail is associated with the wave and the wave characteristics resemble qualitatively the recent field observations of Shroyer et al [E. L. Shroyer, J. N. Moum and J. D. Nash, J. Geophys. Res. 115, C07001 (2010)].

The effect of animal movement on line transect estimates of abundance
http://hdl.handle.net/10023/6466
Abstract: Line transect sampling is a distance sampling method for estimating the abundance of wild animal populations. One key assumption of this method is that all animals are detected at their initial location. Animal movement independent of the transect and observer can thus cause substantial bias. We present an analytic expression for this bias when detection within the transect is certain (strip transect sampling) and use simulation to quantify bias when detection falls off with distance from the line (line transect sampling). We also explore the nonlinear relationship between bias, detection, and animal movement by varying detectability and movement type. We consider animals that move in randomly orientated straight lines, which provides an upper bound on bias, and animals that are constrained to a home range of random radius. We find that bias is reduced when animal movement is constrained, and bias is considerably smaller in line transect sampling than strip transect sampling provided that mean animal speed is less than observer speed. By contrast, when mean animal speed exceeds observer speed the bias in line transect sampling becomes comparable with, and may exceed, that of strip transect sampling. Bias from independent animal movement is reduced by the observer searching further perpendicular to the transect, searching a shorter distance ahead and by ignoring animals that may overtake the observer from behind. However, when animals move in response to the observer, the standard practice of searching further ahead should continue as the bias from responsive movement is often greater than that from independent movement.
Description: This work was supported by the University of St Andrews (http://www.standrews.ac.uk/; RG, STB, LT) and by a summer scholarship and PhD grant from The Carnegie Trust for the Universities of Scotland (http://www.carnegietrust.org/) to RG. Date of Acceptance: 10/02/2015
Mon, 23 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/6466
20150323T00:00:00Z
Glennie, R.
Buckland, S.T.
Thomas, L.
Line transect sampling is a distance sampling method for estimating the abundance of wild animal populations. One key assumption of this method is that all animals are detected at their initial location. Animal movement independent of the transect and observer can thus cause substantial bias. We present an analytic expression for this bias when detection within the transect is certain (strip transect sampling) and use simulation to quantify bias when detection falls off with distance from the line (line transect sampling). We also explore the nonlinear relationship between bias, detection, and animal movement by varying detectability and movement type. We consider animals that move in randomly orientated straight lines, which provides an upper bound on bias, and animals that are constrained to a home range of random radius. We find that bias is reduced when animal movement is constrained, and bias is considerably smaller in line transect sampling than strip transect sampling provided that mean animal speed is less than observer speed. By contrast, when mean animal speed exceeds observer speed the bias in line transect sampling becomes comparable with, and may exceed, that of strip transect sampling. Bias from independent animal movement is reduced by the observer searching further perpendicular to the transect, searching a shorter distance ahead and by ignoring animals that may overtake the observer from behind. However, when animals move in response to the observer, the standard practice of searching further ahead should continue as the bias from responsive movement is often greater than that from independent movement.

Mixture models for distance sampling detection functions
http://hdl.handle.net/10023/6463
Abstract: We present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the halfnormal. The models share many of the features of the widelyused “key function plus series adjustment” (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow incorporation of covariates in addition to distance and can be fitted using maximum likelihood. One important advantage over the K+A approach is that the mixtures are automatically monotonic nonincreasing and nonnegative, so constrained optimization is not required to ensure distance sampling assumptions are honoured. We compare the mixture formulation to the K+A approach using simulations to evaluate its applicability in a wide set of challenging situations. We also reanalyze four previously problematic realworld case studies. We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes. We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.
Description: Funding: EPSRC DTG Date of Acceptance: 15/01/2015
Fri, 20 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/6463
20150320T00:00:00Z
Miller, David Lawrence
Thomas, Len
We present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the halfnormal. The models share many of the features of the widelyused “key function plus series adjustment” (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow incorporation of covariates in addition to distance and can be fitted using maximum likelihood. One important advantage over the K+A approach is that the mixtures are automatically monotonic nonincreasing and nonnegative, so constrained optimization is not required to ensure distance sampling assumptions are honoured. We compare the mixture formulation to the K+A approach using simulations to evaluate its applicability in a wide set of challenging situations. We also reanalyze four previously problematic realworld case studies. We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes. We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.

Most switching classes with primitive automorphism groups contain graphs with trivial groups
http://hdl.handle.net/10023/6429
Abstract: The operation of switching a graph Gamma with respect to a subset X of the vertex set interchanges edges and nonedges between X and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set of graphs on a given vertex set, so we can talk about the automorphism group of a switching class of graphs. It might be thought that switching classes with many automorphisms would have the property that all their graphs also have many automorphisms. But the main theorem of this paper shows a different picture: with finitely many exceptions, if a nontrivial switching class S has primitive automorphism group, then it contains a graph whose automorphism group is trivial. We also find all the exceptional switching classes; up to complementation, there are just six.
Description: Date of Acceptance: 20/02/2015
Mon, 01 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6429
20150601T00:00:00Z
Cameron, Peter Jephson
Spiga, Pablo
The operation of switching a graph Gamma with respect to a subset X of the vertex set interchanges edges and nonedges between X and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set of graphs on a given vertex set, so we can talk about the automorphism group of a switching class of graphs. It might be thought that switching classes with many automorphisms would have the property that all their graphs also have many automorphisms. But the main theorem of this paper shows a different picture: with finitely many exceptions, if a nontrivial switching class S has primitive automorphism group, then it contains a graph whose automorphism group is trivial. We also find all the exceptional switching classes; up to complementation, there are just six.

Random coeffcient models for complex longitudinal data
http://hdl.handle.net/10023/6386
Abstract: Longitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data.
Biased inference can occur in linear mixedeffects modelling if subjects are drawn from a number of unknown subpopulations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a twostep approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially nonmonotonic variance and correlation functions.
Spatially explicit capturerecapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multioccasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radiotagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animallevel covariates.
Fri, 27 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/6386
20140627T00:00:00Z
Kidney, Darren
Longitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data.
Biased inference can occur in linear mixedeffects modelling if subjects are drawn from a number of unknown subpopulations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a twostep approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially nonmonotonic variance and correlation functions.
Spatially explicit capturerecapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multioccasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radiotagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animallevel covariates.

MHD simulations of coronal heating
http://hdl.handle.net/10023/6373
Abstract: The problem of heating the solar corona requires the conversion of magnetic energy into thermal energy. Presently, there are two promising mechanisms for heating the solar corona: wave heating and nanoflare heating. In this thesis, we consider nanoflare heating only. Previous modelling has shown that the kink instability can trigger energy release and heating in large scale loops, as the field rapidly relaxes to a lower energy state under the Taylor relaxation theory. Two distinct experiments were developed to understand the coronal heating problem: the avalanche effect within a multiple loop system, and the importance of thermal conduction and optically thin radiation during the evolution of the kinkedunstable coronal magnetic field.
The first experiment showed that a kinkunstable thread can also destabilise nearby threads under some conditions. The second experiment showed that the inclusion of thermal conduction and optically thin radiation causes significant change to the internal energy of the coronal loop. After the initial instability occurs, there is continual heating throughout the relaxation process. Our simulation results show that the data is consistent with observation values, and the relaxation process can take over 200 seconds to reach the final relaxed state. The inclusion of both effects perhaps provides a more realistic and rapid heating experiment compared to previous investigations.
Mon, 01 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/6373
20141201T00:00:00Z
Tam, Kuan V.
The problem of heating the solar corona requires the conversion of magnetic energy into thermal energy. Presently, there are two promising mechanisms for heating the solar corona: wave heating and nanoflare heating. In this thesis, we consider nanoflare heating only. Previous modelling has shown that the kink instability can trigger energy release and heating in large scale loops, as the field rapidly relaxes to a lower energy state under the Taylor relaxation theory. Two distinct experiments were developed to understand the coronal heating problem: the avalanche effect within a multiple loop system, and the importance of thermal conduction and optically thin radiation during the evolution of the kinkedunstable coronal magnetic field.
The first experiment showed that a kinkunstable thread can also destabilise nearby threads under some conditions. The second experiment showed that the inclusion of thermal conduction and optically thin radiation causes significant change to the internal energy of the coronal loop. After the initial instability occurs, there is continual heating throughout the relaxation process. Our simulation results show that the data is consistent with observation values, and the relaxation process can take over 200 seconds to reach the final relaxed state. The inclusion of both effects perhaps provides a more realistic and rapid heating experiment compared to previous investigations.

Peter Guthrie Tait : new insights into aspects of his life and work : and associated topics in the history of mathematics
http://hdl.handle.net/10023/6330
Abstract: In this thesis I present new insights into aspects of Peter Guthrie Tait’s life and work, derived principally from largelyunexplored primary source material: Tait’s scrapbook, the Tait–Maxwell schoolbook and Tait’s pocket notebook. By way of associated historical insights, I also come to discuss the innovative and farreaching mathematics of the elusive Frenchman, C.V. Mourey.
P. G. Tait (1831–1901) F.R.S.E., Professor of Mathematics at the Queen’s College, Belfast (1854–1860) and of Natural Philosophy at the University of Edinburgh (1860–1901), was one of the leading physicists and mathematicians in Europe in the nineteenth century. His expertise encompassed the breadth of physical science and mathematics. However, since the nineteenth century he has been unfortunately overlooked—overshadowed, perhaps, by the brilliance of his personal friends, James Clerk Maxwell (1831–1879), Sir William Rowan Hamilton (1805–1865) and William Thomson (1824–1907), later Lord Kelvin.
Here I present the results of extensive research into the Tait family history. I explore the spiritual aspect of Tait’s life in connection with The Unseen Universe (1875) which Tait coauthored with Balfour Stewart (1828–1887). I also reveal Tait’s surprising involvement in statistics and give an account of his introduction to complex numbers, as a schoolboy at the Edinburgh Academy. A highlight of the thesis is a reevaluation of C.V. Mourey’s 1828 work, La Vraie Théorie des quantités négatives et des quantités prétendues imaginaires, which I consider from the perspective of algebraic reform. The thesis also contains: (i) a transcription of an unpublished paper by Hamilton on the fundamental theorem of algebra which was inspired by Mourey and (ii) new biographical information on Mourey.
Fri, 26 Jun 2015 00:00:00 GMT
http://hdl.handle.net/10023/6330
20150626T00:00:00Z
Lewis, Elizabeth Faith
In this thesis I present new insights into aspects of Peter Guthrie Tait’s life and work, derived principally from largelyunexplored primary source material: Tait’s scrapbook, the Tait–Maxwell schoolbook and Tait’s pocket notebook. By way of associated historical insights, I also come to discuss the innovative and farreaching mathematics of the elusive Frenchman, C.V. Mourey.
P. G. Tait (1831–1901) F.R.S.E., Professor of Mathematics at the Queen’s College, Belfast (1854–1860) and of Natural Philosophy at the University of Edinburgh (1860–1901), was one of the leading physicists and mathematicians in Europe in the nineteenth century. His expertise encompassed the breadth of physical science and mathematics. However, since the nineteenth century he has been unfortunately overlooked—overshadowed, perhaps, by the brilliance of his personal friends, James Clerk Maxwell (1831–1879), Sir William Rowan Hamilton (1805–1865) and William Thomson (1824–1907), later Lord Kelvin.
Here I present the results of extensive research into the Tait family history. I explore the spiritual aspect of Tait’s life in connection with The Unseen Universe (1875) which Tait coauthored with Balfour Stewart (1828–1887). I also reveal Tait’s surprising involvement in statistics and give an account of his introduction to complex numbers, as a schoolboy at the Edinburgh Academy. A highlight of the thesis is a reevaluation of C.V. Mourey’s 1828 work, La Vraie Théorie des quantités négatives et des quantités prétendues imaginaires, which I consider from the perspective of algebraic reform. The thesis also contains: (i) a transcription of an unpublished paper by Hamilton on the fundamental theorem of algebra which was inspired by Mourey and (ii) new biographical information on Mourey.

On residual finiteness of monoids, their Schützenberger groups and associated actions
http://hdl.handle.net/10023/6310
Abstract: In this paper we discuss connections between the following properties: (RFM) residual finiteness of a monoid M ; (RFSG) residual finiteness of Schützenberger groups of M ; and (RFRL) residual finiteness of the natural actions of M on its Green's R and Lclasses. The general question is whether (RFM) implies (RFSG) and/or (RFRL), and vice versa. We consider these questions in all the possible combinations of the following situations: M is an arbitrary monoid; M is an arbitrary regular monoid; every Jclass of M has finitely many R and Lclasses; M has finitely many left and right ideals. In each case we obtain complete answers, which are summarised in a table.
Description: RG was supported by an EPSRC Postdoctoral Fellowship EP/E043194/1 held at the University of St Andrews, Scotland.
Sun, 01 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/6310
20140601T00:00:00Z
Gray, R
Ruskuc, Nik
In this paper we discuss connections between the following properties: (RFM) residual finiteness of a monoid M ; (RFSG) residual finiteness of Schützenberger groups of M ; and (RFRL) residual finiteness of the natural actions of M on its Green's R and Lclasses. The general question is whether (RFM) implies (RFSG) and/or (RFRL), and vice versa. We consider these questions in all the possible combinations of the following situations: M is an arbitrary monoid; M is an arbitrary regular monoid; every Jclass of M has finitely many R and Lclasses; M has finitely many left and right ideals. In each case we obtain complete answers, which are summarised in a table.

The motion of point vortices on closed surfaces
http://hdl.handle.net/10023/6297
Abstract: We develop a mathematical framework for the dynamics of a set of point vortices on a class of differentiable surfaces conformal to the unit sphere. When the sum of the vortex circulations is nonzero, a compensating uniform vorticity field is required to satisfy the Gauss condition (that the integral of the LaplaceBeltrami operator must vanish). On variable Gaussian curvature surfaces, this results in selfinduced vortex motion, a feature entirely absent on the plane, the sphere or the hyperboloid.We derive explicit equations of motion for vortices on surfaces of revolution and compute their solutions for a variety of surfaces. We also apply these equations to study the linear stability of a ring of vortices on any surface of revolution. On an ellipsoid of revolution, as few as 2 vortices can be unstable on oblate surfaces or sufficiently prolate ones. This extends known results for the plane, where 7 vortices are marginally unstable [1,2], and the sphere, where 4 vortices may be unstable if sufficiently close to the equator [3].
Description: Date of Acceptance: 29/01/2015
Wed, 25 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/6297
20150225T00:00:00Z
Dritschel, David Gerard
Boatto, S
We develop a mathematical framework for the dynamics of a set of point vortices on a class of differentiable surfaces conformal to the unit sphere. When the sum of the vortex circulations is nonzero, a compensating uniform vorticity field is required to satisfy the Gauss condition (that the integral of the LaplaceBeltrami operator must vanish). On variable Gaussian curvature surfaces, this results in selfinduced vortex motion, a feature entirely absent on the plane, the sphere or the hyperboloid.We derive explicit equations of motion for vortices on surfaces of revolution and compute their solutions for a variety of surfaces. We also apply these equations to study the linear stability of a ring of vortices on any surface of revolution. On an ellipsoid of revolution, as few as 2 vortices can be unstable on oblate surfaces or sufficiently prolate ones. This extends known results for the plane, where 7 vortices are marginally unstable [1,2], and the sphere, where 4 vortices may be unstable if sufficiently close to the equator [3].

Understanding the Mg II and Hα spectra in a highly dynamical solar prominence
http://hdl.handle.net/10023/6190
Abstract: Mg ii h and k and Hα spectra in a dynamical prominence have been obtained along the slit of the Interface Region Imaging Spectrograph (IRIS) and with the Meudon Multichannel Subtractive Double Pass spectrograph on 2013 September 24, respectively. Single Mg ii line profiles are not much reversed, while at some positions along the IRIS slit the profiles show several discrete peaks that are Dopplershifted. The intensity of these peaks is generally decreasing with their increasing Doppler shift. We interpret this unusual behavior as being due to the Doppler dimming effect. We discuss the possibility to interpret the unreversed single profiles by using a twodimensional (2D) model of the entire prominence body with specific radiative boundary conditions. We have performed new 2D isothermal–isobaric modeling of both Hα and Mg ii lines and show the ability of such models to account for the line profile variations as observed. However, the Mg ii linecenter intensities require the model with a temperature increase toward the prominence boundary. We show that even simple onedimensional (1D) models with a prominencetocorona transition region (PCTR) fit the observed Mg ii and Hα lines quite well, while the isothermal–isobaric models (1D or 2D) are inconsistent with simultaneous observations in the Mg ii h and k and Hα lines, meaning that the Hα line provides a strong additional constraint on the modeling. IRIS farUV detection of the C ii lines in this prominence seems to provide a direct constraint on the PCTR part of the model.
Description: Date of Acceptance: 08/01/2015
Tue, 10 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/6190
20150210T00:00:00Z
Heinzel, P.
Schmieder, B.
Mein, N.
Gunar, S.
Mg ii h and k and Hα spectra in a dynamical prominence have been obtained along the slit of the Interface Region Imaging Spectrograph (IRIS) and with the Meudon Multichannel Subtractive Double Pass spectrograph on 2013 September 24, respectively. Single Mg ii line profiles are not much reversed, while at some positions along the IRIS slit the profiles show several discrete peaks that are Dopplershifted. The intensity of these peaks is generally decreasing with their increasing Doppler shift. We interpret this unusual behavior as being due to the Doppler dimming effect. We discuss the possibility to interpret the unreversed single profiles by using a twodimensional (2D) model of the entire prominence body with specific radiative boundary conditions. We have performed new 2D isothermal–isobaric modeling of both Hα and Mg ii lines and show the ability of such models to account for the line profile variations as observed. However, the Mg ii linecenter intensities require the model with a temperature increase toward the prominence boundary. We show that even simple onedimensional (1D) models with a prominencetocorona transition region (PCTR) fit the observed Mg ii and Hα lines quite well, while the isothermal–isobaric models (1D or 2D) are inconsistent with simultaneous observations in the Mg ii h and k and Hα lines, meaning that the Hα line provides a strong additional constraint on the modeling. IRIS farUV detection of the C ii lines in this prominence seems to provide a direct constraint on the PCTR part of the model.

Simplyconnected vortexpatch shallowwater quasiequilibria
http://hdl.handle.net/10023/6179
Abstract: We examine the form, properties, stability and evolution of simplyconnected vortexpatch relative quasiequilibria in the singlelayer ƒplane shallowwater model of geophysical fluid dynamics. We examine the effects of the size, shape and strength of vortices in this system, represented by three distinct parameters completely describing the families of the quasiequilibria. Namely, these are the ratio γ=L/LD between the horizontal size of the vortices and the Rossby deformation length; the aspect ratio λ between the minor to major axes of the vortex; and a potential vorticity (PV)based Rossby number Ro=q′/ƒ, the ratio of the PV anomaly q′ within the vortex to the Coriolis frequency ƒ. By defining an appropriate steadiness parameter, we find that the quasiequilibria remain steady for long times, enabling us to determine the boundary of stability λc=λc(γ, Ro), for 0.25≤γ≤6 and Ro≤1. By calling two states which share γ,Ro and λ ‘equivalent’, we find a clear asymmetry in the stability of cyclonic (Ro>0) and anticyclonic (Ro<0) equilibria, with cyclones being able to sustain greater deformations than anticyclones before experiencing an instability. We find that ageostrophic motions stabilise cyclones and destabilise anticyclones. Both types of vortices undergo the same main types of unstable evolution, albeit in different ranges of the parameter space, (a) vacillations for largeγ, largeRo states, (b) filamentation for smallγ states and (c) vortex splitting, asymmetric for intermediateγ and symmetric for largeγ states.
Description: This work is supported by a UK Natural Environment Research Council studentship
Wed, 05 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/6179
20140305T00:00:00Z
Plotka, Hanna
Dritschel, David Gerard
We examine the form, properties, stability and evolution of simplyconnected vortexpatch relative quasiequilibria in the singlelayer ƒplane shallowwater model of geophysical fluid dynamics. We examine the effects of the size, shape and strength of vortices in this system, represented by three distinct parameters completely describing the families of the quasiequilibria. Namely, these are the ratio γ=L/LD between the horizontal size of the vortices and the Rossby deformation length; the aspect ratio λ between the minor to major axes of the vortex; and a potential vorticity (PV)based Rossby number Ro=q′/ƒ, the ratio of the PV anomaly q′ within the vortex to the Coriolis frequency ƒ. By defining an appropriate steadiness parameter, we find that the quasiequilibria remain steady for long times, enabling us to determine the boundary of stability λc=λc(γ, Ro), for 0.25≤γ≤6 and Ro≤1. By calling two states which share γ,Ro and λ ‘equivalent’, we find a clear asymmetry in the stability of cyclonic (Ro>0) and anticyclonic (Ro<0) equilibria, with cyclones being able to sustain greater deformations than anticyclones before experiencing an instability. We find that ageostrophic motions stabilise cyclones and destabilise anticyclones. Both types of vortices undergo the same main types of unstable evolution, albeit in different ranges of the parameter space, (a) vacillations for largeγ, largeRo states, (b) filamentation for smallγ states and (c) vortex splitting, asymmetric for intermediateγ and symmetric for largeγ states.

Bayesian hierarchical modelling of continuous nonnegative longitudinal data with a spike at zero : an application to a study of birds visiting gardens in winter
http://hdl.handle.net/10023/6164
Abstract: The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zeroinflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about meanvariance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase.
Description: Date of Acceptance: 14/01/2015
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/6164
20150101T00:00:00Z
Swallow, Benjamin Thomas
Buckland, Stephen Terrence
King, Ruth
Toms, Mike
The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zeroinflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about meanvariance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase.

Statistical ecology comes of age
http://hdl.handle.net/10023/6128
Abstract: The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1 –4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.
Description: Date of Acceptance: 04/12/2015
Wed, 24 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/6128
20141224T00:00:00Z
Gimenez, Olivier
Buckland, Stephen Terrence
Morgan, Byron J. T.
Bez, Nicolas
Bertrand, Sophie
Choquet, Remi
Dray, Stephane
Etienne, MariePierre
Fewster, Rachel
Gosselin, Frederic
Merigot, Bastien
Monestiez, Pascal
Morales, Juan M.
Mortier, Frederic
Munoz, Francois
Ovaskainen, Otso
Pavoine, Sandrine
Pradel, Roger
Schurr, Frank M.
Thomas, Len
Thuiller, Wilfried
Trenkel, Verena
de Valpine, Perry
Rexstad, Eric
The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1 –4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.

The formation and stability of Petschek reconnection
http://hdl.handle.net/10023/6100
Abstract: A combined analytical and numerical study of magnetic reconnection in twodimensional resistive magnetohydrodynamics is carried out by using different explicit spatial variations of the resistivity. A special emphasis on the existence of stable/unstable Petschek's solutions is taken, comparing with the recent analytical model given by Forbes et al. [Phys. Plasmas 20, 052902 (2013)]. Our results show good quantitative agreement between the analytical theory and the numerical solutions for a Petschektype solution to within an accuracy of about 10% or better. Our simulations also show that if the resistivity profile is relatively flat near the Xpoint, one of two possible asymmetric solutions will occur. Which solution occurs depends on small random perturbations of the initial conditions. The existence of two possible asymmetric solutions, in a system which is otherwise symmetric, constitutes an example of spontaneous symmetry breaking.
Description: E. R. Priest is grateful to the Leverhulme Trust. T. G. Forbes received support from NASA grant NNX10AC04G to the University of New Hampshire. H. Baty acknowledges support by French National Research Agency (ANR) through Grant ANR13JS05000301 (Project EMPERE). Date of Acceptance: 19/11/2014
Sat, 01 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/6100
20141101T00:00:00Z
Baty, H.
Forbes, T.G.
Priest, E.R.
A combined analytical and numerical study of magnetic reconnection in twodimensional resistive magnetohydrodynamics is carried out by using different explicit spatial variations of the resistivity. A special emphasis on the existence of stable/unstable Petschek's solutions is taken, comparing with the recent analytical model given by Forbes et al. [Phys. Plasmas 20, 052902 (2013)]. Our results show good quantitative agreement between the analytical theory and the numerical solutions for a Petschektype solution to within an accuracy of about 10% or better. Our simulations also show that if the resistivity profile is relatively flat near the Xpoint, one of two possible asymmetric solutions will occur. Which solution occurs depends on small random perturbations of the initial conditions. The existence of two possible asymmetric solutions, in a system which is otherwise symmetric, constitutes an example of spontaneous symmetry breaking.

Helical blowout jets in the sun : untwisting and propagation of waves
http://hdl.handle.net/10023/6097
Abstract: We report on a numerical experiment of the recurrent onset of helical "blowout" jets in an emerging flux region. We find that these jets are running with velocities of ∼100250 km s1 and they transfer a vast amount of heavy plasma into the outer solar atmosphere. During their emission, they undergo an untwisting motion as a result of reconnection between the twisted emerging and the nontwisted preexisting magnetic field in the solar atmosphere. For the first time in the context of blowout jets, we provide direct evidence that their untwisting motion is associated with the propagation of torsional Alfvén waves in the corona.
Description: Date of Acceptance: 01/12/2014
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/6097
20150101T00:00:00Z
Lee, E.J.
Archontis, V.
Hood, A.W.
We report on a numerical experiment of the recurrent onset of helical "blowout" jets in an emerging flux region. We find that these jets are running with velocities of ∼100250 km s1 and they transfer a vast amount of heavy plasma into the outer solar atmosphere. During their emission, they undergo an untwisting motion as a result of reconnection between the twisted emerging and the nontwisted preexisting magnetic field in the solar atmosphere. For the first time in the context of blowout jets, we provide direct evidence that their untwisting motion is associated with the propagation of torsional Alfvén waves in the corona.

Interannual and seasonal trends in cetacean distribution, density and abundance off southern California
http://hdl.handle.net/10023/6088
Abstract: Trends in cetacean density and distribution off southern California were assessed through visual linetransect surveys during thirtyseven California Cooperative Oceanic Fisheries Investigations (CalCOFI) cruises from July 2004–November 2013. From sightings of the six most commonly encountered cetacean species, seasonal, annual and overall density estimates were calculated. Blue whales (Balaenoptera musculus), fin whales (Balaenoptera physalus) and humpback whales (Megaptera novaeangliae) were the most frequently sighted baleen whales with overall densities of 0.91/1000 km2 (CV=0.27), 2.73/1000 km2 (CV=0.19), and 1.17/1000 km2 (CV=0.21) respectively. Species specific density estimates, stratified by cruise, were analyzed using a generalized additive model to estimate longterm trends and correct for seasonal imbalances. Variances were estimated using a nonparametric bootstrap with one day of effort as the sampling unit. Blue whales were primarily observed during summer and fall while fin and humpback whales were observed yearround with peaks in density during summer and spring respectively. Shortbeaked common dolphins (Delphinus delphis), Pacific whitesided dolphins (Lagenorhynchus obliquidens) and Dall’s porpoise (Phocoenoidesdalli) were the most frequently encountered small cetaceans with overall densities of 705.83/1000 km2 (CV=0.22), 51.98/1000 km2 (CV=0.27), and 21.37/1000 km2 (CV=0.19) respectively. Seasonally, shortbeaked common dolphins were most abundant in winter whereas Pacific whitesided dolphins and Dall’s porpoise were most abundant during spring. There were no significant longterm changes in blue whale, fin whale, humpback whale, shortbeaked common dolphin or Dall’s porpoise densities while Pacific whitesided dolphins exhibited a significant decrease in density across the tenyear study. The results from this study were fundamentally consistent with earlier studies, but provide greater temporal and seasonal resolution
Description: Funding was provided by the Chief of Naval Operations Environmental Readiness Division, the United States Navy’s Pacific Fleet, the Naval Postgraduate School Grant #N00244111027, and the Naval Facilities Engineering Command Living Marine Resources Program.
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/6088
20150201T00:00:00Z
Campbell, G.S.
Thomas, L.
Whitaker, K.
Douglas, A.B.
Calambokidis, J.
Hildebrand, J.A.
Trends in cetacean density and distribution off southern California were assessed through visual linetransect surveys during thirtyseven California Cooperative Oceanic Fisheries Investigations (CalCOFI) cruises from July 2004–November 2013. From sightings of the six most commonly encountered cetacean species, seasonal, annual and overall density estimates were calculated. Blue whales (Balaenoptera musculus), fin whales (Balaenoptera physalus) and humpback whales (Megaptera novaeangliae) were the most frequently sighted baleen whales with overall densities of 0.91/1000 km2 (CV=0.27), 2.73/1000 km2 (CV=0.19), and 1.17/1000 km2 (CV=0.21) respectively. Species specific density estimates, stratified by cruise, were analyzed using a generalized additive model to estimate longterm trends and correct for seasonal imbalances. Variances were estimated using a nonparametric bootstrap with one day of effort as the sampling unit. Blue whales were primarily observed during summer and fall while fin and humpback whales were observed yearround with peaks in density during summer and spring respectively. Shortbeaked common dolphins (Delphinus delphis), Pacific whitesided dolphins (Lagenorhynchus obliquidens) and Dall’s porpoise (Phocoenoidesdalli) were the most frequently encountered small cetaceans with overall densities of 705.83/1000 km2 (CV=0.22), 51.98/1000 km2 (CV=0.27), and 21.37/1000 km2 (CV=0.19) respectively. Seasonally, shortbeaked common dolphins were most abundant in winter whereas Pacific whitesided dolphins and Dall’s porpoise were most abundant during spring. There were no significant longterm changes in blue whale, fin whale, humpback whale, shortbeaked common dolphin or Dall’s porpoise densities while Pacific whitesided dolphins exhibited a significant decrease in density across the tenyear study. The results from this study were fundamentally consistent with earlier studies, but provide greater temporal and seasonal resolution

Codimension formulae for the intersection of fractal subsets of Cantor spaces
http://hdl.handle.net/10023/6030
Abstract: We examine the dimensions of the intersection of a subset E of an mary Cantor space Cm with the image of a subset F under a random isometry with respect to a natural metric. We obtain almost sure upper bounds for the Hausdorff and upper boxcounting dimensions of the intersection, and a lower bound for the essential supremum of the Hausdorff dimension. The dimensions of the intersections are typically max{dim E +dim F dim Cm, 0}, akin to other codimension theorems. The upper estimates come from the expected sizes of coverings, whilst the lower estimate is more intricate, using martingales to define a random measure on the intersection to facilitate a potential theoretic argument.
Description: Date of Acceptance: 16/01/2015
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/6030
20150101T00:00:00Z
Donoven, Casey
Falconer, Kenneth John
We examine the dimensions of the intersection of a subset E of an mary Cantor space Cm with the image of a subset F under a random isometry with respect to a natural metric. We obtain almost sure upper bounds for the Hausdorff and upper boxcounting dimensions of the intersection, and a lower bound for the essential supremum of the Hausdorff dimension. The dimensions of the intersections are typically max{dim E +dim F dim Cm, 0}, akin to other codimension theorems. The upper estimates come from the expected sizes of coverings, whilst the lower estimate is more intricate, using martingales to define a random measure on the intersection to facilitate a potential theoretic argument.

Statistical evidence for the existence of Alfvénic turbulence in solar coronal loops
http://hdl.handle.net/10023/5987
Abstract: Recent observations have demonstrated that waves capable of carrying large amounts of energy are ubiquitous throughout the solar corona. However, the question of how this wave energy is dissipated (on which timescales and length scales) and released into the plasma remains largely unanswered. Both analytic and numerical models have previously shown that Alfvénic turbulence may play a key role not only in the generation of the fast solar wind, but in the heating of coronal loops. In an effort to bridge the gap between theory and observations, we expand on a recent study by analyzing 37 clearly isolated coronal loops using data from the Coronal Multichannel Polarimeter instrument.We observe Alfvénic perturbations with phase speeds which range from 250 to 750 km s1 and periods from 140 to 270 s for the chosen loops. While excesses of highfrequency wave power are observed near the apex of some loops (tentatively supporting the onset of Alfvénic turbulence), we show that this excess depends on loop length and the wavelength of the observed oscillations. In deriving a proportional relationship between the loop length/wavelength ratio and the enhanced wave power at the loop apex, and from the analysis of the line widths associated with these loops, our findings are supportive of the existence of Alfvénic turbulence in coronal loops.
Description: The authors acknowledge support from NASA contracts NNX08BA99G, NNX11AN98G, NNM12AB40P, NNG09FA40C (IRIS), and NNM07AA01C (Hinode). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/ 20072013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/solspanet). Date of Acceptance: 25/09/2014
Wed, 10 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/5987
20141210T00:00:00Z
Liu, J.
Mcintosh, S.W.
De Moortel, I.
Threlfall, J.
Bethge, C.
Recent observations have demonstrated that waves capable of carrying large amounts of energy are ubiquitous throughout the solar corona. However, the question of how this wave energy is dissipated (on which timescales and length scales) and released into the plasma remains largely unanswered. Both analytic and numerical models have previously shown that Alfvénic turbulence may play a key role not only in the generation of the fast solar wind, but in the heating of coronal loops. In an effort to bridge the gap between theory and observations, we expand on a recent study by analyzing 37 clearly isolated coronal loops using data from the Coronal Multichannel Polarimeter instrument.We observe Alfvénic perturbations with phase speeds which range from 250 to 750 km s1 and periods from 140 to 270 s for the chosen loops. While excesses of highfrequency wave power are observed near the apex of some loops (tentatively supporting the onset of Alfvénic turbulence), we show that this excess depends on loop length and the wavelength of the observed oscillations. In deriving a proportional relationship between the loop length/wavelength ratio and the enhanced wave power at the loop apex, and from the analysis of the line widths associated with these loops, our findings are supportive of the existence of Alfvénic turbulence in coronal loops.

Hölder differentiability of selfconformal devil's staircases
http://hdl.handle.net/10023/5980
Abstract: In this paper we consider the probability distribution function of a Gibbs measure supported on a selfconformal set given by an iterated function system (devil's staircase) applied to a compact subset of ℝ. We use thermodynamic multifractal formalism to calculate the Hausdorff dimension of the sets Sα 0, Sα ∞ and Sα, the set of points at which this function has, respectively, Hölder derivative 0, ∞ or no derivative in the general sense. This extends recent work by Darst, Dekking, Falconer, Kesseböhmer and Stratmann, and Yao, Zhang and Li by considering arbitrary such Gibbs measures given by a potential function independent of the geometric potential.
Sat, 01 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/5980
20140301T00:00:00Z
Troscheit, S.
In this paper we consider the probability distribution function of a Gibbs measure supported on a selfconformal set given by an iterated function system (devil's staircase) applied to a compact subset of ℝ. We use thermodynamic multifractal formalism to calculate the Hausdorff dimension of the sets Sα 0, Sα ∞ and Sα, the set of points at which this function has, respectively, Hölder derivative 0, ∞ or no derivative in the general sense. This extends recent work by Darst, Dekking, Falconer, Kesseböhmer and Stratmann, and Yao, Zhang and Li by considering arbitrary such Gibbs measures given by a potential function independent of the geometric potential.

Higher biodiversity is required to sustain multiple ecosystem processes across temperature regimes
http://hdl.handle.net/10023/5975
Abstract: Biodiversity loss is occurring rapidly worldwide, yet it is uncertain whether few or many species are required to sustain ecosystem functioning in the face of environmental change. The importance of biodiversity might be enhanced when multiple ecosystem processes (termed multifunctionality) and environmental contexts are considered, yet no studies have quantified this explicitly to date. We measured five key processes and their combined multifunctionality at three temperatures (5, 10 and 15 °C) in freshwater aquaria containing different animal assemblages (14 benthic macroinvertebrate species). For single processes, biodiversity effects were weak and were best predicted by additivebased models, i.e. polyculture performances represented the sum of their monoculture parts. There were, however, significant effects of biodiversity on multifunctionality at the low and the high (but not the intermediate) temperature. Variation in the contribution of species to processes across temperatures meant that greater biodiversity was required to sustain multifunctionality across different temperatures than was the case for single processes. This suggests that previous studies might have underestimated the importance of biodiversity in sustaining ecosystem functioning in a changing environment.
Description: The authors thank the Natural Environment Research Council for financial support awarded to G. W. (Grant reference: NE/D013305/1) that funded D. M. P.'s research. Accepted 11 July 2014.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/5975
20150101T00:00:00Z
Perkins, D.M.
Bailey, R.A.
Dossena, M.
Gamfeldt, L.
Reiss, J.
Trimmer, M.
Woodward, G.
Biodiversity loss is occurring rapidly worldwide, yet it is uncertain whether few or many species are required to sustain ecosystem functioning in the face of environmental change. The importance of biodiversity might be enhanced when multiple ecosystem processes (termed multifunctionality) and environmental contexts are considered, yet no studies have quantified this explicitly to date. We measured five key processes and their combined multifunctionality at three temperatures (5, 10 and 15 °C) in freshwater aquaria containing different animal assemblages (14 benthic macroinvertebrate species). For single processes, biodiversity effects were weak and were best predicted by additivebased models, i.e. polyculture performances represented the sum of their monoculture parts. There were, however, significant effects of biodiversity on multifunctionality at the low and the high (but not the intermediate) temperature. Variation in the contribution of species to processes across temperatures meant that greater biodiversity was required to sustain multifunctionality across different temperatures than was the case for single processes. This suggests that previous studies might have underestimated the importance of biodiversity in sustaining ecosystem functioning in a changing environment.

Assouad type dimensions and homogeneity of fractals
http://hdl.handle.net/10023/5941
Abstract: We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural 'dimension pair'. In particular, we compute these dimensions for certain classes of selfaffine sets and quasiselfsimilar sets and study their relationships with other notions of dimension, such as the Hausdorff dimension for example. We also investigate some basic properties of these dimensions including their behaviour regarding unions and products and their set theoretic complexity.
Description: Date of Acceptance: 05/05/2013 The author was supported by an EPSRC Doctoral Training Grant
Mon, 01 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/5941
20141201T00:00:00Z
Fraser, Jonathan M.
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural 'dimension pair'. In particular, we compute these dimensions for certain classes of selfaffine sets and quasiselfsimilar sets and study their relationships with other notions of dimension, such as the Hausdorff dimension for example. We also investigate some basic properties of these dimensions including their behaviour regarding unions and products and their set theoretic complexity.

Analysing markrecapturerecovery data in the presence of missing covariate data via multiple imputation
http://hdl.handle.net/10023/5932
Abstract: We consider mark–recapture–recovery data with additional individual timevarying continuous covariate data. For such data it is common to specify the model parameters, and in particular the survival probabilities, as a function of these covariates to incorporate individual heterogeneity. However, an issue arises in relation to missing covariate values, for (at least) the times when an individual is not observed, leading to an analytically intractable likelihood. We propose a twostep multiple imputation approach to obtain estimates of the demographic parameters. Firstly, a model is fitted to only the observed covariate values. Conditional on the fitted covariate model, multiple “complete” datasets are generated (i.e. all missing covariate values are imputed). Secondly, for each complete dataset, a closed form complete data likelihood can be maximised to obtain estimates of the model parameters which are subsequently combined to obtain an overall estimate of the parameters. Associated standard errors and 95 % confidence intervals are obtained using a nonparametric bootstrap. A simulation study is undertaken to assess the performance of the proposed twostep approach. We apply the method to data collected on a wellstudied population of Soay sheep and compare the results with a Bayesian data augmentation approach. Supplementary materials accompanying this paper appear online.
Description: Date of Acceptance: 11/09/2014
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/5932
20150301T00:00:00Z
Worthington, Hannah
King, Ruth
Buckland, Stephen Terrence
We consider mark–recapture–recovery data with additional individual timevarying continuous covariate data. For such data it is common to specify the model parameters, and in particular the survival probabilities, as a function of these covariates to incorporate individual heterogeneity. However, an issue arises in relation to missing covariate values, for (at least) the times when an individual is not observed, leading to an analytically intractable likelihood. We propose a twostep multiple imputation approach to obtain estimates of the demographic parameters. Firstly, a model is fitted to only the observed covariate values. Conditional on the fitted covariate model, multiple “complete” datasets are generated (i.e. all missing covariate values are imputed). Secondly, for each complete dataset, a closed form complete data likelihood can be maximised to obtain estimates of the model parameters which are subsequently combined to obtain an overall estimate of the parameters. Associated standard errors and 95 % confidence intervals are obtained using a nonparametric bootstrap. A simulation study is undertaken to assess the performance of the proposed twostep approach. We apply the method to data collected on a wellstudied population of Soay sheep and compare the results with a Bayesian data augmentation approach. Supplementary materials accompanying this paper appear online.

On the topology of global coronal magnetic fields
http://hdl.handle.net/10023/5896
Abstract: This thesis considers the magnetic topology of the global solar corona. To understand the magnetic topology we use the magnetic skeleton which provides us with a robust description of the magnetic field. To do this we use a Potential Field model extrapolated from observations of the photospheric magnetic field. Various measurements of the photospheric magnetic field are used from both groundbased observatories (KittPeak and SOLIS) and spacebased observatories (MDI and HMI).
Using the magnetic skeleton we characterise particular topological structures and discuss their variations throughout the solar cycle. We find that, from the topology, there are two types of solar minimum magnetic field and one type of solar maximum. The global structure of the coronal magnetic field depends on the relative strengths of the polar fields and the lowlatitude fields. During a strong solar dipole minimum the heliospheric current sheet sits near the equator and the heliospheric current sheet curtains enclose a large amount of mixed polarity field which is associated with many lowaltitude null points. In a weak solar dipole minimum the heliospheric current sheet becomes warped and large scale topological features can form that are associated with weak magnetic field regions. At solar maximum the heliospheric current sheet is highly warped and there are more null points at high altitudes than at solar minimum.
The number of null points in a magnetic field can be seen as a measure of the complexity of the field so this is investigated. We find that the number of nulls above 10Mm falls off with height as a power law whose slope depends on the phase of the solar cycle.
We compare the magnetic topology we found at particular times with observations of the Doppler velocity and intensity around particular active regions to see if it is possible to determine whether plasma upflows at the edge of active regions are linked to open field regions.
Mon, 01 Dec 2014 00:00:00 GMT
http://hdl.handle.net/10023/5896
20141201T00:00:00Z
Edwards, Sarah J.
This thesis considers the magnetic topology of the global solar corona. To understand the magnetic topology we use the magnetic skeleton which provides us with a robust description of the magnetic field. To do this we use a Potential Field model extrapolated from observations of the photospheric magnetic field. Various measurements of the photospheric magnetic field are used from both groundbased observatories (KittPeak and SOLIS) and spacebased observatories (MDI and HMI).
Using the magnetic skeleton we characterise particular topological structures and discuss their variations throughout the solar cycle. We find that, from the topology, there are two types of solar minimum magnetic field and one type of solar maximum. The global structure of the coronal magnetic field depends on the relative strengths of the polar fields and the lowlatitude fields. During a strong solar dipole minimum the heliospheric current sheet sits near the equator and the heliospheric current sheet curtains enclose a large amount of mixed polarity field which is associated with many lowaltitude null points. In a weak solar dipole minimum the heliospheric current sheet becomes warped and large scale topological features can form that are associated with weak magnetic field regions. At solar maximum the heliospheric current sheet is highly warped and there are more null points at high altitudes than at solar minimum.
The number of null points in a magnetic field can be seen as a measure of the complexity of the field so this is investigated. We find that the number of nulls above 10Mm falls off with height as a power law whose slope depends on the phase of the solar cycle.
We compare the magnetic topology we found at particular times with observations of the Doppler velocity and intensity around particular active regions to see if it is possible to determine whether plasma upflows at the edge of active regions are linked to open field regions.

Validation of the magnetic energy vs. helicity scaling in solar magnetic structures
http://hdl.handle.net/10023/5872
Abstract: Aims. We assess the validity of the free magnetic energy – relative magnetic helicity diagram for solar magnetic structures. Methods. We used two different methods of calculating the free magnetic energy and the relative magnetic helicity budgets: a classical, volumecalculation nonlinear forcefree (NLFF) method applied to finite coronal magnetic structures and a surfacecalculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic activeregion cases obtained by threedimensional magnetohydrodynamic (MHD) simulations and observed activeregion cases, which include both eruptive and noneruptive magnetic structures. Results. The derived energyhelicity diagram shows a consistent monotonic scaling between relative helicity and free energy with a scaling index 0.84 ± 0.05 for both data sets and calculation methods. It also confirms the segregation between noneruptive and eruptive active regions and the existence of thresholds in both free energy and relative helicity for active regions to enter eruptive territory. Conclusions. We consider the previously reported energyhelicity diagram of solar magnetic structures as adequately validated and envision a significant role of the uncovered scaling in future studies of solar magnetism.
Description: V.A. acknowledges support by the Royal Society. This work was supported from the EU’s Seventh Framework Program under grant agreement n° PIRG07GA2010268245. It has been also cofinanced by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: Thales.
Wed, 01 Oct 2014 00:00:00 GMT
http://hdl.handle.net/10023/5872
20141001T00:00:00Z
Tziotziou, K.
Moraitis, K.
Georgoulis, M.K.
Archontis, V.
Aims. We assess the validity of the free magnetic energy – relative magnetic helicity diagram for solar magnetic structures. Methods. We used two different methods of calculating the free magnetic energy and the relative magnetic helicity budgets: a classical, volumecalculation nonlinear forcefree (NLFF) method applied to finite coronal magnetic structures and a surfacecalculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic activeregion cases obtained by threedimensional magnetohydrodynamic (MHD) simulations and observed activeregion cases, which include both eruptive and noneruptive magnetic structures. Results. The derived energyhelicity diagram shows a consistent monotonic scaling between relative helicity and free energy with a scaling index 0.84 ± 0.05 for both data sets and calculation methods. It also confirms the segregation between noneruptive and eruptive active regions and the existence of thresholds in both free energy and relative helicity for active regions to enter eruptive territory. Conclusions. We consider the previously reported energyhelicity diagram of solar magnetic structures as adequately validated and envision a significant role of the uncovered scaling in future studies of solar magnetism.

Negative ion sound solitary waves revisited
http://hdl.handle.net/10023/5845
Abstract: Some years ago, a group including the present author and Padma Shukla showed that a suitable nonthermal electron distribution allows the formation of ion sound solitary waves with either positive or negative density perturbations, whereas with Maxwellian electrons only a positive density perturbation is possible. The present paper discusses the qualitative features of this distribution allowing the negative waves and shared with suitable twotemperature distributions.
Sun, 01 Dec 2013 00:00:00 GMT
http://hdl.handle.net/10023/5845
20131201T00:00:00Z
Cairns, R. A.
Some years ago, a group including the present author and Padma Shukla showed that a suitable nonthermal electron distribution allows the formation of ion sound solitary waves with either positive or negative density perturbations, whereas with Maxwellian electrons only a positive density perturbation is possible. The present paper discusses the qualitative features of this distribution allowing the negative waves and shared with suitable twotemperature distributions.

Simulating AIA observations of a flux rope ejection
http://hdl.handle.net/10023/5821
Abstract: Context. Coronal mass ejections (CMEs) are the most violent phenomena observed on the Sun. Currently, extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. In particular, observations now show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. While this is the case, these observations are difficult to interpret in terms of basic physical mechanisms and quantities. To fully understand CMEs we need to compare equivalent quantities derived from both observations and theoretical models. This will aid in bridging the gap between observations and models. Aims: To this end, we aim to produce synthesised AIA observations from simulations of a flux rope ejection. To carry this out we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. Methods: We perform a simulation where a flux rope is ejected from the solar corona. From the density and temperature of the plasma in the simulation we synthesise AIA observations. The emission is then integrated along the line of sight using the instrumental response function of AIA. Results: We sythesise observations of AIA in the channels at 304 Å, 171 Å, 335 Å, and 94 Å. The synthesised observations show a number of features similar to actual observations and in particular reproduce the general development of CMEs in the low corona as observed by AIA. In particular we reproduce an erupting and expanding arcade in the 304 Å and 171 Å channels with a high density core. Conclusions: The ejection of a flux rope reproduces many of the features found in the AIA observations. This work is therefore a step forward in bridging the gap between observations and models, and can lead to more direct interpretations of EUV observations in terms of flux rope ejections. We plan to improve the model in future studies in order to perform a more quantitative comparison. Movies associated with Figs. 3, 9, and 10 are available in electronic form at http://www.aanda.org
Description: D.H.M. would like to thank STFC, the Leverhulme Trust and the European Commission’s Seventh Framework Programme (FP7/20072013) for their financial support. P.P. would like to thank the European Commission’s Seventh Framework Programme (FP7/20072013) under grant agreement SWIFF (project 263340, http://www.swiff.eu) and STFC for financial support. These results were obtained in the framework of the projects GOA/2009009 (KU Leuven), G.0729.11 (FWOVlaanderen) and C 90347 (ESA Prodex 9). The research leading to these results has also received funding from the European Commission’s Seventh Framework Programme (FP7/20072013) under the grant agreements SOLSPANET (project No. 269299, http:// www.solspanet.eu), SPACECAST (project No. 262468, fp7spacecast.eu), eHeroes (project n 284461, http://www.eheroes.eu). The computational work for this paper was carried out on the joint STFC and SFC (SRIF) funded cluster at the University of St Andrews (Scotland, UK).
Fri, 01 Aug 2014 00:00:00 GMT
http://hdl.handle.net/10023/5821
20140801T00:00:00Z
Pagano, Paolo
Mackay, Duncan Hendry
Poedts, Stephan
Context. Coronal mass ejections (CMEs) are the most violent phenomena observed on the Sun. Currently, extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. In particular, observations now show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. While this is the case, these observations are difficult to interpret in terms of basic physical mechanisms and quantities. To fully understand CMEs we need to compare equivalent quantities derived from both observations and theoretical models. This will aid in bridging the gap between observations and models. Aims: To this end, we aim to produce synthesised AIA observations from simulations of a flux rope ejection. To carry this out we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. Methods: We perform a simulation where a flux rope is ejected from the solar corona. From the density and temperature of the plasma in the simulation we synthesise AIA observations. The emission is then integrated along the line of sight using the instrumental response function of AIA. Results: We sythesise observations of AIA in the channels at 304 Å, 171 Å, 335 Å, and 94 Å. The synthesised observations show a number of features similar to actual observations and in particular reproduce the general development of CMEs in the low corona as observed by AIA. In particular we reproduce an erupting and expanding arcade in the 304 Å and 171 Å channels with a high density core. Conclusions: The ejection of a flux rope reproduces many of the features found in the AIA observations. This work is therefore a step forward in bridging the gap between observations and models, and can lead to more direct interpretations of EUV observations in terms of flux rope ejections. We plan to improve the model in future studies in order to perform a more quantitative comparison. Movies associated with Figs. 3, 9, and 10 are available in electronic form at http://www.aanda.org

Stellar differential rotation and coronal timescales
http://hdl.handle.net/10023/5820
Abstract: We investigate the timescales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this, we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equatorpole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the lap time and the surface diffusion timescale through the relation tau_Form ∝ &surd;{tau_Laptau_Diff}. In contrast, the lifetimes of flux ropes are proportional to the lap time (tauLife∝tauLap). With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than 2 d. As a consequence, we propose that features such as solarlike quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae.
Description: GPSG would like to thank the STFC for financial support. DHM would like to thank the STFC and the Leverhulme Trust for financial support.
Wed, 01 Oct 2014 00:00:00 GMT
http://hdl.handle.net/10023/5820
20141001T00:00:00Z
Gibb, Gordon Peter Samuel
Jardine, Moira Mary
Mackay, Duncan Hendry
We investigate the timescales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this, we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equatorpole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the lap time and the surface diffusion timescale through the relation tau_Form ∝ &surd;{tau_Laptau_Diff}. In contrast, the lifetimes of flux ropes are proportional to the lap time (tauLife∝tauLap). With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than 2 d. As a consequence, we propose that features such as solarlike quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae.

An explicit upper bound for the Helfgott delta in SL(2,p)
http://hdl.handle.net/10023/5819
Abstract: Helfgott proved that there exists a δ>0 such that if S is a symmetric generating subset of SL(2,p) containing 1 then either S3=SL(2,p) or S3 ≥S1+δ. It is known that δ ≥ 1/3024. Here we show that δ ≤(log2(7)1)/6 ≈ 0.3012 and we present evidence suggesting that this might be the true value of δ.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/5819
20150101T00:00:00Z
Button, Jack
RoneyDougal, Colva
Helfgott proved that there exists a δ>0 such that if S is a symmetric generating subset of SL(2,p) containing 1 then either S3=SL(2,p) or S3 ≥S1+δ. It is known that δ ≥ 1/3024. Here we show that δ ≤(log2(7)1)/6 ≈ 0.3012 and we present evidence suggesting that this might be the true value of δ.

Backward wave cyclotronmaser emission in the auroral magnetosphere
http://hdl.handle.net/10023/5802
Abstract: In this Letter, we present theory and particleincell simulations describing cyclotron radio emission from Earth's auroral region and similar phenomena in other astrophysical environments. In particular, we find that the radiation, generated by a downgoing electron horseshoe distribution is due to a backward wave cyclotronmaser emission process. The backward wave nature of the radiation contributes to upward refraction of the radiation that is also enhanced by a density inhomogeneity. We also show that the radiation is preferentially amplified along the auroral oval rather than transversely. The results are in agreement with recent Cluster observations.
Description: This work was supported by EPSRC Grant No. EP/G04239X/1.
Tue, 07 Oct 2014 00:00:00 GMT
http://hdl.handle.net/10023/5802
20141007T00:00:00Z
Speirs, D. C.
Bingham, R.
Cairns, R. A.
Vorgul, I.
Kellett, B. J.
Phelps, A. D. R.
Ronald, K.
In this Letter, we present theory and particleincell simulations describing cyclotron radio emission from Earth's auroral region and similar phenomena in other astrophysical environments. In particular, we find that the radiation, generated by a downgoing electron horseshoe distribution is due to a backward wave cyclotronmaser emission process. The backward wave nature of the radiation contributes to upward refraction of the radiation that is also enhanced by a density inhomogeneity. We also show that the radiation is preferentially amplified along the auroral oval rather than transversely. The results are in agreement with recent Cluster observations.

A unifying model for capturerecapture and distance sampling surveys of wildlife populations
http://hdl.handle.net/10023/5797
Abstract: Spatially explicit capturerecapture (SECR) methods extend traditional capturerecapture methods for estimating population density by using information contained in the location of traps. The The central feature of the improvement is estimation from the locations of traps at which animals were and were not captured to estimate of the distance over which animals are susceptible to capture. We show that standard SECR models are a special case of a more general class of model in which animal detection is not certain, but some information is available about the location of detected animals. The model class accommodates a range of spatial data types and includes as a special case markrecapture distance sampling, where distances to detected animals are recorded by multiple observers. Other examples of additional information that can be included are bearing to detected animals, strength of acoustic signals received from detected animals, and time of arrival of acoustic signals at detectors. Errors in variables are easily incorporated. We illustrate the versatility of the model and method through a number of applications, in each case using real and simulated data, and comparing our results with those from previous studies where these are available.
Description: Funding: Partfunded by Fundacao Nacional para a Cienca e Technologia, Portugal (FCT) under the project PEst OE/MAT/UI0006/2011 (Marques) and the UK Engineering and Physical Sciences Research Council EP/I000917/1
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/5797
20150101T00:00:00Z
Borchers, D. L.
Stevenson, B.C.
Kidney, D.
Thomas, L.
Marques, T.A.
Spatially explicit capturerecapture (SECR) methods extend traditional capturerecapture methods for estimating population density by using information contained in the location of traps. The The central feature of the improvement is estimation from the locations of traps at which animals were and were not captured to estimate of the distance over which animals are susceptible to capture. We show that standard SECR models are a special case of a more general class of model in which animal detection is not certain, but some information is available about the location of detected animals. The model class accommodates a range of spatial data types and includes as a special case markrecapture distance sampling, where distances to detected animals are recorded by multiple observers. Other examples of additional information that can be included are bearing to detected animals, strength of acoustic signals received from detected animals, and time of arrival of acoustic signals at detectors. Errors in variables are easily incorporated. We illustrate the versatility of the model and method through a number of applications, in each case using real and simulated data, and comparing our results with those from previous studies where these are available.

Maximal subsemigroups of the semigroup of all mappings on an infinite set
http://hdl.handle.net/10023/5793
Abstract: We classify the maximal subsemigroups of the semigroup ΩΩ of all mappings on an infinite set Ω that contain one of the following groups: the symmetric group on Ω, the setwise stabilizer of a nonempty finite subset of Ω, the stabilizer of a finite partition of Ω, or the stabilizer of an ultrafilter on Ω. If G is any of these groups, then we also characterise the mappings f,g ∈ ΩΩ such that the semigroup G, f, g generated by G ∪ {f,g} equals ΩΩ. We also show that the setwise stabiliser of a nonempty finite set, the almost stabiliser of a finite partition, and the stabiliser of an ultrafilter are maximal subsemigroups of the symmetric group.
Sun, 01 Mar 2015 00:00:00 GMT
http://hdl.handle.net/10023/5793
20150301T00:00:00Z
East, J.
Mitchell, James David
Péresse, Y.
We classify the maximal subsemigroups of the semigroup ΩΩ of all mappings on an infinite set Ω that contain one of the following groups: the symmetric group on Ω, the setwise stabilizer of a nonempty finite subset of Ω, the stabilizer of a finite partition of Ω, or the stabilizer of an ultrafilter on Ω. If G is any of these groups, then we also characterise the mappings f,g ∈ ΩΩ such that the semigroup G, f, g generated by G ∪ {f,g} equals ΩΩ. We also show that the setwise stabiliser of a nonempty finite set, the almost stabiliser of a finite partition, and the stabiliser of an ultrafilter are maximal subsemigroups of the symmetric group.

Acoustic and foraging behavior of a Baird’s beaked whale, Berardius bairdii, exposed to simulated sonar
http://hdl.handle.net/10023/5787
Abstract: Beaked whales are hypothesized to be particularly sensitive to anthropogenic noise, based on previous strandings and limited experimental and observational data. However, few species have been studied in detail. We describe the underwater behavior of a Baird's beaked whale (Berardius bairdii) from the first deployment of a multisensor acoustic tag on this species. The animal exhibited shallow (23 ± 15 m max depth), intermediate (324 ± 49 m), and deep (1138 ± 243 m) dives. Echolocation clicks were produced with a mean interclick interval of approximately 300 ms and peak frequency of 25 kHz. Two deep dives included presumed foraging behavior, with echolocation pulsed sounds (presumed prey capture attempts) associated with increased maneuvering, and sustained inverted swimming during the bottom phase of the dive. A controlled exposure to simulated midfrequency active sonar (3.5–4 kHz) was conducted 4 hours after tag deployment, and within 3 minutes of exposure onset, the tagged whale increased swim speed and body movement, and continued to show unusual dive behavior for each of its next three dives, one of each type. These are the first data on the acoustic foraging behavior in this largest beaked whale species, and the first experimental demonstration of a response to simulated sonar.
Description: Research was supported by the US Navy Chief of Naval Operations, Environmental Readiness Program, the Office of Naval Research, the Naval Postgraduate School, and the National Research Council.
Thu, 13 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/5787
20141113T00:00:00Z
Stimpert, Alison
De Ruiter, Stacy Lynn
Southall, Brandon
Moretti, David
Falcone, Erin
Goldbogen, Jeremy
Friedlaender, Ari
Schorr, Greg
Calambokidis, John
Beaked whales are hypothesized to be particularly sensitive to anthropogenic noise, based on previous strandings and limited experimental and observational data. However, few species have been studied in detail. We describe the underwater behavior of a Baird's beaked whale (Berardius bairdii) from the first deployment of a multisensor acoustic tag on this species. The animal exhibited shallow (23 ± 15 m max depth), intermediate (324 ± 49 m), and deep (1138 ± 243 m) dives. Echolocation clicks were produced with a mean interclick interval of approximately 300 ms and peak frequency of 25 kHz. Two deep dives included presumed foraging behavior, with echolocation pulsed sounds (presumed prey capture attempts) associated with increased maneuvering, and sustained inverted swimming during the bottom phase of the dive. A controlled exposure to simulated midfrequency active sonar (3.5–4 kHz) was conducted 4 hours after tag deployment, and within 3 minutes of exposure onset, the tagged whale increased swim speed and body movement, and continued to show unusual dive behavior for each of its next three dives, one of each type. These are the first data on the acoustic foraging behavior in this largest beaked whale species, and the first experimental demonstration of a response to simulated sonar.

The nature of separator current layers in MHS equilibria I. Current parallel to the separator
http://hdl.handle.net/10023/5785
Abstract: Separators, which are in many ways the threedimensional equivalent to twodimensional nulls, are important sites for magnetic reconnection. Magnetic reconnection occurs in strong current layers which have very short length scales. The aim of this work is to explore the nature of current layers around separators. A separator is a special field line which lies along the intersection of two separatrix surfaces and forms the boundary between four topologically distinct flux domains. In particular, here the current layer about a separator that joins two 3D nulls and lies along the intersection of their separatrix surfaces is investigated. A magnetic configuration containing a single separator embedded in a uniform plasma with a uniform electric current parallel to the separator is considered. This initial magnetic setup, which is not in equilibrium, relaxes in a nonresistive manner to form an equilibrium. The relaxation is achieved using the 3D MHD code, Lare3d, with resistivity set to zero. A series of experiments with varying initial current are run to investigate the characteristics of the resulting current layers present in the final (quasi) equilibrium states. In each experiment, the separator collapses and a current layer forms along it. The dimensions and strength of the current layer increase with initial current. It is found that separator current layers formed from current parallel to the separator are twisted. Also the collapse of the separator is a process that evolves like an infinitetime singularity where the length, width and peak current in the layer grow slowly whilst the depth of the current layer decreases.
Description: JEHS would like to thank STFC for financial support during her Ph.D and CEP acknowledges support from the STFC consolidated grant. Date of Acceptance: 28/10/2014
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/5785
20150101T00:00:00Z
Stevenson, Julie Elizabeth Helen
Parnell, Clare Elizabeth
Priest, Eric Ronald
Haynes, Andrew Lewis
Separators, which are in many ways the threedimensional equivalent to twodimensional nulls, are important sites for magnetic reconnection. Magnetic reconnection occurs in strong current layers which have very short length scales. The aim of this work is to explore the nature of current layers around separators. A separator is a special field line which lies along the intersection of two separatrix surfaces and forms the boundary between four topologically distinct flux domains. In particular, here the current layer about a separator that joins two 3D nulls and lies along the intersection of their separatrix surfaces is investigated. A magnetic configuration containing a single separator embedded in a uniform plasma with a uniform electric current parallel to the separator is considered. This initial magnetic setup, which is not in equilibrium, relaxes in a nonresistive manner to form an equilibrium. The relaxation is achieved using the 3D MHD code, Lare3d, with resistivity set to zero. A series of experiments with varying initial current are run to investigate the characteristics of the resulting current layers present in the final (quasi) equilibrium states. In each experiment, the separator collapses and a current layer forms along it. The dimensions and strength of the current layer increase with initial current. It is found that separator current layers formed from current parallel to the separator are twisted. Also the collapse of the separator is a process that evolves like an infinitetime singularity where the length, width and peak current in the layer grow slowly whilst the depth of the current layer decreases.

Particle acceleration at a reconnecting magnetic separator
http://hdl.handle.net/10023/5782
Abstract: While the exact acceleration mechanism of energetic particles during solar flares is (as yet) unknown, magnetic reconnection plays a key role both in the release of stored magnetic energy of the solar corona and the magnetic restructuring during a flare. Recent work has shown that special field lines, called separators, are common sites of reconnection in 3D numerical experiments. To date, 3D separator reconnection sites have received little attention as particle accelerators. We investigate the effectiveness of separator reconnection as a particle acceleration mechanism for electrons and protons. We study the particle acceleration using a relativistic guidingcentre particle code in a timedependent kinematic model of magnetic reconnection at a separator. The effect upon particle behaviour of initial position, pitch angle and initial kinetic energy are examined in detail, both for specific (single) particle examples and for large distributions of initial conditions. The separator reconnection model contains several free parameters and we study the effect of changing these parameters upon particle acceleration, in particular in view of the final particle energy ranges which agree with observed energy spectra.
Description: Date of Acceptance: 22/10/2014
Sun, 01 Feb 2015 00:00:00 GMT
http://hdl.handle.net/10023/5782
20150201T00:00:00Z
Threlfall, J.
Neukirch, T.
Parnell, Clare Elizabeth
Eradat Oskoui, S.
While the exact acceleration mechanism of energetic particles during solar flares is (as yet) unknown, magnetic reconnection plays a key role both in the release of stored magnetic energy of the solar corona and the magnetic restructuring during a flare. Recent work has shown that special field lines, called separators, are common sites of reconnection in 3D numerical experiments. To date, 3D separator reconnection sites have received little attention as particle accelerators. We investigate the effectiveness of separator reconnection as a particle acceleration mechanism for electrons and protons. We study the particle acceleration using a relativistic guidingcentre particle code in a timedependent kinematic model of magnetic reconnection at a separator. The effect upon particle behaviour of initial position, pitch angle and initial kinetic energy are examined in detail, both for specific (single) particle examples and for large distributions of initial conditions. The separator reconnection model contains several free parameters and we study the effect of changing these parameters upon particle acceleration, in particular in view of the final particle energy ranges which agree with observed energy spectra.

Optimal crossover designs for full interaction models
http://hdl.handle.net/10023/5768
Abstract: We consider repeated measurement designs when a residual or carryover effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment effects, we consider a model with interactions between carryover and direct treatment effects. When the aim of the experiment is to study the effects of a treatment used alone, we obtain universally optimal approximate designs. We also propose some efficient designs with a reduced number of subjects.
Description: July 2014
Sat, 01 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/5768
20141101T00:00:00Z
Bailey, Rosemary Anne
Druilhet, Pierre
We consider repeated measurement designs when a residual or carryover effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment effects, we consider a model with interactions between carryover and direct treatment effects. When the aim of the experiment is to study the effects of a treatment used alone, we obtain universally optimal approximate designs. We also propose some efficient designs with a reduced number of subjects.

Computing in permutation groups without memory
http://hdl.handle.net/10023/5727
Abstract: Memoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since they typically involve updates of single registers. The memoryless computation model can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we consider how efficiently permutations can be computed without memory. We determine the minimum number of basic updates required to compute any permutation, or any even permutation. The small number of required instructions shows that very small instruction sets could be encoded on cores to perform memoryless computation. We then start looking at a possible compromise between the size of the instruction set and the length of the resulting programs. We consider updates only involving a limited number of registers. In particular, we show that binary instructions are not enough to compute all permutations without memory when the alphabet size is even. These results, though expressed as properties of special generating sets of the symmetric or alternating groups, provide guidelines on the implementation of memoryless computation.
Description: Funding: UK Engineering and Physical Sciences Research Council (EP/K033956/1)
Sun, 02 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/5727
20141102T00:00:00Z
Cameron, Peter Jephson
Fairbairn, Ben
Gadouleau, Maximilien
Memoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since they typically involve updates of single registers. The memoryless computation model can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we consider how efficiently permutations can be computed without memory. We determine the minimum number of basic updates required to compute any permutation, or any even permutation. The small number of required instructions shows that very small instruction sets could be encoded on cores to perform memoryless computation. We then start looking at a possible compromise between the size of the instruction set and the length of the resulting programs. We consider updates only involving a limited number of registers. In particular, we show that binary instructions are not enough to compute all permutations without memory when the alphabet size is even. These results, though expressed as properties of special generating sets of the symmetric or alternating groups, provide guidelines on the implementation of memoryless computation.

Computing in matrix groups without memory
http://hdl.handle.net/10023/5715
Abstract: Memoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they typically involve updates of single registers. The computation model of memoryless computation can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we view registers as elements of a finite field and we compute linear permutations without memory. We first determine the maximum complexity of a linear function when only linear instructions are allowed. We also determine which linear functions are hardest to compute when the field in question is the binary field and the number of registers is even. Secondly, we investigate some matrix groups, thus showing that the special linear group is internally computable but not fast. Thirdly, we determine the smallest set of instructions required to generate the special and general linear groups. These results are important for memoryless computation, for they show that linear functions can be computed very fast or that very few instructions are needed to compute any linear function. They thus indicate new advantages of using memoryless computation.
Description: Funding: UK Engineering and Physical Sciences Research Council award EP/K033956/1
Sun, 02 Nov 2014 00:00:00 GMT
http://hdl.handle.net/10023/5715
20141102T00:00:00Z
Cameron, Peter Jephson
Fairbairn, Ben
Gadouleau, Maximilien
Memoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they typically involve updates of single registers. The computation model of memoryless computation can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we view registers as elements of a finite field and we compute linear permutations without memory. We first determine the maximum complexity of a linear function when only linear instructions are allowed. We also determine which linear functions are hardest to compute when the field in question is the binary field and the number of registers is even. Secondly, we investigate some matrix groups, thus showing that the special linear group is internally computable but not fast. Thirdly, we determine the smallest set of instructions required to generate the special and general linear groups. These results are important for memoryless computation, for they show that linear functions can be computed very fast or that very few instructions are needed to compute any linear function. They thus indicate new advantages of using memoryless computation.

Alfvén wave boundary condition for responsive magnetosphere ionosphere coupling
http://hdl.handle.net/10023/5660
Abstract: The solution of electric fields and currents in a heightresolved ionosphere is traditionally solved as an elliptic equation with Dirichlet or Neumann boundary condition in which the magnetosphere is represented as an unresponsive (prescribed) voltage generator or current source. In this paper we derive an alternative boundary condition based upon Alfvén waves in which only the Alfvén wave from the magnetosphere that is incident upon the ionosphere (E) is prescribed. For a uniform magnetosphere the new boundary condition reduces to ∂φ/∂z=(∂2φ/ ∂x2+2∂Exi/∂x)/(μ0VAσ≥) and is evaluated at the magnetosphereionosphere interface. The resulting solution is interpreted as a responsive magnetosphere and establishes a key stage in the full selfconsistent and nonlinear coupling of the magnetosphere and ionosphere.
Description: A.J.B.R. thanks STFC for present support through consolidated grant ST/K000993/1 and gratefully acknowledges a Royal Commission for the Exhibition of 1851 Research Fellowship that also assisted this work.
Thu, 01 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5660
20140501T00:00:00Z
Wright, A.N.
Russell, A.J.B.
The solution of electric fields and currents in a heightresolved ionosphere is traditionally solved as an elliptic equation with Dirichlet or Neumann boundary condition in which the magnetosphere is represented as an unresponsive (prescribed) voltage generator or current source. In this paper we derive an alternative boundary condition based upon Alfvén waves in which only the Alfvén wave from the magnetosphere that is incident upon the ionosphere (E) is prescribed. For a uniform magnetosphere the new boundary condition reduces to ∂φ/∂z=(∂2φ/ ∂x2+2∂Exi/∂x)/(μ0VAσ≥) and is evaluated at the magnetosphereionosphere interface. The resulting solution is interpreted as a responsive magnetosphere and establishes a key stage in the full selfconsistent and nonlinear coupling of the magnetosphere and ionosphere.

The probability of generating a finite simple group
http://hdl.handle.net/10023/5658
Abstract: We study the probability of generating a finite simple group, together with its generalisation PG,socG(d), the conditional probability of generating an almost simple finite group G by d elements, given that these elements generate G/ socG. We prove that PG,socG(2) ⩾ 53/90, with equality if and only if G is A6 or S6, and establish a similar result for PG,socG(3). Positive answers to longstanding questions of Wiegold on direct products, and of Mel’nikov on profinite groups, follow easily from our results.
Fri, 01 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/5658
20131101T00:00:00Z
Menezes, Nina Emma
Quick, Martyn
RoneyDougal, Colva Mary
We study the probability of generating a finite simple group, together with its generalisation PG,socG(d), the conditional probability of generating an almost simple finite group G by d elements, given that these elements generate G/ socG. We prove that PG,socG(2) ⩾ 53/90, with equality if and only if G is A6 or S6, and establish a similar result for PG,socG(3). Positive answers to longstanding questions of Wiegold on direct products, and of Mel’nikov on profinite groups, follow easily from our results.

Most primitive groups are full automorphism groups of edgetransitive hypergraphs
http://hdl.handle.net/10023/5580
Abstract: We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,YG) = G for a random subset Y of X, tends to 1 as n tends to infinity. So the property of the title holds for all primitive groups except the alternating groups and finitely many others. This answers a question of M. Klin. Moreover, we give an upper bound n1/2+ε for the minimum size of the edges in such a hypergraph. This is essentially best possible.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10023/5580
20150101T00:00:00Z
Babai, Laszlo
Cameron, Peter Jephson
We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,YG) = G for a random subset Y of X, tends to 1 as n tends to infinity. So the property of the title holds for all primitive groups except the alternating groups and finitely many others. This answers a question of M. Klin. Moreover, we give an upper bound n1/2+ε for the minimum size of the edges in such a hypergraph. This is essentially best possible.

Exact dimensionality and projections of random selfsimilar measures and sets
http://hdl.handle.net/10023/5514
Abstract: We study the geometric properties of random multiplicative cascade measures defined on selfsimilar sets. We show that such measures and their projections and sections are almost surely exactdimensional, generalizing Feng and Hu's result for selfsimilar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin's theorems on projections of deterministic selfsimilar measures to these random measures without requiring any separation conditions on the underlying sets. We give applications to selfsimilar sets and fractal percolation, including new results on projections, C1images and distance sets.
Mon, 01 Sep 2014 00:00:00 GMT
http://hdl.handle.net/10023/5514
20140901T00:00:00Z
Falconer, Kenneth
Jin, Xiong
We study the geometric properties of random multiplicative cascade measures defined on selfsimilar sets. We show that such measures and their projections and sections are almost surely exactdimensional, generalizing Feng and Hu's result for selfsimilar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin's theorems on projections of deterministic selfsimilar measures to these random measures without requiring any separation conditions on the underlying sets. We give applications to selfsimilar sets and fractal percolation, including new results on projections, C1images and distance sets.

The cooling of coronal plasmas. IV. Catastrophic cooling of loops
http://hdl.handle.net/10023/5503
Abstract: We examine the radiative cooling of coronal loops and demonstrate that the recently identified catastrophic cooling is due to the inability of a loop to sustain radiative/enthalpy cooling below a critical temperature, which can be >1 MK in flares, 0.51 MK in active regions, and 0.1 MK in long tenuous loops. Catastrophic cooling is characterized by a rapid fall in coronal temperature, while the coronal density changes by a small amount. Analytic expressions for the critical temperature are derived and show good agreement with numerical results. This effect considerably limits the lifetime of coronal plasmas below the critical temperature.
Sat, 20 Jul 2013 00:00:00 GMT
http://hdl.handle.net/10023/5503
20130720T00:00:00Z
Cargill, P.J.
Bradshaw, S.J.
We examine the radiative cooling of coronal loops and demonstrate that the recently identified catastrophic cooling is due to the inability of a loop to sustain radiative/enthalpy cooling below a critical temperature, which can be >1 MK in flares, 0.51 MK in active regions, and 0.1 MK in long tenuous loops. Catastrophic cooling is characterized by a rapid fall in coronal temperature, while the coronal density changes by a small amount. Analytic expressions for the critical temperature are derived and show good agreement with numerical results. This effect considerably limits the lifetime of coronal plasmas below the critical temperature.

Ultraviolet and extremeultraviolet emissions at the flare footpoints observed by atmosphere imaging assembly
http://hdl.handle.net/10023/5499
Abstract: A solar flare is composed of impulsive energy release events by magnetic reconnection, which forms and heats flare loops. Recent studies have revealed a twophase evolution pattern of UV 1600 Å emission at the feet of these loops: a rapid pulse lasting for a few seconds to a few minutes, followed by a gradual decay on timescales of a few tens of minutes. Multiple band EUV observations by the Atmosphere Imaging Assembly further reveal very similar signatures. These two phases represent different but related signatures of an impulsive energy release in the corona. The rapid pulse is an immediate response of the lower atmosphere to an intense thermal conduction flux resulting from the sudden heating of the corona to high temperatures (we rule out energetic particles due to a lack of significant hard Xray emission). The gradual phase is associated with the cooling of hot plasma that has been evaporated into the corona. The observed footpoint emission is again powered by thermal conduction (and enthalpy), but now during a period when approximate steadystate conditions are established in the loop. UV and EUV light curves of individual pixels may therefore be separated into contributions from two distinct physical mechanisms to shed light on the nature of energy transport in a flare. We demonstrate this technique using coordinated, spatially resolved observations of UV and EUV emissions from the footpoints of a C3.2 thermal flare.
Sun, 01 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5499
20130901T00:00:00Z
Qiu, J.
Sturrock, Z.
Longcope, D.W.
Klimchuk, J.A.
Liu, W.J.
A solar flare is composed of impulsive energy release events by magnetic reconnection, which forms and heats flare loops. Recent studies have revealed a twophase evolution pattern of UV 1600 Å emission at the feet of these loops: a rapid pulse lasting for a few seconds to a few minutes, followed by a gradual decay on timescales of a few tens of minutes. Multiple band EUV observations by the Atmosphere Imaging Assembly further reveal very similar signatures. These two phases represent different but related signatures of an impulsive energy release in the corona. The rapid pulse is an immediate response of the lower atmosphere to an intense thermal conduction flux resulting from the sudden heating of the corona to high temperatures (we rule out energetic particles due to a lack of significant hard Xray emission). The gradual phase is associated with the cooling of hot plasma that has been evaporated into the corona. The observed footpoint emission is again powered by thermal conduction (and enthalpy), but now during a period when approximate steadystate conditions are established in the loop. UV and EUV light curves of individual pixels may therefore be separated into contributions from two distinct physical mechanisms to shed light on the nature of energy transport in a flare. We demonstrate this technique using coordinated, spatially resolved observations of UV and EUV emissions from the footpoints of a C3.2 thermal flare.

Nonlinear forcefree magnetic dip models of quiescent prominence fine structures
http://hdl.handle.net/10023/5476
Abstract: Aims. We use 3D nonlinear forcefree magnetic field modeling of prominence/filament magnetic fields to develop the first 2D models of individual prominence fine structures based on the 3D configuration of the magnetic field of the whole prominence. Methods. We use an iterative technique to fill the magnetic dips produced by the 3D modeling with realistic prominence plasma in hydrostatic equilibrium and with a temperature structure that contains the prominencecorona transition region. With this welldefined plasma structure the radiative transfer can be treated in detail in 2D and the resulting synthetic emission can be compared with prominence/filament observations. Results. Newly developed nonlinear forcefree magnetic dip models are able to produce synthetic hydrogen Lyman spectra in a qualitative agreement with a range of quiescent prominence observations. Moreover, the plasma structure of these models agrees with the gravity induced prominence fine structure models which have already been shown to produce synthetic spectra in good qualitative agreement with several observed prominences. Conclusions. We describe in detail the iterative technique which can be used to produce realistic plasma models of prominence fine structures located in prominence magnetic field configurations containing dips, obtained using any kind of magnetic field modeling.
Description: S.G. and P.H. acknowledge the support from grant 209/12/0906 of the Grant Agency of the Czech Republic. P.H. acknowledges the support from grant P209/10/1680 of the Grant Agency of the Czech Republic. S.G. and P.H. acknowledge the support from the MPA Garching; U.A. thanks for support from the Ondřejov Observatory. S.G. acknowledges the support from St Andrews University. Work of S.G. and P.H. was supported by the project RVO: 67985815. DHM acknowledges financial support from the STFC and the Leverhulme Trust. In addition research leading to these results has received funding from the European Commission’s Seventh Framework Programme (FP7/20072013) under the grant agreement SWIFF (project N° 263340, http://www.swiff.eu).
Fri, 01 Mar 2013 00:00:00 GMT
http://hdl.handle.net/10023/5476
20130301T00:00:00Z
Gunar, Stanislav
Mackay, Duncan Hendry
Anzer, U
Heinzel, Petr
Aims. We use 3D nonlinear forcefree magnetic field modeling of prominence/filament magnetic fields to develop the first 2D models of individual prominence fine structures based on the 3D configuration of the magnetic field of the whole prominence. Methods. We use an iterative technique to fill the magnetic dips produced by the 3D modeling with realistic prominence plasma in hydrostatic equilibrium and with a temperature structure that contains the prominencecorona transition region. With this welldefined plasma structure the radiative transfer can be treated in detail in 2D and the resulting synthetic emission can be compared with prominence/filament observations. Results. Newly developed nonlinear forcefree magnetic dip models are able to produce synthetic hydrogen Lyman spectra in a qualitative agreement with a range of quiescent prominence observations. Moreover, the plasma structure of these models agrees with the gravity induced prominence fine structure models which have already been shown to produce synthetic spectra in good qualitative agreement with several observed prominences. Conclusions. We describe in detail the iterative technique which can be used to produce realistic plasma models of prominence fine structures located in prominence magnetic field configurations containing dips, obtained using any kind of magnetic field modeling.

Effects of M dwarf magnetic fields on potentially habitable planets
http://hdl.handle.net/10023/5462
Abstract: We investigate the effect of the magnetic fields of M dwarf (dM) stars on potentially habitable Earthlike planets. These fields can reduce the size of planetary magnetospheres to such an extent that a significant fraction of the planet’s atmosphere may be exposed to erosion by the stellar wind. We used a sample of 15 active dM stars, for which surface magneticfield maps were reconstructed, to determine the magnetic pressure at the planet orbit and hence the largest size of its magnetosphere, which would only be decreased by considering the stellar wind. Our method provides a fast means to assess which planets are most affected by the stellar magnetic field, which can be used as a first study to be followed by more sophisticated models. We show that hypothetical Earthlike planets with similar terrestrial magnetisation (~1 G) orbiting at the inner (outer) edge of the habitable zone of these stars would present magnetospheres that extend at most up to 6 (11.7) planetary radii. To be able to sustain an Earthsized magnetosphere, with the exception of only a few cases, the terrestrial planet would either (1) need to orbit significantly farther out than the traditional limits of the habitable zone; or else, (2) if it were orbiting within the habitable zone, it would require at least a magnetic field ranging from a few G to up to a few thousand G. By assuming a magnetospheric size that is more appropriate for the youngEarth (3.4 Gyr ago), the required planetary magnetic fields are one order of magnitude weaker. However, in this case, the polarcap area of the planet, which is unprotected from transport of particles to/from interplanetary space, is twice as large. At present, we do not know how small the smallest area of the planetary surface is that could be exposed and would still not affect the potential for formation and development of life in a planet. As the star becomes older and, therefore, its rotation rate and magnetic field reduce, the interplanetary magnetic pressure decreases and the magnetosphere of planets probably expands. Using an empirically derived rotationactivity/magnetism relation, we provide an analytical expression for estimating the shortest stellar rotation period for which an Earthanalogue in the habitable zone could sustain an Earthsized magnetosphere. We find that the required rotation rate of the early and middM stars (with periods ≳37–202 days) is slower than the solar one, and even slower for the latedM stars (≳63–263 days). Planets orbiting in the habitable zone of dM stars that rotate faster than this have smaller magnetospheric sizes than that of the Earth magnetosphere. Because many latedM stars are fast rotators, conditions for terrestrial planets to harbour Earthsized magnetospheres are more easily achieved for planets orbiting slowly rotating early and middM stars.
Description: A.A.V. acknowledges support from the Royal Astronomical Society through a postdoctoral fellowship. J.M. acknowledges support from a fellowship of the Alexander von Humboldt foundation. P.L. acknowledges funding from a STFC scholarship. AJBR is a Research Fellow of the Royal Commission for the Exhibition of 1851.
Mon, 02 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5462
20130902T00:00:00Z
Vidotto, A.A.
Jardine, M.
Morin, J.
Donati, J.F.
Lang, P.
Russell, A.J.B.
We investigate the effect of the magnetic fields of M dwarf (dM) stars on potentially habitable Earthlike planets. These fields can reduce the size of planetary magnetospheres to such an extent that a significant fraction of the planet’s atmosphere may be exposed to erosion by the stellar wind. We used a sample of 15 active dM stars, for which surface magneticfield maps were reconstructed, to determine the magnetic pressure at the planet orbit and hence the largest size of its magnetosphere, which would only be decreased by considering the stellar wind. Our method provides a fast means to assess which planets are most affected by the stellar magnetic field, which can be used as a first study to be followed by more sophisticated models. We show that hypothetical Earthlike planets with similar terrestrial magnetisation (~1 G) orbiting at the inner (outer) edge of the habitable zone of these stars would present magnetospheres that extend at most up to 6 (11.7) planetary radii. To be able to sustain an Earthsized magnetosphere, with the exception of only a few cases, the terrestrial planet would either (1) need to orbit significantly farther out than the traditional limits of the habitable zone; or else, (2) if it were orbiting within the habitable zone, it would require at least a magnetic field ranging from a few G to up to a few thousand G. By assuming a magnetospheric size that is more appropriate for the youngEarth (3.4 Gyr ago), the required planetary magnetic fields are one order of magnitude weaker. However, in this case, the polarcap area of the planet, which is unprotected from transport of particles to/from interplanetary space, is twice as large. At present, we do not know how small the smallest area of the planetary surface is that could be exposed and would still not affect the potential for formation and development of life in a planet. As the star becomes older and, therefore, its rotation rate and magnetic field reduce, the interplanetary magnetic pressure decreases and the magnetosphere of planets probably expands. Using an empirically derived rotationactivity/magnetism relation, we provide an analytical expression for estimating the shortest stellar rotation period for which an Earthanalogue in the habitable zone could sustain an Earthsized magnetosphere. We find that the required rotation rate of the early and middM stars (with periods ≳37–202 days) is slower than the solar one, and even slower for the latedM stars (≳63–263 days). Planets orbiting in the habitable zone of dM stars that rotate faster than this have smaller magnetospheric sizes than that of the Earth magnetosphere. Because many latedM stars are fast rotators, conditions for terrestrial planets to harbour Earthsized magnetospheres are more easily achieved for planets orbiting slowly rotating early and middM stars.

On the nature of reconnection at a solar coronal null point above a separatrix dome
http://hdl.handle.net/10023/5459
Abstract: Threedimensional magnetic null points are ubiquitous in the solar corona and in any generic mixedpolarity magnetic field. We consider magnetic reconnection at an isolated coronal null point whose fan field lines form a dome structure. Using analytical and computational models, we demonstrate several features of spinefan reconnection at such a null, including the fact that substantial magnetic flux transfer from one region of field line connectivity to another can occur. The flux transfer occurs across the current sheet that forms around the null point during spinefan reconnection, and there is no separator present. Also, flipping of magnetic field lines takes place in a manner similar to that observed in the quasiseparatrix layer or sliprunning reconnection.
Tue, 10 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5459
20130910T00:00:00Z
Pontin, D. I.
Priest, E. R.
Galsgaard, K.
Threedimensional magnetic null points are ubiquitous in the solar corona and in any generic mixedpolarity magnetic field. We consider magnetic reconnection at an isolated coronal null point whose fan field lines form a dome structure. Using analytical and computational models, we demonstrate several features of spinefan reconnection at such a null, including the fact that substantial magnetic flux transfer from one region of field line connectivity to another can occur. The flux transfer occurs across the current sheet that forms around the null point during spinefan reconnection, and there is no separator present. Also, flipping of magnetic field lines takes place in a manner similar to that observed in the quasiseparatrix layer or sliprunning reconnection.

Numerical simulation of a selfsimilar cascade of filament instabilities in the surface quasigeostrophic system
http://hdl.handle.net/10023/5436
Abstract: We provide numerical evidence for the existence of a cascade of filament instabilities in the surface quasigeostrophic system for rotating, stratified flow near a horizontal boundary. The cascade involves geometrically shrinking spatial and temporal scales and implies the singular collapse of the filament width to zero in a finite time. The numerical method is both spatially and temporally adaptive, permitting the accurate simulation of the evolution over an unprecedented range of spatial scales spanning over ten orders of magnitude. It provides the first convincing demonstration of the cascade, in which the large separation of scales between subsequent instabilities has made previous numerical simulation difficult.
Fri, 11 Apr 2014 00:00:00 GMT
http://hdl.handle.net/10023/5436
20140411T00:00:00Z
Scott, R. K.
Dritschel, D. G.
We provide numerical evidence for the existence of a cascade of filament instabilities in the surface quasigeostrophic system for rotating, stratified flow near a horizontal boundary. The cascade involves geometrically shrinking spatial and temporal scales and implies the singular collapse of the filament width to zero in a finite time. The numerical method is both spatially and temporally adaptive, permitting the accurate simulation of the evolution over an unprecedented range of spatial scales spanning over ten orders of magnitude. It provides the first convincing demonstration of the cascade, in which the large separation of scales between subsequent instabilities has made previous numerical simulation difficult.

On magnetic reconnection and flux rope topology in solar flux emergence
http://hdl.handle.net/10023/5393
Abstract: We present an analysis of the formation of atmospheric flux ropes in a magnetohydrodynamic solar flux emergence simulation. The simulation domain ranges from the top of the solar interior to the low corona. A twisted magnetic flux tube emerges from the solar interior and into the atmosphere where it interacts with the ambient magnetic field. By studying the connectivity of the evolving magnetic field, we are able to better understand the process of flux rope formation in the solar atmosphere. In the simulation, two flux ropes are produced as a result of flux emergence. Each has a different evolution resulting in different topological structures. These are determined by plasma flows and magnetic reconnection. As the flux rope is the basic structure of the coronal mass ejection, we discuss the implications of our findings for solar eruptions.
Fri, 21 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/5393
20140221T00:00:00Z
MacTaggart, David
Haynes, Andrew Lewis
We present an analysis of the formation of atmospheric flux ropes in a magnetohydrodynamic solar flux emergence simulation. The simulation domain ranges from the top of the solar interior to the low corona. A twisted magnetic flux tube emerges from the solar interior and into the atmosphere where it interacts with the ambient magnetic field. By studying the connectivity of the evolving magnetic field, we are able to better understand the process of flux rope formation in the solar atmosphere. In the simulation, two flux ropes are produced as a result of flux emergence. Each has a different evolution resulting in different topological structures. These are determined by plasma flows and magnetic reconnection. As the flux rope is the basic structure of the coronal mass ejection, we discuss the implications of our findings for solar eruptions.

Inertialrange dynamics and scaling laws of twodimensional magnetic turbulence in the weakfield regime
http://hdl.handle.net/10023/5358
Abstract: We study inertialrange dynamics and scaling laws in unforced twodimensional magnetohydrodynamic turbulence in the regime of moderately small and small initial magnetictokinetic energy ratio $r_0$, with an emphasis on the latter. The regime of small $r_0$ corresponds to a relatively weak field and strong magnetic stretching, whereby the turbulence is characterized by an intense conversion of kinetic into magnetic energy (dynamo action in the threedimensional context). This conversion is an inertialrange phenomenon and, upon becoming quasisaturated, deposits the converted energy within the inertial range rather than transferring it to the small scales. As a result, the magnetic energy spectrum $E_\b(k)$ in the inertial range can become quite shallow and may not be adequately explained or understood in terms of conventional cascade theories. It is demonstrated by numerical simulations at high Reynolds numbers (and unity magnetic Prandtl number) that the energetics and inertialrange scaling depend strongly on $r_0$. In particular, for fully developed turbulence with $r_0$ in the range $[1/4,1/4096]$, $E_\b(k)$ is found to scale as $k^{\alpha}$, where $\alpha\gtrsim1$, including $\alpha>0$. The extent of such a shallow spectrum is limited, becoming broader as $r_0$ is decreased. The slope $\alpha$ increases as $r_0$ is decreased, appearing to tend to $+1$ in the limit of small $r_0$. This implies equipartition of magnetic energy among the Fourier modes of the inertial range and the scaling $k^{1}$ of the magnetic potential variance, whose flux is direct rather than inverse. This behavior of the potential resembles that of a passive scalar. However, unlike a passive scalar whose variance dissipation rate slowly vanishes in the diffusionless limit, the dissipation rate of the magnetic potential variance scales linearly with the diffusivity in that limit. Meanwhile, the kinetic energy spectrum is relatively steep, followed by a much shallower tail due to strong antidynamo excitation. This gives rise to a total energy spectrum poorly obeying a powerlaw scaling.
Description: The work reported here was partially supported by an EPSRC postgraduate studentship to L.A.K.B. L.A.K.B. was further supported by an EPSRC doctoral prize.
Thu, 21 Aug 2014 00:00:00 GMT
http://hdl.handle.net/10023/5358
20140821T00:00:00Z
Blackbourn, Luke Austen Kazimierz
Tran, Chuong Van
We study inertialrange dynamics and scaling laws in unforced twodimensional magnetohydrodynamic turbulence in the regime of moderately small and small initial magnetictokinetic energy ratio $r_0$, with an emphasis on the latter. The regime of small $r_0$ corresponds to a relatively weak field and strong magnetic stretching, whereby the turbulence is characterized by an intense conversion of kinetic into magnetic energy (dynamo action in the threedimensional context). This conversion is an inertialrange phenomenon and, upon becoming quasisaturated, deposits the converted energy within the inertial range rather than transferring it to the small scales. As a result, the magnetic energy spectrum $E_\b(k)$ in the inertial range can become quite shallow and may not be adequately explained or understood in terms of conventional cascade theories. It is demonstrated by numerical simulations at high Reynolds numbers (and unity magnetic Prandtl number) that the energetics and inertialrange scaling depend strongly on $r_0$. In particular, for fully developed turbulence with $r_0$ in the range $[1/4,1/4096]$, $E_\b(k)$ is found to scale as $k^{\alpha}$, where $\alpha\gtrsim1$, including $\alpha>0$. The extent of such a shallow spectrum is limited, becoming broader as $r_0$ is decreased. The slope $\alpha$ increases as $r_0$ is decreased, appearing to tend to $+1$ in the limit of small $r_0$. This implies equipartition of magnetic energy among the Fourier modes of the inertial range and the scaling $k^{1}$ of the magnetic potential variance, whose flux is direct rather than inverse. This behavior of the potential resembles that of a passive scalar. However, unlike a passive scalar whose variance dissipation rate slowly vanishes in the diffusionless limit, the dissipation rate of the magnetic potential variance scales linearly with the diffusivity in that limit. Meanwhile, the kinetic energy spectrum is relatively steep, followed by a much shallower tail due to strong antidynamo excitation. This gives rise to a total energy spectrum poorly obeying a powerlaw scaling.

Distribution of electric currents in solar active regions
http://hdl.handle.net/10023/5322
Abstract: There has been a longstanding debate on the question of whether or not electric currents in solar active regions are neutralized. That is, whether or not the main (or direct) coronal currents connecting the active region polarities are surrounded by shielding (or return) currents of equal total value and opposite direction. Both theory and observations are not yet fully conclusive regarding this question, and numerical simulations have, surprisingly, barely been used to address it. Here we quantify the evolution of electric currents during the formation of a bipolar active region by considering a threedimensional magnetohydrodynamic simulation of the emergence of a subphotospheric, currentneutralized magnetic flux rope into the solar atmosphere. We find that a strong deviation from current neutralization develops simultaneously with the onset of significant flux emergence into the corona, accompanied by the development of substantial magnetic shear along the active region's polarity inversion line. After the region has formed and flux emergence has ceased, the strong magnetic fields in the region's center are connected solely by direct currents, and the total direct current is several times larger than the total return current. These results suggest that active regions, the main sources of coronal mass ejections and flares, are born with substantial net currents, in agreement with recent observations. Furthermore, they support eruption models that employ preeruption magnetic fields containing such currents.
Description: The contributions of T.T., V.S.T., and Z.M. were supported by NASA's HTP, LWS, and SR&T programs. J.E.L and M.G.L. were supported by NASA/LWS. M.G.L. received support also from the ONR 6.1 program. The simulation was performed under grant of computer time from the D.o.D. HPC Program. B.K. was supported by the DFG. V.A. acknowledges support through the IEF272549 grant.
Mon, 10 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/5322
20140210T00:00:00Z
Török, T.
Leake, J.E.
Titov, V.S.
Archontis, V.
Mikić, Z.
Linton, M.G.
Dalmasse, K.
Aulanier, G.
Kliem, B.
There has been a longstanding debate on the question of whether or not electric currents in solar active regions are neutralized. That is, whether or not the main (or direct) coronal currents connecting the active region polarities are surrounded by shielding (or return) currents of equal total value and opposite direction. Both theory and observations are not yet fully conclusive regarding this question, and numerical simulations have, surprisingly, barely been used to address it. Here we quantify the evolution of electric currents during the formation of a bipolar active region by considering a threedimensional magnetohydrodynamic simulation of the emergence of a subphotospheric, currentneutralized magnetic flux rope into the solar atmosphere. We find that a strong deviation from current neutralization develops simultaneously with the onset of significant flux emergence into the corona, accompanied by the development of substantial magnetic shear along the active region's polarity inversion line. After the region has formed and flux emergence has ceased, the strong magnetic fields in the region's center are connected solely by direct currents, and the total direct current is several times larger than the total return current. These results suggest that active regions, the main sources of coronal mass ejections and flares, are born with substantial net currents, in agreement with recent observations. Furthermore, they support eruption models that employ preeruption magnetic fields containing such currents.

Recurrent explosive eruptions and the "sigmoidtoarcade" transformation in the Sun driven by dynamical magnetic flux emergence
http://hdl.handle.net/10023/5319
Abstract: We report on threedimensional MHD simulations of recurrent mini coronal mass ejection (CME)like eruptions in a small active region (AR), which is formed by the dynamical emergence of a twisted (not kink unstable) flux tube from the solar interior. The eruptions develop as a result of the repeated formation and expulsion of new flux ropes due to continuous emergence and reconnection of sheared field lines along the polarity inversion line of the AR. The acceleration of the eruptions is triggered by tethercutting reconnection at the current sheet underneath the erupting field. We find that each explosive eruption is followed by reformation of a sigmoidal structure and a subsequent "sigmoidtoflare arcade" transformation in the AR. These results might have implications for recurrent CMEs and eruptive sigmoids/flares observations and theoretical studies.
Description: The authors acknowledge support by EU (IEF272549 grant) and the Royal Society.
Sat, 10 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5319
20140510T00:00:00Z
Archontis, V.
Hood, A.W.
Tsinganos, K.
We report on threedimensional MHD simulations of recurrent mini coronal mass ejection (CME)like eruptions in a small active region (AR), which is formed by the dynamical emergence of a twisted (not kink unstable) flux tube from the solar interior. The eruptions develop as a result of the repeated formation and expulsion of new flux ropes due to continuous emergence and reconnection of sheared field lines along the polarity inversion line of the AR. The acceleration of the eruptions is triggered by tethercutting reconnection at the current sheet underneath the erupting field. We find that each explosive eruption is followed by reformation of a sigmoidal structure and a subsequent "sigmoidtoflare arcade" transformation in the AR. These results might have implications for recurrent CMEs and eruptive sigmoids/flares observations and theoretical studies.

Observations of a hybrid doublestreamer/pseudostreamer in the solar corona
http://hdl.handle.net/10023/5318
Abstract: We report on the first observation of a single hybrid magnetic structure that contains both a pseudostreamer and a double streamer. This structure was originally observed by the SWAP instrument on board the PROBA2 satellite between 2013 May 5 and 10. It consists of a pair of filament channels near the south pole of the Sun. On the western edge of the structure, the magnetic morphology above the filaments is that of a sidebyside double streamer, with open field between the two channels. On the eastern edge, the magnetic morphology is that of a coronal pseudostreamer without the central open field. We investigated this structure with multiple observations and modeling techniques. We describe the topology and dynamic consequences of such a unified structure.
Description: D.B.S. and L.A.R. acknowledge support from the Belgian Federal Science Policy Office (BELSPO) through the ESAPRODEX program, grant No. 4000103240. S.J.P. acknowledges the financial support of the Isle of Man Government.
Tue, 20 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5318
20140520T00:00:00Z
Rachmeler, L.A.
Platten, S.J.
Bethge, C.
Seaton, D.B.
Yeates, A.R.
We report on the first observation of a single hybrid magnetic structure that contains both a pseudostreamer and a double streamer. This structure was originally observed by the SWAP instrument on board the PROBA2 satellite between 2013 May 5 and 10. It consists of a pair of filament channels near the south pole of the Sun. On the western edge of the structure, the magnetic morphology above the filaments is that of a sidebyside double streamer, with open field between the two channels. On the eastern edge, the magnetic morphology is that of a coronal pseudostreamer without the central open field. We investigated this structure with multiple observations and modeling techniques. We describe the topology and dynamic consequences of such a unified structure.

Clusters of small eruptive flares produced by magnetic reconnection in the Sun
http://hdl.handle.net/10023/5316
Abstract: We report on the formation of small solar flares produced by patchy magnetic reconnection between interacting magnetic loops. A threedimensional (3D) magnetohydrodynamic (MHD) numerical experiment was performed, where a uniform magnetic flux sheet was injected into a fully developed convective layer. The gradual emergence of the field into the solar atmosphere results in a network of magnetic loops, which interact dynamically forming current layers at their interfaces. The formation and ejection of plasmoids out of the current layers leads to patchy reconnection and the spontaneous formation of several small (size ≈12 Mm) flares. We find that these flares are shortlived (30 s3 minutes) bursts of energy in the range O(10251027) erg, which is basically the nanoflaremicroflare range. Their persistent formation and cooperative action and evolution leads to recurrent emission of fast EUV/Xray jets and considerable plasma heating in the active corona.
Description: This research was supported by the Research Council of Norway through the grant "Solar Atmospheric Modelling" and through grants of computing time from the Programme for Supercomputing, by the European Research Council under the European Union's Seventh Framework Programme (FP7/20072013)/ERC Grant agreement No. 291058 and by computing project s1061 from the High End Computing Division of NASA. The authors acknowledge support by the EU (IEF272549 grant) and the Royal Society.
Tue, 10 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/5316
20140610T00:00:00Z
Archontis, V.
Hansteen, V.
We report on the formation of small solar flares produced by patchy magnetic reconnection between interacting magnetic loops. A threedimensional (3D) magnetohydrodynamic (MHD) numerical experiment was performed, where a uniform magnetic flux sheet was injected into a fully developed convective layer. The gradual emergence of the field into the solar atmosphere results in a network of magnetic loops, which interact dynamically forming current layers at their interfaces. The formation and ejection of plasmoids out of the current layers leads to patchy reconnection and the spontaneous formation of several small (size ≈12 Mm) flares. We find that these flares are shortlived (30 s3 minutes) bursts of energy in the range O(10251027) erg, which is basically the nanoflaremicroflare range. Their persistent formation and cooperative action and evolution leads to recurrent emission of fast EUV/Xray jets and considerable plasma heating in the active corona.

Active region emission measure distributions and implications for nanoflare heating
http://hdl.handle.net/10023/5305
Abstract: The temperature dependence of the emission measure (EM) in the core of active regions coronal loops is an important diagnostic of heating processes. Observations indicate that EM(T) ~ T a below approximately 4 MK, with 2 < a < 5. Zerodimensional hydrodynamic simulations of nanoflare trains are used to demonstrate the dependence of a on the time between individual nanoflares (NT) and the distribution of nanoflare energies. If TN is greater than a few thousand seconds, a < 3. For smaller values, trains of equally spaced nanoflares cannot account for the observed range of a if the distribution of nanoflare energies is either constant, randomly distributed, or a power law. Power law distributions where there is a delay between consecutive nanoflares proportional to the energy of the second nanoflare do lead to the observed range of a. However, TN must then be of the order of hundreds to no more than a few thousand seconds. If a nanoflare leads to the relaxation of a stressed coronal field to a nearpotential state, the time taken to build up the required magnetic energy is thus too long to account for the EM measurements. Instead, it is suggested that a nanoflare involves the relaxation from one stressed coronal state to another, dissipating only a small fraction of the available magnetic energy. A consequence is that nanoflare energies may be smaller than previously envisioned.
Thu, 20 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/5305
20140320T00:00:00Z
Cargill, P.J.
The temperature dependence of the emission measure (EM) in the core of active regions coronal loops is an important diagnostic of heating processes. Observations indicate that EM(T) ~ T a below approximately 4 MK, with 2 < a < 5. Zerodimensional hydrodynamic simulations of nanoflare trains are used to demonstrate the dependence of a on the time between individual nanoflares (NT) and the distribution of nanoflare energies. If TN is greater than a few thousand seconds, a < 3. For smaller values, trains of equally spaced nanoflares cannot account for the observed range of a if the distribution of nanoflare energies is either constant, randomly distributed, or a power law. Power law distributions where there is a delay between consecutive nanoflares proportional to the energy of the second nanoflare do lead to the observed range of a. However, TN must then be of the order of hundreds to no more than a few thousand seconds. If a nanoflare leads to the relaxation of a stressed coronal field to a nearpotential state, the time taken to build up the required magnetic energy is thus too long to account for the EM measurements. Instead, it is suggested that a nanoflare involves the relaxation from one stressed coronal state to another, dissipating only a small fraction of the available magnetic energy. A consequence is that nanoflare energies may be smaller than previously envisioned.

Space exploration using parallel orbits : a study in parallel symbolic computing
http://hdl.handle.net/10023/5303
Abstract: Orbit enumerations represent an important class of mathematical algorithms which is widely used in computational discrete mathematics. In this paper, we present a new sharedmemory implementation of a generic Orbit skeleton in the GAP computer algebra system [5]. By defining a skeleton, we are easily able to capture a wide variety of concrete Orbit enumerations that can exploit the same underlying parallel implementation. We also propose a generic cost model for predicting the speedups that our Orbit skeleton will deliver for a given application on a given parallel system. We demonstrate the scalability of our implementation on a 64core sharedmemory machine. Our results show that we are able to obtain good speedups over sequential GAP programs (up to 25.27 on 64 cores).
Sun, 01 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5303
20130901T00:00:00Z
Janjic, Vladimir
Brown, Christopher Mark
Neunhoeffer, Max
Hammond, Kevin
Linton, Stephen Alexander
Loidl, HansWolfgang
Orbit enumerations represent an important class of mathematical algorithms which is widely used in computational discrete mathematics. In this paper, we present a new sharedmemory implementation of a generic Orbit skeleton in the GAP computer algebra system [5]. By defining a skeleton, we are easily able to capture a wide variety of concrete Orbit enumerations that can exploit the same underlying parallel implementation. We also propose a generic cost model for predicting the speedups that our Orbit skeleton will deliver for a given application on a given parallel system. We demonstrate the scalability of our implementation on a 64core sharedmemory machine. Our results show that we are able to obtain good speedups over sequential GAP programs (up to 25.27 on 64 cores).

Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope
http://hdl.handle.net/10023/5291
Abstract: The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the currentcarrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions.
Description: B.K. acknowledges support by the Chinese Academy of Sciences under grant No. 2012T1J0017. He also acknowledges support by the DFG, the STFC, and the NSF. J.L.'s work was supported by 973 Program grants 2013CB815103 and 2011CB811403, NSFC grants 11273055, and 11333007, and CAS grant KJCX2EWT07 to Yunnan Observatory. E.R.P. is grateful to the Leverhulme Trust for financial support. The contribution of T.T. was supported by NASA's HTP, LWS, and SR&T programs and by NSF.
Tue, 01 Jul 2014 00:00:00 GMT
http://hdl.handle.net/10023/5291
20140701T00:00:00Z
Kliem, B.
Lin, J.
Forbes, T. G.
Priest, E. R.
Toeroek, T.
The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the currentcarrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions.

Loss cone evolution and particle escape in collapsing magnetic trap models in solar flares
http://hdl.handle.net/10023/5275
Abstract: Context. Collapsing magnetic traps (CMTs) have been suggested as one possible mechanism responsible for the acceleration of highenergy particles during solar flares. An important question regarding the CMT acceleration mechanism is which particle orbits escape and which are trapped during the time evolution of a CMT. While some models predict the escape of the majority of particle orbits, other more sophisticated CMT models show that, in particular, the highestenergy particles remain trapped at all times. The exact prediction is not straightforward because both the loss cone angle and the particle orbit pitch angle evolve in time in a CMT. Aims. Our aim is to gain a better understanding of the conditions leading to either particle orbit escape or trapping in CMTs. Methods. We present a detailed investigation of the time evolution of particle orbit pitch angles in the CMT model of Giuliani and collaborators and compare this with the time evolution of the loss cone angle. The nonrelativistic guiding centre approximation is used to calculate the particle orbits. We also use simplified models to corroborate the findings of the particle orbit calculations. Results. We find that there is a critical initial pitch angle for each field line of a CMT that divides trapped and escaping particle orbits. This critical initial pitch angle is greater than the initial loss cone angle, but smaller than the asymptotic (final) loss cone angle for that field line. As the final loss cone angle in CMTs is larger than the initial loss cone angle, particle orbits with pitch angles that cross into the loss cone during their time evolution will escape whereas all other particle orbits are trapped. We find that in realistic CMT models, Fermi acceleration will only dominate in the initial phase of the CMT evolution and, in this case, can reduce the pitch angle, but that betatron acceleration will dominate for later stages of the CMT evolution leading to a systematic increase of the pitch angle. Whether a particle escapes or remains trapped depends critically on the relative importance of the two acceleration mechanisms, which cannot be decoupled in more sophisticated CMT models.
Description: This work was financially supported by the UK’s Science and Technology Facilities Council.
Wed, 12 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/5275
20140312T00:00:00Z
Neukirch, Thomas
Eradat Oskoui, Solmaz
Grady, Keith James
Context. Collapsing magnetic traps (CMTs) have been suggested as one possible mechanism responsible for the acceleration of highenergy particles during solar flares. An important question regarding the CMT acceleration mechanism is which particle orbits escape and which are trapped during the time evolution of a CMT. While some models predict the escape of the majority of particle orbits, other more sophisticated CMT models show that, in particular, the highestenergy particles remain trapped at all times. The exact prediction is not straightforward because both the loss cone angle and the particle orbit pitch angle evolve in time in a CMT. Aims. Our aim is to gain a better understanding of the conditions leading to either particle orbit escape or trapping in CMTs. Methods. We present a detailed investigation of the time evolution of particle orbit pitch angles in the CMT model of Giuliani and collaborators and compare this with the time evolution of the loss cone angle. The nonrelativistic guiding centre approximation is used to calculate the particle orbits. We also use simplified models to corroborate the findings of the particle orbit calculations. Results. We find that there is a critical initial pitch angle for each field line of a CMT that divides trapped and escaping particle orbits. This critical initial pitch angle is greater than the initial loss cone angle, but smaller than the asymptotic (final) loss cone angle for that field line. As the final loss cone angle in CMTs is larger than the initial loss cone angle, particle orbits with pitch angles that cross into the loss cone during their time evolution will escape whereas all other particle orbits are trapped. We find that in realistic CMT models, Fermi acceleration will only dominate in the initial phase of the CMT evolution and, in this case, can reduce the pitch angle, but that betatron acceleration will dominate for later stages of the CMT evolution leading to a systematic increase of the pitch angle. Whether a particle escapes or remains trapped depends critically on the relative importance of the two acceleration mechanisms, which cannot be decoupled in more sophisticated CMT models.

The solar cycle variation of topological structures in the global solar corona
http://hdl.handle.net/10023/5271
Abstract: Context. The complicated distribution of magnetic flux across the solar photosphere results in a complex web of coronal magnetic field structures. To understand this complexity, the magnetic skeleton of the coronal field can be calculated. The skeleton highlights the (separatrix) surfaces that divide the field into topologically distinct regions, allowing openfield regions on the solar surface to be located. Furthermore, separatrix surfaces and their intersections with other separatrix surfaces (i.e., separators) are important likely energy release sites. Aims. The aim of this paper is to investigate, throughout the solar cycle, the nature of coronal magneticfield topologies that arise under the potentialfield sourcesurface approximation. In particular, we characterise the typical global fields at solar maximum and minimum. Methods. Global magnetic fields are extrapolated from observed Kitt Peak and SOLIS synoptic magnetograms, from Carrington rotations 1645 to 2144, using the potentialfield sourcesurface model. This allows the variations in the coronal skeleton to be studied over three solar cycles. Results. The main building blocks which make up magnetic fields are identified and classified according to the nature of their separatrix surfaces. The magnetic skeleton reveals that, at solar maximum, the global coronal field involves a multitude of topological structures at all latitudes crisscrossing throughout the atmosphere. Many openfield regions exist originating anywhere on the photosphere. At solar minimum, the coronal topology is heavily influenced by the solar magnetic dipole. A strong dipole results in a simple largescale structure involving just two large polar openfield regions, but, at short radial distances between ± 60° latitude, the smallscale topology is complex. If the solar magnetic dipole if weak, as in the recent minimum, then the lowlatitude quietsun magnetic fields may be globally significant enough to create many disconnected openfield regions between ± 60° latitude, in addition to the two polar openfield regions.
Description: S.J.P. acknowledges financial support from the Isle of Man Government. E.R.P. is grateful to the Leverhulme Trust for his emeritus fellowship. The research leading to these results has received funding from the European Commission’s Seventh Framework Programme (FP7/20072013) under the grant agreement SWIFF (project No. 263340, www.swiff.eu).
Thu, 01 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5271
20140501T00:00:00Z
Platten, S.J.
Parnell, C.E.
Haynes, A.L.
Priest, E.R.
MacKay, D.H.
Context. The complicated distribution of magnetic flux across the solar photosphere results in a complex web of coronal magnetic field structures. To understand this complexity, the magnetic skeleton of the coronal field can be calculated. The skeleton highlights the (separatrix) surfaces that divide the field into topologically distinct regions, allowing openfield regions on the solar surface to be located. Furthermore, separatrix surfaces and their intersections with other separatrix surfaces (i.e., separators) are important likely energy release sites. Aims. The aim of this paper is to investigate, throughout the solar cycle, the nature of coronal magneticfield topologies that arise under the potentialfield sourcesurface approximation. In particular, we characterise the typical global fields at solar maximum and minimum. Methods. Global magnetic fields are extrapolated from observed Kitt Peak and SOLIS synoptic magnetograms, from Carrington rotations 1645 to 2144, using the potentialfield sourcesurface model. This allows the variations in the coronal skeleton to be studied over three solar cycles. Results. The main building blocks which make up magnetic fields are identified and classified according to the nature of their separatrix surfaces. The magnetic skeleton reveals that, at solar maximum, the global coronal field involves a multitude of topological structures at all latitudes crisscrossing throughout the atmosphere. Many openfield regions exist originating anywhere on the photosphere. At solar minimum, the coronal topology is heavily influenced by the solar magnetic dipole. A strong dipole results in a simple largescale structure involving just two large polar openfield regions, but, at short radial distances between ± 60° latitude, the smallscale topology is complex. If the solar magnetic dipole if weak, as in the recent minimum, then the lowlatitude quietsun magnetic fields may be globally significant enough to create many disconnected openfield regions between ± 60° latitude, in addition to the two polar openfield regions.

Dynamic properties of bright points in an active region
http://hdl.handle.net/10023/5264
Abstract: Context. Bright points (BPs) are smallscale, magnetic features ubiquitous across the solar surface. Previously, we have observed and noted their properties for quiet Sun regions. Here, we determine the dynamic properties of BPs using simultaneous quiet Sun and active region data. Aims. The aim of this paper is to compare the properties of BPs in both active and quiet Sun regions and to determine any difference in the dynamics and general properties of BPs as a result of the varying magnetic activity within these two regions. Methods. High spatial and temporal resolution Gband observations of active region AR11372 were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope. Three subfields of varying polarity and magnetic flux density were selected with the aid of magnetograms obtained from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Bright points within these subfields were subsequently tracked and analysed. Results. It is found that BPs within active regions display attenuated velocity distributions with an average horizontal velocity of ∼0.6 km s1, compared to the quiet region which had an average velocity of 0.9 km s1. Active region BPs are also ∼21% larger than quiet region BPs and have longer average lifetimes (∼132 s) than their quiet region counterparts (88 s). No preferential flow directions are observed within the active region subfields. The diffusion index (γ) is estimated at ∼1.2 for the three regions. Conclusions. We confirm that the dynamic properties of BPs arise predominately from convective motions. The presence of stronger field strengths within active regions is the likely reason behind the varying properties observed. We believe that larger amounts of magnetic flux will attenuate BP velocities by a combination of restricting motion within the intergranular lanes and by increasing the number of stagnation points produced by inhibited convection. Larger BPs are found in regions of higher magnetic flux density and we believe that lifetimes increase in active regions as the magnetic flux stabilises the BPs.
Description: This work has been supported by the UK Science and Technology Facilities Council (STFC). Observations were obtained at the National Solar Observatory, operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under cooperative agreement with the National Science Foundation. D.B.J. would like to thank the STFC for an Ernest Rutherford Fellowship. We are also grateful for support sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF under grant number FA86550913085.
Fri, 20 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/5264
20140620T00:00:00Z
Keys, P.H.
Mathioudakis, M.
Jess, D.B.
MacKay, D.H.
Keenan, F.P.
Context. Bright points (BPs) are smallscale, magnetic features ubiquitous across the solar surface. Previously, we have observed and noted their properties for quiet Sun regions. Here, we determine the dynamic properties of BPs using simultaneous quiet Sun and active region data. Aims. The aim of this paper is to compare the properties of BPs in both active and quiet Sun regions and to determine any difference in the dynamics and general properties of BPs as a result of the varying magnetic activity within these two regions. Methods. High spatial and temporal resolution Gband observations of active region AR11372 were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope. Three subfields of varying polarity and magnetic flux density were selected with the aid of magnetograms obtained from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Bright points within these subfields were subsequently tracked and analysed. Results. It is found that BPs within active regions display attenuated velocity distributions with an average horizontal velocity of ∼0.6 km s1, compared to the quiet region which had an average velocity of 0.9 km s1. Active region BPs are also ∼21% larger than quiet region BPs and have longer average lifetimes (∼132 s) than their quiet region counterparts (88 s). No preferential flow directions are observed within the active region subfields. The diffusion index (γ) is estimated at ∼1.2 for the three regions. Conclusions. We confirm that the dynamic properties of BPs arise predominately from convective motions. The presence of stronger field strengths within active regions is the likely reason behind the varying properties observed. We believe that larger amounts of magnetic flux will attenuate BP velocities by a combination of restricting motion within the intergranular lanes and by increasing the number of stagnation points produced by inhibited convection. Larger BPs are found in regions of higher magnetic flux density and we believe that lifetimes increase in active regions as the magnetic flux stabilises the BPs.

Free products in R. Thompson’s group V
http://hdl.handle.net/10023/5237
Abstract: We investigate some product structures in R. Thompson's group $ V$, primarily by studying the topological dynamics associated with $ V$'s action on the Cantor set C. We draw attention to the class D(V,C) of groups which have embeddings as demonstrative subgroups of V whose class can be used to assist in forming various products. Note that D(V,C) contains all finite groups, the free group on two generators, and Q/Z, and is closed under passing to subgroups and under taking direct products of any member by any finite member. If G≤V and H ∈ D(V,C), then G~H embeds into V. Finally, if G, H ∈ D(V,C), then G*H embeds in V. Using a dynamical approach, we also show the perhaps surprising result that Z2 * Z does not embed in V, even though V has many embedded copies of Z2 and has many embedded copies of free products of various pairs of its subgroups.
Fri, 01 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/5237
20131101T00:00:00Z
Bleak, Collin Patrick
SalazarDiaz, Olga
We investigate some product structures in R. Thompson's group $ V$, primarily by studying the topological dynamics associated with $ V$'s action on the Cantor set C. We draw attention to the class D(V,C) of groups which have embeddings as demonstrative subgroups of V whose class can be used to assist in forming various products. Note that D(V,C) contains all finite groups, the free group on two generators, and Q/Z, and is closed under passing to subgroups and under taking direct products of any member by any finite member. If G≤V and H ∈ D(V,C), then G~H embeds into V. Finally, if G, H ∈ D(V,C), then G*H embeds in V. Using a dynamical approach, we also show the perhaps surprising result that Z2 * Z does not embed in V, even though V has many embedded copies of Z2 and has many embedded copies of free products of various pairs of its subgroups.

Vortical control of forced twodimensional turbulence
http://hdl.handle.net/10023/5236
Abstract: A new numerical technique for the simulation of forced twodimensional turbulence[D. Dritschel and J. Fontane, “The combined Lagrangian advection method,” J. Comput. Phys.229, 5408–5417 (Year: 2010)10.1016/j.jcp.2010.03.048] is used to examine the validity of KraichnanBatchelor scaling laws at higher Reynolds number than previously accessible with classical pseudospectral methods, making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasisteady state. Our results support the recent finding of Scott [R. Scott, “Nonrobustness of the twodimensional turbulent inverse cascade,” Phys. Rev. E75, 046301 (Year: 2007)10.1103/PhysRevE.75.046301], namely that when a direct enstrophy cascading range is wellrepresented numerically, a steeper energy spectrum proportional to k−2 is obtained in place of the classical k −5/3 prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t −1 rather than Kraichnan's prediction of t −3/2. The deviation from Kraichnan's theory is related to the emergence of a population of vortices that dominate the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. An analytical model is proposed which closely matches the numerical spectra between the large scales and the forcing scale.
Description: Jérôme Fontane is supported by the European Community in the framework of the CONVECT project under Grant No. PIEFGA2008221003.
Mon, 14 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/5236
20130114T00:00:00Z
Fontane, Jerome Jacob Louis
Dritschel, David Gerard
Scott, Richard Kirkness
A new numerical technique for the simulation of forced twodimensional turbulence[D. Dritschel and J. Fontane, “The combined Lagrangian advection method,” J. Comput. Phys.229, 5408–5417 (Year: 2010)10.1016/j.jcp.2010.03.048] is used to examine the validity of KraichnanBatchelor scaling laws at higher Reynolds number than previously accessible with classical pseudospectral methods, making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasisteady state. Our results support the recent finding of Scott [R. Scott, “Nonrobustness of the twodimensional turbulent inverse cascade,” Phys. Rev. E75, 046301 (Year: 2007)10.1103/PhysRevE.75.046301], namely that when a direct enstrophy cascading range is wellrepresented numerically, a steeper energy spectrum proportional to k−2 is obtained in place of the classical k −5/3 prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t −1 rather than Kraichnan's prediction of t −3/2. The deviation from Kraichnan's theory is related to the emergence of a population of vortices that dominate the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. An analytical model is proposed which closely matches the numerical spectra between the large scales and the forcing scale.

Indeterminacy and instability in Petschek reconnection
http://hdl.handle.net/10023/5234
Abstract: We explain two puzzling aspects of Petschek's model for fast reconnection. One is its failure to occur in plasma simulations with uniform resistivity. The other is its inability to provide anything more than an upper limit for the reconnection rate. We have found that previously published analytical solutions based on Petschek's model are structurally unstable if the electrical resistivity is uniform. The structural instability is associated with the presence of an essential singularity at the Xline that is unphysical. By requiring that such a singularity does not exist, we obtain a formula that predicts a specific rate of reconnection. For uniform resistivity, reconnection can only occur at the slow, SweetParker rate. For nonuniform resistivity, reconnection can occur at a much faster rate provided that the resistivity profile is not too flat near the Xline. If this condition is satisfied, then the scale length of the nonuniformity determines the reconnection rate.
Description: This work was supported by NSF Grants ATM0734032 and AGS0962698, NASA Grants NNX08AG44G and NNX10AC04G to the University of New Hampshire, and subcontract SVT7702 from the Smithsonian Astrophysical Observatory in support of their NASA Grants NNM07AA02C and NNM07AB07C. D. B. Seaton was supported by PRODEX Grant C90193 managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office, and by Grant FP7/20072013 from the European Commission's Seventh Framework Program under the agreement eHeroes (Project No. 284461). Additional support was provided by the Leverhulme Trust to E. R. Priest.
Mon, 13 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/5234
20130513T00:00:00Z
Forbes, T.G.
Priest, E.R.
Seaton, D.B.
Litvinenko, Y.E.
We explain two puzzling aspects of Petschek's model for fast reconnection. One is its failure to occur in plasma simulations with uniform resistivity. The other is its inability to provide anything more than an upper limit for the reconnection rate. We have found that previously published analytical solutions based on Petschek's model are structurally unstable if the electrical resistivity is uniform. The structural instability is associated with the presence of an essential singularity at the Xline that is unphysical. By requiring that such a singularity does not exist, we obtain a formula that predicts a specific rate of reconnection. For uniform resistivity, reconnection can only occur at the slow, SweetParker rate. For nonuniform resistivity, reconnection can occur at a much faster rate provided that the resistivity profile is not too flat near the Xline. If this condition is satisfied, then the scale length of the nonuniformity determines the reconnection rate.

Resistive magnetohydrodynamic reconnection : resolving longterm, chaotic dynamics
http://hdl.handle.net/10023/5233
Abstract: In this paper, we address the longterm evolution of an idealised double current system entering reconnection regimes where chaotic behavior plays a prominent role. Our aim is to quantify the energetics in high magnetic Reynolds number evolutions, enriched by secondary tearing events, multiple magnetic island coalescence, and compressive versus resistive heating scenarios. Our study will pay particular attention to the required numerical resolutions achievable by modern (gridadaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shockcapturing, conservative, gridadaptive simulations for investigating trends dominated by both physical (resistivity) and numerical (resolution) parameters, and confront them with (visco)resistive magnetohydrodynamic simulations performed with very different, but equally widely used discretization schemes. This will allow us to comment on the obtained evolutions in a manner irrespective of the adopted discretization strategy. Our findings demonstrate that all schemes used (finite volume based shockcapturing, high order finite differences, and particle in celllike methods) qualitatively agree on the various evolutionary stages, and that resistivity values of order 0.001 already can lead to chaotic island appearance. However, none of the methods exploited demonstrates convergence in the strong sense in these chaotic regimes. At the same time, nonperturbed tests for showing convergence over long time scales in ideal to resistive regimes are provided as well, where all methods are shown to agree. Both the advantages and disadvantages of specific discretizations as applied to this challenging problem are discussed.
Description: We acknowledge financial support from the EC FP7/20072013 Grant Agreement SWIFF (No. 263340) and from project GOA/2009/009 (KU Leuven). This research has been funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office (IAP P7/08 CHARM). Part of the simulations used the infrastructure of the VSCFlemish Supercomputer Center, funded by the Hercules Foundation and the Flemish GovernmentDepartment EWI. Another part of the simulations was done at the former Danish Center for Scientific Computing at Copenhagen University which is now part of DeIC Danish eInfrastructure Cooperation.
Fri, 13 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5233
20130913T00:00:00Z
Keppens, R.
Porth, O.
Galsgaard, K.
Frederiksen, J.T.
Restante, A.L.
Lapenta, G.
Parnell, C.
In this paper, we address the longterm evolution of an idealised double current system entering reconnection regimes where chaotic behavior plays a prominent role. Our aim is to quantify the energetics in high magnetic Reynolds number evolutions, enriched by secondary tearing events, multiple magnetic island coalescence, and compressive versus resistive heating scenarios. Our study will pay particular attention to the required numerical resolutions achievable by modern (gridadaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shockcapturing, conservative, gridadaptive simulations for investigating trends dominated by both physical (resistivity) and numerical (resolution) parameters, and confront them with (visco)resistive magnetohydrodynamic simulations performed with very different, but equally widely used discretization schemes. This will allow us to comment on the obtained evolutions in a manner irrespective of the adopted discretization strategy. Our findings demonstrate that all schemes used (finite volume based shockcapturing, high order finite differences, and particle in celllike methods) qualitatively agree on the various evolutionary stages, and that resistivity values of order 0.001 already can lead to chaotic island appearance. However, none of the methods exploited demonstrates convergence in the strong sense in these chaotic regimes. At the same time, nonperturbed tests for showing convergence over long time scales in ideal to resistive regimes are provided as well, where all methods are shown to agree. Both the advantages and disadvantages of specific discretizations as applied to this challenging problem are discussed.

The effect of slip length on vortex rebound from a rigid boundary
http://hdl.handle.net/10023/5232
Abstract: The problem of a dipole incident normally on a rigid boundary, for moderate to large Reynolds numbers, has recently been treated numerically using a volume penalisation method by Nguyen van yen, Farge, and Schneider [Phys. Rev. Lett.106, 184502 (2011)]. Their results indicate that energy dissipating structures persist in the inviscid limit. They found that the use of penalisation methods intrinsically introduces some slip at the boundary wall, where the slip approaches zero as the Reynolds number goes to infinity, so reducing to the noslip case in this limit. We study the same problem, for both noslip and partial slip cases, using compact differences on a Chebyshev grid in the direction normal to the wall and Fourier methods in the direction along the wall. We find that for the noslip case there is no indication of the persistence of energy dissipating structures in the limit as viscosity approaches zero and that this also holds for any fixed slip length. However, when the slip length is taken to vary inversely with Reynolds number then the results of Nguyen van yen et al. are regained. It therefore appears that the prediction that energy dissipating structures persist in the inviscid limit follows from the two limits of wall slip length going to zero, and viscosity going to zero, not being treated independently in their use of the volume penalisation method.
Mon, 23 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/5232
20130923T00:00:00Z
Sutherland, D.
Macaskill, C.
Dritschel, D.G.
The problem of a dipole incident normally on a rigid boundary, for moderate to large Reynolds numbers, has recently been treated numerically using a volume penalisation method by Nguyen van yen, Farge, and Schneider [Phys. Rev. Lett.106, 184502 (2011)]. Their results indicate that energy dissipating structures persist in the inviscid limit. They found that the use of penalisation methods intrinsically introduces some slip at the boundary wall, where the slip approaches zero as the Reynolds number goes to infinity, so reducing to the noslip case in this limit. We study the same problem, for both noslip and partial slip cases, using compact differences on a Chebyshev grid in the direction normal to the wall and Fourier methods in the direction along the wall. We find that for the noslip case there is no indication of the persistence of energy dissipating structures in the limit as viscosity approaches zero and that this also holds for any fixed slip length. However, when the slip length is taken to vary inversely with Reynolds number then the results of Nguyen van yen et al. are regained. It therefore appears that the prediction that energy dissipating structures persist in the inviscid limit follows from the two limits of wall slip length going to zero, and viscosity going to zero, not being treated independently in their use of the volume penalisation method.

Progress towards numerical and experimental simulations of fusion relevant beam instabilities
http://hdl.handle.net/10023/5186
Abstract: In certain plasmas, nonthermal electron distributions can produce instabilities. These instabilities may be useful or potentially disruptive. Therefore the study of these instabilities is of importance in a variety of fields including fusion science and astrophysics. Following on from previous work conducted at the University of Strathclyde on the cyclotron resonance maser instability that was relevant to astrophysical radiowave generation, further instabilities are being investigated. Particular instabilities of interest are the anomalous Doppler instability which can occur in magnetic confinement fusion plasmas and the twostream instability that is of importance in fastignition inertial confinement fusion. To this end, computational simulations have been undertaken to investigate the behaviour of both the anomalous Doppler and twostream instabilities with the goal of designing an experiment to observe these behaviours in a laboratory.
Wed, 07 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5186
20140507T00:00:00Z
King, M.
Bryson, R.
Ronald, K.
Cairns, R. A.
McConville, S. L.
Speirs, D. C.
Phelps, A. D. R.
Bingham, R.
Gillespie, K. M.
Cross, A. W.
Vorgul, I.
Trines, R.
In certain plasmas, nonthermal electron distributions can produce instabilities. These instabilities may be useful or potentially disruptive. Therefore the study of these instabilities is of importance in a variety of fields including fusion science and astrophysics. Following on from previous work conducted at the University of Strathclyde on the cyclotron resonance maser instability that was relevant to astrophysical radiowave generation, further instabilities are being investigated. Particular instabilities of interest are the anomalous Doppler instability which can occur in magnetic confinement fusion plasmas and the twostream instability that is of importance in fastignition inertial confinement fusion. To this end, computational simulations have been undertaken to investigate the behaviour of both the anomalous Doppler and twostream instabilities with the goal of designing an experiment to observe these behaviours in a laboratory.

Scaled Experiment to Investigate Auroral Kilometric Radiation Mechanisms in the Presence of Background Electrons
http://hdl.handle.net/10023/5185
Abstract: Auroral Kilometric Radiation (AKR) emissions occur at frequencies similar to 300kHz polarised in the Xmode with efficiencies similar to 12% [1,2] in the auroral density cavity in the polar regions of the Earth's magnetosphere, a region of low density plasma similar to 3200km above the Earth's surface, where electrons are accelerated down towards the Earth whilst undergoing magnetic compression. As a result of this magnetic compression the electrons acquire a horseshoe distribution function in velocity space. Previous theoretical studies have predicted that this distribution is capable of driving the cyclotron maser instability. To test this theory a scaled laboratory experiment was constructed to replicate this phenomenon in a controlled environment, [35] whilst 2D and 3D simulations are also being conducted to predict the experimental radiation power and mode, [69]. The experiment operates in the microwave frequency regime and incorporates a region of increasing magnetic field as found at the Earth's pole using magnet solenoids to encase the cylindrical interaction waveguide through which an initially rectilinear electron beam (12A) was accelerated by a 75keV pulse. Experimental results showed evidence of the formation of the horseshoe distribution function. The radiation was produced in the near cutoff TE01 mode, comparable with Xmode characteristics, at 4.42GHz. Peak microwave output power was measured similar to 35kW and peak efficiency of emission similar to 2%, [3]. A Penning trap was constructed and inserted into the interaction waveguide to enable generation of a background plasma which would lead to closer comparisons with the magnetospheric conditions. Initial design and measurements are presented showing the principle features of the new geometry.
Wed, 07 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5185
20140507T00:00:00Z
McConville, S. L.
Ronald, K.
Speirs, D. C.
Gillespie, K. M.
Phelps, A. D. R.
Cross, A. W.
Bingham, R.
Robertson, C. W.
Whyte, C. G.
He, W.
King, M.
Bryson, R.
Vorgul, I.
Cairns, R. A.
Kellett, B. J.
Auroral Kilometric Radiation (AKR) emissions occur at frequencies similar to 300kHz polarised in the Xmode with efficiencies similar to 12% [1,2] in the auroral density cavity in the polar regions of the Earth's magnetosphere, a region of low density plasma similar to 3200km above the Earth's surface, where electrons are accelerated down towards the Earth whilst undergoing magnetic compression. As a result of this magnetic compression the electrons acquire a horseshoe distribution function in velocity space. Previous theoretical studies have predicted that this distribution is capable of driving the cyclotron maser instability. To test this theory a scaled laboratory experiment was constructed to replicate this phenomenon in a controlled environment, [35] whilst 2D and 3D simulations are also being conducted to predict the experimental radiation power and mode, [69]. The experiment operates in the microwave frequency regime and incorporates a region of increasing magnetic field as found at the Earth's pole using magnet solenoids to encase the cylindrical interaction waveguide through which an initially rectilinear electron beam (12A) was accelerated by a 75keV pulse. Experimental results showed evidence of the formation of the horseshoe distribution function. The radiation was produced in the near cutoff TE01 mode, comparable with Xmode characteristics, at 4.42GHz. Peak microwave output power was measured similar to 35kW and peak efficiency of emission similar to 2%, [3]. A Penning trap was constructed and inserted into the interaction waveguide to enable generation of a background plasma which would lead to closer comparisons with the magnetospheric conditions. Initial design and measurements are presented showing the principle features of the new geometry.

3D PiC code investigations of Auroral Kilometric Radiation mechanisms
http://hdl.handle.net/10023/5184
Abstract: Efficient (similar to 1%) electron cyclotron radio emissions are known to originate in the X mode from regions of locally depleted plasma in the Earths polar magnetosphere. These emissions are commonly referred to as the Auroral Kilometric Radiation (AKR). AKR occurs naturally in these polar regions where electrons are accelerated by electric fields into the increasing planetary magnetic dipole. Here conservation of the magnetic moment converts axial to rotational momentum forming a horseshoe distribution in velocity phase space. This distribution is unstable to cyclotron emission with radiation emitted in the Xmode. Initial studies were conducted in the form of 2D PiC code simulations [1] and a scaled laboratory experiment that was constructed to reproduce the mechanism of AKR. As studies progressed, 3D PiC code simulations were conducted to enable complete investigation of the complex interaction dimensions. A maximum efficiency of 1.25% is predicted from these simulations in the same mode and frequency as measured in the experiment. This is also consistent with geophysical observations and the predictions of theory.
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/5184
20140101T00:00:00Z
Gillespie, K. M.
McConville, S. L.
Speirs, D. C.
Ronald, K.
Phelps, A. D. R.
Bingham, R.
Cross, A. W.
Robertson, C. W.
Whyte, C. G.
He, W.
Vorgul, I.
Cairns, R. A.
Kellett, B. J.
Efficient (similar to 1%) electron cyclotron radio emissions are known to originate in the X mode from regions of locally depleted plasma in the Earths polar magnetosphere. These emissions are commonly referred to as the Auroral Kilometric Radiation (AKR). AKR occurs naturally in these polar regions where electrons are accelerated by electric fields into the increasing planetary magnetic dipole. Here conservation of the magnetic moment converts axial to rotational momentum forming a horseshoe distribution in velocity phase space. This distribution is unstable to cyclotron emission with radiation emitted in the Xmode. Initial studies were conducted in the form of 2D PiC code simulations [1] and a scaled laboratory experiment that was constructed to reproduce the mechanism of AKR. As studies progressed, 3D PiC code simulations were conducted to enable complete investigation of the complex interaction dimensions. A maximum efficiency of 1.25% is predicted from these simulations in the same mode and frequency as measured in the experiment. This is also consistent with geophysical observations and the predictions of theory.

Numerical simulation of unconstrained cyclotron resonant maser emission
http://hdl.handle.net/10023/5183
Abstract: When a mainly rectilinear electron beam is subject to significant magnetic compression, conservation of magnetic moment results in the formation of a horseshoe shaped velocity distribution. It has been shown that such a distribution is unstable to cyclotron emission and may be responsible for the generation of Auroral Kilometric Radiation (AKR) an intense rf emission sourced at high altitudes in the terrestrial auroral magnetosphere. PiC code simulations have been undertaken to investigate the dynamics of the cyclotron emission process in the absence of cavity boundaries with particular consideration of the spatial growth rate, spectral output and rf conversion efficiency. Computations reveal that a welldefined cyclotron emission process occurs albeit with a low spatial growth rate compared to waveguide bounded simulations. The rf output is near perpendicular to the electron beam with a slight backwardwave character reflected in the spectral output with a well defined peak at 2.68GHz, just below the relativistic electron cyclotron frequency. The corresponding rf conversion efficiency of 1.1% is comparable to waveguide bounded simulations and consistent with the predictions of kinetic theory that suggest efficient, spectrally well defined radiation emission can be obtained from an electron horseshoe distribution in the absence of radiation boundaries.
Wed, 07 May 2014 00:00:00 GMT
http://hdl.handle.net/10023/5183
20140507T00:00:00Z
Speirs, D. C.
Gillespie, K. M.
Ronald, K.
McConville, S. L.
Phelps, A. D. R.
Cross, A. W.
Bingham, R.
Kellett, B. J.
Cairns, R. A.
Vorgul, I.
When a mainly rectilinear electron beam is subject to significant magnetic compression, conservation of magnetic moment results in the formation of a horseshoe shaped velocity distribution. It has been shown that such a distribution is unstable to cyclotron emission and may be responsible for the generation of Auroral Kilometric Radiation (AKR) an intense rf emission sourced at high altitudes in the terrestrial auroral magnetosphere. PiC code simulations have been undertaken to investigate the dynamics of the cyclotron emission process in the absence of cavity boundaries with particular consideration of the spatial growth rate, spectral output and rf conversion efficiency. Computations reveal that a welldefined cyclotron emission process occurs albeit with a low spatial growth rate compared to waveguide bounded simulations. The rf output is near perpendicular to the electron beam with a slight backwardwave character reflected in the spectral output with a well defined peak at 2.68GHz, just below the relativistic electron cyclotron frequency. The corresponding rf conversion efficiency of 1.1% is comparable to waveguide bounded simulations and consistent with the predictions of kinetic theory that suggest efficient, spectrally well defined radiation emission can be obtained from an electron horseshoe distribution in the absence of radiation boundaries.

Laminar shocks in high power laser plasma interactions
http://hdl.handle.net/10023/5180
Abstract: We propose a theory to describe laminar ion sound structures in a collisionless plasma. Reflection of a small fraction of the upstream ions converts the well known ion acoustic soliton into a structure with a steep potential gradient upstream and with downstream oscillations. The theory provides a simple interpretation of results dating back more than forty years but, more importantly, is shown to provide an explanation for recent observations on laser produced plasmas relevant to inertial fusion and to ion acceleration. (C) 2014 AIP Publishing LLC.
Sat, 01 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/5180
20140201T00:00:00Z
Cairns, R. A.
Bingham, R.
Norreys, P.
Trines, R.
We propose a theory to describe laminar ion sound structures in a collisionless plasma. Reflection of a small fraction of the upstream ions converts the well known ion acoustic soliton into a structure with a steep potential gradient upstream and with downstream oscillations. The theory provides a simple interpretation of results dating back more than forty years but, more importantly, is shown to provide an explanation for recent observations on laser produced plasmas relevant to inertial fusion and to ion acceleration. (C) 2014 AIP Publishing LLC.

Effect of collisions on amplification of laser beams by Brillouin scattering in plasmas
http://hdl.handle.net/10023/5173
Abstract: We report on particle in cell simulations of energy transfer between a laser pump beam and a counterpropagating seed beam using the Brillouin scattering process in uniform plasma including collisions. The results presented show that the ion acoustic waves excited through naturally occurring Brillouin scattering of the pump field are preferentially damped without affecting the driven Brillouin scattering process resulting from the beating of the pump and seed fields together. We find that collisions, including the effects of Landau damping, allow for a more efficient transfer of energy between the laser beams, and a significant reduction in the amount of seed prepulse produced.
Description: Authors KH, RT, DCS, RAC, RB were supported by EPSRC grant EP/G04239X/1.
Tue, 01 Oct 2013 00:00:00 GMT
http://hdl.handle.net/10023/5173
20131001T00:00:00Z
Humphrey, K. A.
Trines, R. M. G. M.
Fiuza, F.
Speirs, D. C.
Norreys, P.
Cairns, R. A.
Silva, L. O.
Bingham, R.
We report on particle in cell simulations of energy transfer between a laser pump beam and a counterpropagating seed beam using the Brillouin scattering process in uniform plasma including collisions. The results presented show that the ion acoustic waves excited through naturally occurring Brillouin scattering of the pump field are preferentially damped without affecting the driven Brillouin scattering process resulting from the beating of the pump and seed fields together. We find that collisions, including the effects of Landau damping, allow for a more efficient transfer of energy between the laser beams, and a significant reduction in the amount of seed prepulse produced.

Quasigeostrophic shallowwater doublyconnected vortex equilibria and their stability
http://hdl.handle.net/10023/5172
Abstract: We examine the form, properties, stability and evolution of doublyconnected (twovortex) relative equilibria in the singlelayer ƒplane quasigeostrophic shallowwater model of geophysical fluid dynamics. Three parameters completely describe families of equilibria in this system: the ratio γ =L/LD between the horizontal size of the vortices and the Rossby deformation length; the area ratio α of the smaller to the larger vortex; and the minimum distance δ between the two vortices. We vary 0 < γ ≤ 10 and 0.1 ≤ α ≤ 1.0, determining the boundary of stability δ = δC(γ,α). We also examine the nonlinear development of the instabilities and the transitions to other nearequilibrium configurations. Two modes of instability occur when δ < δC: a small γ asymmetric (wave 3) mode, which is absent for α ≳ 0.6; and a large γ mode. In general, major structural changes take place during the nonlinear evolution of the vortices, which near δC may be classified as follows: (i) vacillations about equilibrium for γ ≳ 2.5; (ii) partial straining out, associated with the small γ mode, where either one or both of the vortices get smaller for γ ≲ 2.5 and α ≲ 0.6; (iii) partial merger, occurring at the transition region between the two modes of instability, where one of the vortices gets bigger, and (iv) complete merger, associated with the largeγ mode. We also find that although conservative inviscid transitions to equilibria with the same energy, angular momentum and circulation are possible, they are not the preferred evolutionary path.
Description: H.P. acknowledges the support of a NERC studentship. D.G.D. received support for this research from the UK Engineering and Physical Sciences Research Council (grant EP/H001794/1).
Wed, 01 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/5172
20130501T00:00:00Z
Plotka, Hanna
Dritschel, David Gerard
We examine the form, properties, stability and evolution of doublyconnected (twovortex) relative equilibria in the singlelayer ƒplane quasigeostrophic shallowwater model of geophysical fluid dynamics. Three parameters completely describe families of equilibria in this system: the ratio γ =L/LD between the horizontal size of the vortices and the Rossby deformation length; the area ratio α of the smaller to the larger vortex; and the minimum distance δ between the two vortices. We vary 0 < γ ≤ 10 and 0.1 ≤ α ≤ 1.0, determining the boundary of stability δ = δC(γ,α). We also examine the nonlinear development of the instabilities and the transitions to other nearequilibrium configurations. Two modes of instability occur when δ < δC: a small γ asymmetric (wave 3) mode, which is absent for α ≳ 0.6; and a large γ mode. In general, major structural changes take place during the nonlinear evolution of the vortices, which near δC may be classified as follows: (i) vacillations about equilibrium for γ ≳ 2.5; (ii) partial straining out, associated with the small γ mode, where either one or both of the vortices get smaller for γ ≲ 2.5 and α ≲ 0.6; (iii) partial merger, occurring at the transition region between the two modes of instability, where one of the vortices gets bigger, and (iv) complete merger, associated with the largeγ mode. We also find that although conservative inviscid transitions to equilibria with the same energy, angular momentum and circulation are possible, they are not the preferred evolutionary path.

The effects of acoustic misclassification on cetacean species abundance estimation
http://hdl.handle.net/10023/5163
Abstract: To estimate the density or abundance of a cetacean species using acoustic detection data, it is necessary to correctly identify the species that are detected. Developing an automated species classifier with 100% correct classification rate for any species is likely to stay out of reach. It is therefore necessary to consider the effect of misidentified detections on the number of observed data and consequently on abundance or density estimation, and develop methods to cope with these misidentifications. If misclassification rates are known, it is possible to estimate the true numbers of detected calls without bias. However, misclassification and uncertainties in the level of misclassification increase the variance of the estimates. If the true numbers of calls from different species are similar, then a small amount of misclassification between species and a small amount of uncertainty around the classification probabilities does not have an overly detrimental effect on the overall variance. However, if there is a difference in the encounter rate between species calls and/or a large amount of uncertainty in misclassification rates, then the variance of the estimates becomes very large and this dramatically increases the variance of the final abundance estimate.
Description: This work was funded through the Natural Environment Research Council and SMRU Ltd.
Wed, 25 Dec 2013 00:00:00 GMT
http://hdl.handle.net/10023/5163
20131225T00:00:00Z
Caillat, Marjolaine Annie
Thomas, Len
Gillespie, Douglas Michael
To estimate the density or abundance of a cetacean species using acoustic detection data, it is necessary to correctly identify the species that are detected. Developing an automated species classifier with 100% correct classification rate for any species is likely to stay out of reach. It is therefore necessary to consider the effect of misidentified detections on the number of observed data and consequently on abundance or density estimation, and develop methods to cope with these misidentifications. If misclassification rates are known, it is possible to estimate the true numbers of detected calls without bias. However, misclassification and uncertainties in the level of misclassification increase the variance of the estimates. If the true numbers of calls from different species are similar, then a small amount of misclassification between species and a small amount of uncertainty around the classification probabilities does not have an overly detrimental effect on the overall variance. However, if there is a difference in the encounter rate between species calls and/or a large amount of uncertainty in misclassification rates, then the variance of the estimates becomes very large and this dramatically increases the variance of the final abundance estimate.

The influence of the magnetic field on running penumbral waves in the solar chromosphere
http://hdl.handle.net/10023/5155
Abstract: We use images of high spatial and temporal resolution, obtained using both ground and spacebased instrumentation, to investigate the role magnetic field inclination angles play in the propagation characteristics of running penumbral waves in the solar chromosphere. Analysis of a nearcircular sunspot, close to the center of the solar disk, reveals a smooth rise in oscillatory period as a function of distance from the umbral barycenter. However, in one directional quadrant, corresponding to the north direction, a pronounced kink in the perioddistance diagram is found. Utilizing a combination of the inversion of magnetic Stokes vectors and forcefree field extrapolations, we attribute this behavior to the cutoff frequency imposed by the magnetic field geometry in this location. A rapid, localized inclination of the magnetic field lines in the north direction results in a faster increase in the dominant periodicity due to an accelerated reduction in the cutoff frequency. For the first time, we reveal how the spatial distribution of dominant wave periods, obtained with one of the highest resolution solar instruments currently available, directly reflects the magnetic geometry of the underlying sunspot, thus opening up a wealth of possibilities in future magnetohydrodynamic seismology studies. In addition, the intrinsic relationships we find between the underlying magnetic field geometries connecting the photosphere to the chromosphere, and the characteristics of running penumbral waves observed in the upper chromosphere, directly supports the interpretation that running penumbral wave phenomena are the chromospheric signature of upwardly propagating magnetoacoustic waves generated in the photosphere.
Description: D.B.J. acknowledges the European Commission and the Fonds Wetenschappelijk Onderzoek (FWO) for the award of a Marie Curie Pegasus Fellowship during which this work was initiated, in addition to the UK Science and Technology Facilities Council (STFC) for the award of an Ernest Rutherford Fellowship which allowed the completion of this project. The research carried out by V.E.R. is partly supported by grant MC FP7PEOPLE2011IRSES295272. T.V.D. acknowledges funding from the Odysseus Programme of the FWO Vlaanderen and from the EU's 7th Framework Programme as an ERG with grant number 276808. P.H.K. and D.H.M. are grateful to STFC for research support. This research has been funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office (IAP P7/08 CHARM).
Tue, 03 Dec 2013 00:00:00 GMT
http://hdl.handle.net/10023/5155
20131203T00:00:00Z
Jess, David
Reznikova, V
Van Doorsselaere, Tom
Mackay, Duncan Hendry
Keys, Peter
We use images of high spatial and temporal resolution, obtained using both ground and spacebased instrumentation, to investigate the role magnetic field inclination angles play in the propagation characteristics of running penumbral waves in the solar chromosphere. Analysis of a nearcircular sunspot, close to the center of the solar disk, reveals a smooth rise in oscillatory period as a function of distance from the umbral barycenter. However, in one directional quadrant, corresponding to the north direction, a pronounced kink in the perioddistance diagram is found. Utilizing a combination of the inversion of magnetic Stokes vectors and forcefree field extrapolations, we attribute this behavior to the cutoff frequency imposed by the magnetic field geometry in this location. A rapid, localized inclination of the magnetic field lines in the north direction results in a faster increase in the dominant periodicity due to an accelerated reduction in the cutoff frequency. For the first time, we reveal how the spatial distribution of dominant wave periods, obtained with one of the highest resolution solar instruments currently available, directly reflects the magnetic geometry of the underlying sunspot, thus opening up a wealth of possibilities in future magnetohydrodynamic seismology studies. In addition, the intrinsic relationships we find between the underlying magnetic field geometries connecting the photosphere to the chromosphere, and the characteristics of running penumbral waves observed in the upper chromosphere, directly supports the interpretation that running penumbral wave phenomena are the chromospheric signature of upwardly propagating magnetoacoustic waves generated in the photosphere.

Simulating the formation of a sigmoidal flux rope in AR10977 from SOHO/MDI magnetograms
http://hdl.handle.net/10023/5154
Abstract: The modeling technique of Mackay et al. is applied to simulate the coronal magnetic field of NOAA active region AR10977 over a seven day period (2007 December 210). The simulation is driven with a sequence of lineofsight component magnetograms from SOHO/MDI and evolves the coronal magnetic field though a continuous series of nonlinear forcefree states. Upon comparison with Hinode/XRT observations, results show that the simulation reproduces many features of the active region's evolution. In particular, it describes the formation of a flux rope across the polarity inversion line during flux cancellation. The flux rope forms at the same location as an observed Xray sigmoid. After five days of evolution, the free magnetic energy contained within the flux rope was found to be 3.9 × 1030 erg. This value is more than sufficient to account for the B1.4 GOES flare observed from the active region on 2007 December 7. At the time of the observed eruption, the flux rope was found to contain 20% of the active region flux. We conclude that the modeling technique proposed in Mackay et al.—which directly uses observed magnetograms to energize the coronal field—is a viable method to simulate the evolution of the coronal magnetic field.
Description: G.P.S.G. acknowledges STFC for financial support. D.H.M. acknowledges the STFC, the Leverhulme Trust, and the EU FP7 funded project "SWIFF" (263340) for financial support. L.M.G. acknowledges to the Royal Society for a University Research Fellowship. K.A.M. acknowledges the Leverhulme Trust for financial support. Simulations were carried out on a STFC/SRIF funded UKMHD cluster at St Andrews.
Thu, 20 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/5154
20140220T00:00:00Z
Gibb, Gordon Peter Samuel
Mackay, Duncan Hendry
Green, Lucie
Meyer, Karen Alison
The modeling technique of Mackay et al. is applied to simulate the coronal magnetic field of NOAA active region AR10977 over a seven day period (2007 December 210). The simulation is driven with a sequence of lineofsight component magnetograms from SOHO/MDI and evolves the coronal magnetic field though a continuous series of nonlinear forcefree states. Upon comparison with Hinode/XRT observations, results show that the simulation reproduces many features of the active region's evolution. In particular, it describes the formation of a flux rope across the polarity inversion line during flux cancellation. The flux rope forms at the same location as an observed Xray sigmoid. After five days of evolution, the free magnetic energy contained within the flux rope was found to be 3.9 × 1030 erg. This value is more than sufficient to account for the B1.4 GOES flare observed from the active region on 2007 December 7. At the time of the observed eruption, the flux rope was found to contain 20% of the active region flux. We conclude that the modeling technique proposed in Mackay et al.—which directly uses observed magnetograms to energize the coronal field—is a viable method to simulate the evolution of the coronal magnetic field.

First comparison of wave observations from CoMP and AIA/SDO
http://hdl.handle.net/10023/5153
Abstract: Context. Waves have long been thought to contribute to the heating of the solar corona and the generation of the solar wind. Recent observations have demonstrated evidence of quasiperiodic longitudinal disturbances and ubiquitous transverse wave propagation in many different coronal environments. Aims. This paper investigates signatures of different types of oscillatory behaviour, both above the solar limb and ondisk, by comparing findings from the Coronal Multichannel Polarimeter (CoMP) and the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) for the same active region. Methods. We study both transverse and longitudinal motion by comparing and contrasting timedistance images of parallel and perpendicular cuts along/across active region fan loops. Comparisons between parallel spacetime diagram features in CoMP Doppler velocity and transverse oscillations in AIA images are made, together with spacetime analysis of propagating quasiperiodic intensity features seen near the base of loops in AIA. Results. Signatures of transverse motions are observed along the same magnetic structure using CoMP Doppler velocity (vphase = 600 → 750 km s1, P = 3 → 6 min) and in AIA/SDO above the limb (P = 3 → 8 min). Quasiperiodic intensity features (vphase = 100 → 200 km s1, P = 6 → 11 min) also travel along the base of the same structure. On the disk, signatures of both transverse and longitudinal intensity features were observed by AIA, and both show similar properties to signatures found along structures anchored in the same active region three days earlier above the limb. Correlated features are recovered by spacetime analysis of neighbouring tracks over perpendicular distances of ≲2.6 Mm.
Description: I.D.M. acknowledges support of a Royal Society University Research Fellowship. The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/20072013) under the grant agreements SOLSPANET (project No. 269299, www.solspanet.eu/solspanet).
Thu, 01 Aug 2013 00:00:00 GMT
http://hdl.handle.net/10023/5153
20130801T00:00:00Z
Threlfall, James William
De Moortel, Ineke
McIntosh, Scott
Bethge, Christian
Context. Waves have long been thought to contribute to the heating of the solar corona and the generation of the solar wind. Recent observations have demonstrated evidence of quasiperiodic longitudinal disturbances and ubiquitous transverse wave propagation in many different coronal environments. Aims. This paper investigates signatures of different types of oscillatory behaviour, both above the solar limb and ondisk, by comparing findings from the Coronal Multichannel Polarimeter (CoMP) and the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) for the same active region. Methods. We study both transverse and longitudinal motion by comparing and contrasting timedistance images of parallel and perpendicular cuts along/across active region fan loops. Comparisons between parallel spacetime diagram features in CoMP Doppler velocity and transverse oscillations in AIA images are made, together with spacetime analysis of propagating quasiperiodic intensity features seen near the base of loops in AIA. Results. Signatures of transverse motions are observed along the same magnetic structure using CoMP Doppler velocity (vphase = 600 → 750 km s1, P = 3 → 6 min) and in AIA/SDO above the limb (P = 3 → 8 min). Quasiperiodic intensity features (vphase = 100 → 200 km s1, P = 6 → 11 min) also travel along the base of the same structure. On the disk, signatures of both transverse and longitudinal intensity features were observed by AIA, and both show similar properties to signatures found along structures anchored in the same active region three days earlier above the limb. Correlated features are recovered by spacetime analysis of neighbouring tracks over perpendicular distances of ≲2.6 Mm.

Erratum : "a numerical model of standard to blowout jets" (2013, ApJL, 769, L21)
http://hdl.handle.net/10023/5152
Mon, 10 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/5152
20130610T00:00:00Z
Archontis, Vasilis
Hood, Alan William

The emergence of weakly twisted magnetic fields in the Sun
http://hdl.handle.net/10023/5151
Abstract: We have studied the emergence of a weakly twisted magnetic flux tube from the upper convection zone into the solar atmosphere. It is found that the rising magnetized plasma does not undergo the classical, single Ωshaped loop emergence, but it becomes unstable in two places, forming two magnetic lobes that are anchored in smallscale bipolar structures at the photosphere, between the two main flux concentrations. The two magnetic lobes rise and expand into the corona, forming an overall undulating magnetic flux system. The dynamical interaction of the lobes results in the triggering of highspeed and hot jets and the formation of successive cool and hot loops that coexist in the emerging flux region. Although the initial emerging field is weakly twisted, a highly twisted magnetic flux rope is formed at the low atmosphere, due to shearing and reconnection. The new flux rope (hereafter postemergence flux rope) does not erupt. It remains confined by the overlying field. Although there is no ejective eruption of the postemergence rope, it is found that a considerable amount of axial and azimuthal flux is transferred into the solar atmosphere during the emergence of the magnetic field.
Description: The simulations were performed on the STFC and SRIF funded UKMHD cluster, at the University of St Andrews. K.T. and V.A. acknowledge EU support (IEF272549 grant).
Fri, 01 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/5151
20131101T00:00:00Z
Archontis, Vasilis
Hood, Alan William
Tsinganos, K
We have studied the emergence of a weakly twisted magnetic flux tube from the upper convection zone into the solar atmosphere. It is found that the rising magnetized plasma does not undergo the classical, single Ωshaped loop emergence, but it becomes unstable in two places, forming two magnetic lobes that are anchored in smallscale bipolar structures at the photosphere, between the two main flux concentrations. The two magnetic lobes rise and expand into the corona, forming an overall undulating magnetic flux system. The dynamical interaction of the lobes results in the triggering of highspeed and hot jets and the formation of successive cool and hot loops that coexist in the emerging flux region. Although the initial emerging field is weakly twisted, a highly twisted magnetic flux rope is formed at the low atmosphere, due to shearing and reconnection. The new flux rope (hereafter postemergence flux rope) does not erupt. It remains confined by the overlying field. Although there is no ejective eruption of the postemergence rope, it is found that a considerable amount of axial and azimuthal flux is transferred into the solar atmosphere during the emergence of the magnetic field.

Production of smallscale Alfvén waves by ionospheric depletion, nonlinear magnetosphereionosphere coupling and phase mixing
http://hdl.handle.net/10023/5150
Abstract: Rockets and satellites have previously observed smallscale Alfven waves inside largescale downward fieldaligned currents, and numerical simulations have associated their formation with selfconsistent magnetosphereionosphere coupling. The origin of these waves was previously attributed to ionospheric feedback instability; however, we show that they arise in numerical experiments in which the instability is excluded. A new interpretation is proposed in which strong ionospheric depletion and associated current broadening (a nonlinear steepening/wavebreaking process) form magnetosphereionosphere waves inside a downward current region and these oscillations drive upgoing inertial Alfven waves in the overlying plasma. The resulting waves are governed by characteristic periods, which are a good match to previously observed periods for reasonable assumed conditions. Meanwhile, wavelengths perpendicular to the magnetic field initially map to an ionospheric scale comparable to the electron inertial length for the lowaltitude magnetosphere, but become shorter with time due to frequencybased phase mixing of boundary waves (a new manifestation of phase mixing). Under suitable conditions, these could act as seeds for the ionospheric feedback instability.
Description: The authors acknowledge the International Space Science Institute (Switzerland) for funding the program that inspired this work. AJBR is grateful to the Royal Commission for the Exhibition of 1851 for present support and acknowledges an STFC studentship that funded part of this work.
Wed, 03 Apr 2013 00:00:00 GMT
http://hdl.handle.net/10023/5150
20130403T00:00:00Z
Russell, A. J. B.
Wright, Andrew Nicholas
Streltsov, A. V.
Rockets and satellites have previously observed smallscale Alfven waves inside largescale downward fieldaligned currents, and numerical simulations have associated their formation with selfconsistent magnetosphereionosphere coupling. The origin of these waves was previously attributed to ionospheric feedback instability; however, we show that they arise in numerical experiments in which the instability is excluded. A new interpretation is proposed in which strong ionospheric depletion and associated current broadening (a nonlinear steepening/wavebreaking process) form magnetosphereionosphere waves inside a downward current region and these oscillations drive upgoing inertial Alfven waves in the overlying plasma. The resulting waves are governed by characteristic periods, which are a good match to previously observed periods for reasonable assumed conditions. Meanwhile, wavelengths perpendicular to the magnetic field initially map to an ionospheric scale comparable to the electron inertial length for the lowaltitude magnetosphere, but become shorter with time due to frequencybased phase mixing of boundary waves (a new manifestation of phase mixing). Under suitable conditions, these could act as seeds for the ionospheric feedback instability.

A numerical model of standard to blowout jets
http://hdl.handle.net/10023/5140
Abstract: We report on threedimensional (3D) MHD simulations of the formation of jets produced during the emergence and eruption of solar magnetic fields. The interaction between an emerging and an ambient magnetic field in the solar atmosphere leads to (external) reconnection and the formation of "standard" jets with an inverse Yshaped configuration. Eventually, lowatmosphere (internal) reconnection of sheared fieldlines in the emerging flux region produces an erupting magnetic flux rope and a reconnection jet underneath it. The erupting plasma blows out the ambient field and, moreover, it unwinds as it is ejected into the outer solar atmosphere. The fast emission of the cool material that erupts together with the hot outflows due to external/internal reconnection form a wider "blowout" jet. We show the transition from "standard" to "blowout" jets and report on their 3D structure. The physical plasma properties of the jets are consistent with observational studies.
Thu, 09 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/5140
20130509T00:00:00Z
Archontis, Vasilis
Hood, A. W.
We report on threedimensional (3D) MHD simulations of the formation of jets produced during the emergence and eruption of solar magnetic fields. The interaction between an emerging and an ambient magnetic field in the solar atmosphere leads to (external) reconnection and the formation of "standard" jets with an inverse Yshaped configuration. Eventually, lowatmosphere (internal) reconnection of sheared fieldlines in the emerging flux region produces an erupting magnetic flux rope and a reconnection jet underneath it. The erupting plasma blows out the ambient field and, moreover, it unwinds as it is ejected into the outer solar atmosphere. The fast emission of the cool material that erupts together with the hot outflows due to external/internal reconnection form a wider "blowout" jet. We show the transition from "standard" to "blowout" jets and report on their 3D structure. The physical plasma properties of the jets are consistent with observational studies.

Fitting models of multiplehypotheses to partial population data : investigating the causes of cycles in red grouse
http://hdl.handle.net/10023/5119
Abstract: There are two postulated causes for the observed periodic fluctuations (cycles) in red grouse (Lagopus lagopus scoticus). The first involves interaction with the parasitic nematode Trichostrongylus tenuis. The second invokes delayed regulation through the effect of male aggressiveness on territoriality. Empirical evidence exists to support both hypotheses, and each hypothesis has been modeled deterministically. However, little effort has gone into looking at the combined effects of the two mechanisms or formally fitting the corresponding models to field data. Here we present a model for red grouse dynamics that includes both parasites and territoriality. To explore the single and combined hypotheses, we specify three versions of this model and fit them to data using Bayesian statespace modeling, a method that allows statistical inference to be performed on mechanistic models such as ours. Output from the three models is then examined to determine their goodness of fit and the biological plausibility of the parameter values required by each to fit the population data. While all three models are capable of emulating the observed cyclic dynamics, only the model including both aggression and parasites does so under consistently realistic parameter values, providing theoretical support for the idea that both mechanisms shape red grouse cycles.
Tue, 01 Sep 2009 00:00:00 GMT
http://hdl.handle.net/10023/5119
20090901T00:00:00Z
New, L
Matthiopoulos, Jason
Redpath, S
Buckland, Stephen Terrence
There are two postulated causes for the observed periodic fluctuations (cycles) in red grouse (Lagopus lagopus scoticus). The first involves interaction with the parasitic nematode Trichostrongylus tenuis. The second invokes delayed regulation through the effect of male aggressiveness on territoriality. Empirical evidence exists to support both hypotheses, and each hypothesis has been modeled deterministically. However, little effort has gone into looking at the combined effects of the two mechanisms or formally fitting the corresponding models to field data. Here we present a model for red grouse dynamics that includes both parasites and territoriality. To explore the single and combined hypotheses, we specify three versions of this model and fit them to data using Bayesian statespace modeling, a method that allows statistical inference to be performed on mechanistic models such as ours. Output from the three models is then examined to determine their goodness of fit and the biological plausibility of the parameter values required by each to fit the population data. While all three models are capable of emulating the observed cyclic dynamics, only the model including both aggression and parasites does so under consistently realistic parameter values, providing theoretical support for the idea that both mechanisms shape red grouse cycles.

Doseresponse relationships for the onset of avoidance of sonar by freeranging killer whales
http://hdl.handle.net/10023/5092
Abstract: Eight experimentally controlled exposures to 1−2 kHz or 6−7 kHz sonar signals were conducted with four killer whale groups. The source level and proximity of the source were increased during each exposure in order to reveal response thresholds. Detailed inspection of movements during each exposure session revealed sustained changes in speed and travel direction judged to be avoidance responses during six of eight sessions. Following methods developed for PhaseI clinical trials in human medicine, response thresholds ranging from 94 to 164 dB re 1 μPa received sound pressure level (SPL) were fitted to Bayesian doseresponse functions. Thresholds did not consistently differ by sonar frequency or whether a group had previously been exposed, with a mean SPL response threshold of 142 ± 15 dB (mean ± s.d.). High levels of between and withinindividual variability were identified, indicating that thresholds depended upon other undefined contextual variables. The doseresponse functions indicate that some killer whales started to avoid sonar at received SPL below thresholds assumed by the U.S. Navy. The predicted extent of habitat over which avoidance reactions occur depends upon whether whales responded to proximity or received SPL of the sonar or both, but was large enough to raise concerns about biological consequences to the whales.
Description: The authors acknowledge the support of the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) in the completion of this study. MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.
Sat, 01 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/5092
20140201T00:00:00Z
Miller, Patrick
Antunes, Ricardo Nuno
Wensveen, Paulus Jacobus
Samarra, Filipa Isabel Pereira
Alves, Ana Catarina De Carvalho
Tyack, Peter Lloyd
Kvadsheim, Petter H.
Kleivane, Lars
Lam, FransPeter A.
Ainslie, Michael A.
Thomas, Len
Eight experimentally controlled exposures to 1−2 kHz or 6−7 kHz sonar signals were conducted with four killer whale groups. The source level and proximity of the source were increased during each exposure in order to reveal response thresholds. Detailed inspection of movements during each exposure session revealed sustained changes in speed and travel direction judged to be avoidance responses during six of eight sessions. Following methods developed for PhaseI clinical trials in human medicine, response thresholds ranging from 94 to 164 dB re 1 μPa received sound pressure level (SPL) were fitted to Bayesian doseresponse functions. Thresholds did not consistently differ by sonar frequency or whether a group had previously been exposed, with a mean SPL response threshold of 142 ± 15 dB (mean ± s.d.). High levels of between and withinindividual variability were identified, indicating that thresholds depended upon other undefined contextual variables. The doseresponse functions indicate that some killer whales started to avoid sonar at received SPL below thresholds assumed by the U.S. Navy. The predicted extent of habitat over which avoidance reactions occur depends upon whether whales responded to proximity or received SPL of the sonar or both, but was large enough to raise concerns about biological consequences to the whales.

conting : an R package for Bayesian analysis of complete and incomplete contingency tables
http://hdl.handle.net/10023/5050
Abstract: The aim of this paper is to demonstrate the R package conting for the Bayesian analysis of complete and incomplete contingency tables using hierarchical loglinear models. This package allows a user to identify interactions between categorical factors (via complete contingency tables) and to estimate closed population sizes using capturerecapture studies (via incomplete contingency tables). The models are fitted using Markov chain Monte Carlo methods. In particular, implementations of the MetropolisHastings and reversible jump algorithms appropriate for loglinear models are employed. The conting package is demonstrated on four real examples.
Sun, 01 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/5050
20140601T00:00:00Z
Overstall, Antony
King, Ruth
The aim of this paper is to demonstrate the R package conting for the Bayesian analysis of complete and incomplete contingency tables using hierarchical loglinear models. This package allows a user to identify interactions between categorical factors (via complete contingency tables) and to estimate closed population sizes using capturerecapture studies (via incomplete contingency tables). The models are fitted using Markov chain Monte Carlo methods. In particular, implementations of the MetropolisHastings and reversible jump algorithms appropriate for loglinear models are employed. The conting package is demonstrated on four real examples.

SWIFF : space weather integrated forecasting framework
http://hdl.handle.net/10023/5049
Abstract: SWIFF is a project funded by the Seventh Framework Programme of the European Commission to study the mathematicalphysics models that form the basis for space weather forecasting. The phenomena of space weather span a tremendous scale of densities and temperature with scales ranging 10 orders of magnitude in space and time. Additionally even in local regions there are concurrent processes developing at the electron, ion and global scales strongly interacting with each other. The fundamental challenge in modelling space weather is the need to address multiple physics and multiple scales. Here we present our approach to take existing expertise in fluid and kinetic models to produce an integrated mathematical approach and software infrastructure that allows fluid and kinetic processes to be modelled together. SWIFF aims also at using this new infrastructure to model specific coupled processes at the Solar Corona, in the interplanetary space and in the interaction at the Earth magnetosphere.
Description: This research has received funding from the European Commission’s FP7 Program with the grant agreement SWIFF (Project No. 2633430, swiff.eu). The KU Leuven simulations were conducted on the computational resources provided by the PRACE Tier0 Project No. 2011050747 (Curie supercomputer) and by the Flemish Supercomputer Center (VIC3). Additional computational support is provided at KU Leuven by the NASA NCCS (Discover) and NAS (Pleiades) Divisons, as part of the support to the NASA MMS Mission. UNIPI acknowledges the HPC resources of CINECA made available within the Distributed European Computing Initiative by the PRACE2IP, receiving funding from the European Community’s Seventh Framework Programme (FP7/ 20072013) under Grant Agreement No. nRI283493. Work at UNIPI was supported by the Italian Supercomputing Center – CINECA under the ISCRA initiative. Work at UNIPI was supported by the HPCEUROPA2 project (Project No. 228398) with the support of the European Commission – Capacities Area – Research Infrastructures. Work performed at IAP, ASCR was supported also by the Project RVO: 68378289.
Mon, 18 Feb 2013 00:00:00 GMT
http://hdl.handle.net/10023/5049
20130218T00:00:00Z
Lapenta, Giovanni
Pierrard, Viviane
Keppens, Rony
Markidis, Stefano
Poedts, Stefaan
Šebek, Ondřej
Trávníček, Pavel M
Henri, Pierre
Califano, Francesco
Pegoraro, Francesco
Faganello, Matteo
Olshevsky, Vyacheslav
Restante, Anna Lisa
Nordlund, Åke
Trier Frederiksen, Jacob
Mackay, Duncan Hendry
Parnell, Clare Elizabeth
Bemporad, Alessandro
Susino, Roberto
Borremans, Kris
SWIFF is a project funded by the Seventh Framework Programme of the European Commission to study the mathematicalphysics models that form the basis for space weather forecasting. The phenomena of space weather span a tremendous scale of densities and temperature with scales ranging 10 orders of magnitude in space and time. Additionally even in local regions there are concurrent processes developing at the electron, ion and global scales strongly interacting with each other. The fundamental challenge in modelling space weather is the need to address multiple physics and multiple scales. Here we present our approach to take existing expertise in fluid and kinetic models to produce an integrated mathematical approach and software infrastructure that allows fluid and kinetic processes to be modelled together. SWIFF aims also at using this new infrastructure to model specific coupled processes at the Solar Corona, in the interplanetary space and in the interaction at the Earth magnetosphere.

Frequency of behavior witnessed and conformity in an everyday social context
http://hdl.handle.net/10023/5024
Abstract: Conformity is thought to be an important force in human evolution because it has the potential to stabilize cultural homogeneity within groups and cultural diversity between groups. However, the effects of such conformity on cultural and biological evolution will depend much on the particular way in which individuals are influenced by the frequency of alternative behavioral options they witness. In a previous study we found that in a natural situation people displayed a tendency to be 'linearconformist'. When visitors to a Zoo exhibit were invited to write or draw answers to questions on cards to win a small prize and we manipulated the proportion of text versus drawings on display, we found a strong and significant effect of the proportion of text displayed on the proportion of text in the answers, a conformist effect that was largely linear with a small nonlinear component. However, although this overall effect is important to understand cultural evolution, it might mask a greater diversity of behavioral responses shaped by variables such as age, sex, social environment and attention of the participants. Accordingly we performed a further study explicitly to analyze the effects of these variables, together with the quality of the information participants' responses made available to further visitors. Results again showed a largely linear conformity effect that varied little with the variables analyzed. © 2014 Claidière et al.
Fri, 20 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/5024
20140620T00:00:00Z
Claidière, N.
Bowler, M.
Brookes, S.
Brown, R.
Whiten, A.
Conformity is thought to be an important force in human evolution because it has the potential to stabilize cultural homogeneity within groups and cultural diversity between groups. However, the effects of such conformity on cultural and biological evolution will depend much on the particular way in which individuals are influenced by the frequency of alternative behavioral options they witness. In a previous study we found that in a natural situation people displayed a tendency to be 'linearconformist'. When visitors to a Zoo exhibit were invited to write or draw answers to questions on cards to win a small prize and we manipulated the proportion of text versus drawings on display, we found a strong and significant effect of the proportion of text displayed on the proportion of text in the answers, a conformist effect that was largely linear with a small nonlinear component. However, although this overall effect is important to understand cultural evolution, it might mask a greater diversity of behavioral responses shaped by variables such as age, sex, social environment and attention of the participants. Accordingly we performed a further study explicitly to analyze the effects of these variables, together with the quality of the information participants' responses made available to further visitors. Results again showed a largely linear conformity effect that varied little with the variables analyzed. © 2014 Claidière et al.

Using hidden Markov models to deal with availability bias on line transect surveys
http://hdl.handle.net/10023/5017
Abstract: We develop estimators for line transect surveys of animals that are stochastically unavailable for detection while within detection range. The detection process is formulated as a hidden Markov model with a binary statedependent observation model that depends on both perpendicular and forward distances. This provides a parametric method of dealing with availability bias when estimates of availability process parameters are available even if series of availability events themselves are not. We apply the estimators to an aerial and a shipboard survey of whales, and investigate their properties by simulation. They are shown to be more general and more flexible than existing estimators based on parametric models of the availability process. We also find that methods using availability correction factors can be very biased when surveys are not close to being instantaneous, as can estimators that assume temporal independence in availability when there is temporal dependence.
Description: This work was supported by EPSRC grant EP/I000917/1
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/5017
20130101T00:00:00Z
Borchers, David Louis
Zucchini, Walter
HeideJørgensen, M.P.
Cañadas, A.
Langrock, Roland
We develop estimators for line transect surveys of animals that are stochastically unavailable for detection while within detection range. The detection process is formulated as a hidden Markov model with a binary statedependent observation model that depends on both perpendicular and forward distances. This provides a parametric method of dealing with availability bias when estimates of availability process parameters are available even if series of availability events themselves are not. We apply the estimators to an aerial and a shipboard survey of whales, and investigate their properties by simulation. They are shown to be more general and more flexible than existing estimators based on parametric models of the availability process. We also find that methods using availability correction factors can be very biased when surveys are not close to being instantaneous, as can estimators that assume temporal independence in availability when there is temporal dependence.

J J Thomson and the Discovery of the Electron
http://hdl.handle.net/10023/4991
Abstract: One experiment, more than any other, is often associated with the `discovery of the electron' in 1897. This is J J Thomson's determination of the mass to charge ratio (m/e) of cathode rays by deflecting them in magnetic and electric fields. Yet this experiment was performed two months after Thomson first announced that cathode rays were very small, negatively charged particles. So why was it important? I look at Thomson's route to, and conduct of, the experiment, and then at how his ideas were received.
Fri, 01 Jan 1999 00:00:00 GMT
http://hdl.handle.net/10023/4991
19990101T00:00:00Z
Falconer, Isobel Jessie
One experiment, more than any other, is often associated with the `discovery of the electron' in 1897. This is J J Thomson's determination of the mass to charge ratio (m/e) of cathode rays by deflecting them in magnetic and electric fields. Yet this experiment was performed two months after Thomson first announced that cathode rays were very small, negatively charged particles. So why was it important? I look at Thomson's route to, and conduct of, the experiment, and then at how his ideas were received.

Beyond sumfree sets in the natural numbers
http://hdl.handle.net/10023/4986
Abstract: For an interval [1,N]⊆N, sets S⊆[1,N] with the property that {(x,y)∈S2:x+y∈S}=0, known as sumfree sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)={(x,y)∈S2:x+y∈S}, and analyze its behaviour as S ranges over the subsets of [1,N]. We obtain a comprehensive description of the spectrum of attainable rvalues, constructive existence results and structural characterizations for sets attaining extremal and nearextremal values.
Fri, 07 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/4986
20140207T00:00:00Z
Huczynska, Sophie
For an interval [1,N]⊆N, sets S⊆[1,N] with the property that {(x,y)∈S2:x+y∈S}=0, known as sumfree sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)={(x,y)∈S2:x+y∈S}, and analyze its behaviour as S ranges over the subsets of [1,N]. We obtain a comprehensive description of the spectrum of attainable rvalues, constructive existence results and structural characterizations for sets attaining extremal and nearextremal values.

Injecting drug users in Scotland, 2006 : listing, number, demography, and opiaterelated deathrates
http://hdl.handle.net/10023/4904
Abstract: Using Bayesian capture–recapture analysis, we estimated the number of current injecting drug users (IDUs) in Scotland in 2006 from the crosscounts of 5670 IDUs listed on four datasources: social enquiry reports (901 IDUs listed), hospital records (953), drug treatment agencies (3504), and recent Hepatitis C virus (HCV) diagnoses (827 listed as IDUrisk). Further, we accessed exact numbers of opiaterelated drugsrelated deaths (DRDs) in 2006 and 2007 to improve estimation of Scotland's DRD rates per 100 current IDUs. Using all four datasources, and modelaveraging of standard hierarchical loglinear models to allow for pairwise interactions between datasources and/or demographic classifications, Scotland had an estimated 31700 IDUs in 2006 (95% credible interval: 24900–38700); but 25000 IDUs (95% CI: 20700–35000) by excluding recent HCV diagnoses whose IDUrisk can refer to past injecting. Only in the younger agegroup (15–34 years) were Scotland's opiaterelated DRD rates significantly lower for females than males. Older males’ opiaterelated DRD rate was 1.9 (1.24–2.40) per 100 current IDUs without or 1.3 (0.94–1.64) with inclusion of recent HCV diagnoses. If, indeed, Scotland had only 25000 current IDUs in 2006, with only 8200 of them aged 35+ years, the opiaterelated DRD rate is higher among this older age group than has been appreciated hitherto. There is counterbalancing good news for the public health: the hitherto sharp increase in older current IDUs had stalled by 2006.
Sat, 01 Jun 2013 00:00:00 GMT
http://hdl.handle.net/10023/4904
20130601T00:00:00Z
King, Ruth
Bird, Sheila
Overstall, Antony
Hay, Gordon
Hutchinson, Sharon
Using Bayesian capture–recapture analysis, we estimated the number of current injecting drug users (IDUs) in Scotland in 2006 from the crosscounts of 5670 IDUs listed on four datasources: social enquiry reports (901 IDUs listed), hospital records (953), drug treatment agencies (3504), and recent Hepatitis C virus (HCV) diagnoses (827 listed as IDUrisk). Further, we accessed exact numbers of opiaterelated drugsrelated deaths (DRDs) in 2006 and 2007 to improve estimation of Scotland's DRD rates per 100 current IDUs. Using all four datasources, and modelaveraging of standard hierarchical loglinear models to allow for pairwise interactions between datasources and/or demographic classifications, Scotland had an estimated 31700 IDUs in 2006 (95% credible interval: 24900–38700); but 25000 IDUs (95% CI: 20700–35000) by excluding recent HCV diagnoses whose IDUrisk can refer to past injecting. Only in the younger agegroup (15–34 years) were Scotland's opiaterelated DRD rates significantly lower for females than males. Older males’ opiaterelated DRD rate was 1.9 (1.24–2.40) per 100 current IDUs without or 1.3 (0.94–1.64) with inclusion of recent HCV diagnoses. If, indeed, Scotland had only 25000 current IDUs in 2006, with only 8200 of them aged 35+ years, the opiaterelated DRD rate is higher among this older age group than has been appreciated hitherto. There is counterbalancing good news for the public health: the hitherto sharp increase in older current IDUs had stalled by 2006.

The transterminator ion flow at Venus at solar minimum
http://hdl.handle.net/10023/4795
Abstract: The transterminator ion flow in the Venusian ionosphere is observed at solar minimum for the first time. Such a flow, which transports ions from the day to the nightside, has been observed previously around solar maximum. At solar minimum this transport process is severely inhibited by the lower altitude of the ionopause. The observations presented were those made of the Venusian ionospheric plasma by the ASPERA4 experiment onboard the Venus Express spacecraft, and which constitute the first extensive insitu measurements of the plasma near solar minimum. Observations near the terminator of the energies of ions of ionospheric origin showed asymmetry between the noon and midnight sectors, which indicated an antisunward ion flow with a velocity of (2.5 +/ 1.5) km s(1). It is suggested that this ion flow contributes to maintaining the nightside ionosphere near the terminator region at solar minimum. The interpretation of the result was reinforced by observed asymmetries in the ion number counts. The observed dawndusk asymmetry was consistent with a nightward transport of ions while the noonmidnight observations indicated that the flow was highly variable but could contribute to the maintenance of the nightside ionosphere.
Description: Financial support for this paper was provided by the UK Science and Technology Facilities Council under grant PP/E001157/1.
Sat, 01 Dec 2012 00:00:00 GMT
http://hdl.handle.net/10023/4795
20121201T00:00:00Z
Wood, A. G.
Pryse, S. E.
Grande, M.
Whittaker, I. C.
Coates, A. J.
Husband, K.
Baumjohann, W.
Zhang, T. L.
Mazelle, C.
Kallio, E.
Fraenz, M.
McKennaLawlor, S.
Wurz, P.
The transterminator ion flow in the Venusian ionosphere is observed at solar minimum for the first time. Such a flow, which transports ions from the day to the nightside, has been observed previously around solar maximum. At solar minimum this transport process is severely inhibited by the lower altitude of the ionopause. The observations presented were those made of the Venusian ionospheric plasma by the ASPERA4 experiment onboard the Venus Express spacecraft, and which constitute the first extensive insitu measurements of the plasma near solar minimum. Observations near the terminator of the energies of ions of ionospheric origin showed asymmetry between the noon and midnight sectors, which indicated an antisunward ion flow with a velocity of (2.5 +/ 1.5) km s(1). It is suggested that this ion flow contributes to maintaining the nightside ionosphere near the terminator region at solar minimum. The interpretation of the result was reinforced by observed asymmetries in the ion number counts. The observed dawndusk asymmetry was consistent with a nightward transport of ions while the noonmidnight observations indicated that the flow was highly variable but could contribute to the maintenance of the nightside ionosphere.

Shallowwater vortex equilibria and their stability
http://hdl.handle.net/10023/4762
Abstract: We first describe the equilibrium form and stability of steadilyrotating simplyconnected vortex patches in the singlelayer quasigeostrophic model of geophysical fluid dynamics. This model, valid for rotating shallowwater flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L called the "Rossby deformation length" relating the strength of stratification to that of the background rotation rate. Specifically, L = c/f where c = √gH is a characteristic gravitywave speed, g is gravity (or "reduced" gravity in a twolayer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallowwater model to generate what we call "quasiequilibria". These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasigeostrophic equilibria to obtain shallowwater quasiequilibria at finite Rossby number. We show a few examples of these states in this paper.
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10023/4762
20110101T00:00:00Z
Płotka, H.
Dritschel, D.G.
We first describe the equilibrium form and stability of steadilyrotating simplyconnected vortex patches in the singlelayer quasigeostrophic model of geophysical fluid dynamics. This model, valid for rotating shallowwater flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L called the "Rossby deformation length" relating the strength of stratification to that of the background rotation rate. Specifically, L = c/f where c = √gH is a characteristic gravitywave speed, g is gravity (or "reduced" gravity in a twolayer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallowwater model to generate what we call "quasiequilibria". These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasigeostrophic equilibria to obtain shallowwater quasiequilibria at finite Rossby number. We show a few examples of these states in this paper.

Propagating coupled Alfvén and kink oscillations in an arbitrary inhomogeneous corona
http://hdl.handle.net/10023/4755
Abstract: Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform threedimensional numerical simulations of footpointdriven transverse waves propagating in a low β plasma. We consider the cases of distorted cylindrical flux tubes and a randomly generated inhomogeneous medium. When density structuring is present, mode coupling in inhomogeneous regions leads to the coupling of the kink mode to the Alfvén mode. The decay of the propagating kink wave is observed as energy is transferred to the local Alfvén mode. In all cases considered, modest changes in density were capable of efficiently converting energy from the driving footpoint motion to localized Alfv´en modes. We have demonstrated that mode coupling efficiently couples propagating kink perturbations to Alfvén modes in an arbitrary inhomogeneous medium. This has the consequence that transverse footpoint motions at the base of the corona will deposit energy to Alfvén modes in the corona.
Description: D.J.P. acknowledges financial support from STFC. I.D.M. acknowledges support of a Royal Society University Research Fellowship.
Sun, 10 Apr 2011 00:00:00 GMT
http://hdl.handle.net/10023/4755
20110410T00:00:00Z
Pascoe, David James
Wright, Andrew Nicholas
De Moortel, Ineke
Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform threedimensional numerical simulations of footpointdriven transverse waves propagating in a low β plasma. We consider the cases of distorted cylindrical flux tubes and a randomly generated inhomogeneous medium. When density structuring is present, mode coupling in inhomogeneous regions leads to the coupling of the kink mode to the Alfvén mode. The decay of the propagating kink wave is observed as energy is transferred to the local Alfvén mode. In all cases considered, modest changes in density were capable of efficiently converting energy from the driving footpoint motion to localized Alfv´en modes. We have demonstrated that mode coupling efficiently couples propagating kink perturbations to Alfvén modes in an arbitrary inhomogeneous medium. This has the consequence that transverse footpoint motions at the base of the corona will deposit energy to Alfvén modes in the corona.

Modeling the dispersal of an active region : quantifying energy input into the corona
http://hdl.handle.net/10023/4754
Abstract: In this paper, a new technique for modeling nonlinear forcefree fields directly from lineofsight magnetogram observations is presented. The technique uses sequences of magnetograms directly as lower boundary conditions to drive the evolution of coronal magnetic fields between successive forcefree equilibria over long periods of time. It is illustrated by applying it to SOHO: MDI observations of a decaying active region, NOAA AR 8005. The active region is modeled during a fourday period around its central meridian passage. Over this time, the dispersal of the active region is dominated by random motions due to smallscale convective cells. Through studying the buildup of magnetic energy in the model, it is found that such smallscale motions may inject anywhere from (2.53) × 1025 erg s1 of free magnetic energy into the coronal field. Most of this energy is stored within the center of the active region in the low corona, below 30 Mm. After four days, the buildup of free energy is 10% that of the corresponding potential field. This energy buildup is sufficient to explain the radiative losses at coronal temperatures within the active region. Smallscale convective motions therefore play an integral part in the energy balance of the corona. This new technique has wide ranging applications with the new highresolution, highcadence observations from the SDO:HMI and SDO:AIA instruments.
Description: Funding: UK STFC. Royal Society Research Grants Scheme.
Thu, 10 Mar 2011 00:00:00 GMT
http://hdl.handle.net/10023/4754
20110310T00:00:00Z
Mackay, Duncan Hendry
Green, Lucie
van Ballegooijen, Aad
In this paper, a new technique for modeling nonlinear forcefree fields directly from lineofsight magnetogram observations is presented. The technique uses sequences of magnetograms directly as lower boundary conditions to drive the evolution of coronal magnetic fields between successive forcefree equilibria over long periods of time. It is illustrated by applying it to SOHO: MDI observations of a decaying active region, NOAA AR 8005. The active region is modeled during a fourday period around its central meridian passage. Over this time, the dispersal of the active region is dominated by random motions due to smallscale convective cells. Through studying the buildup of magnetic energy in the model, it is found that such smallscale motions may inject anywhere from (2.53) × 1025 erg s1 of free magnetic energy into the coronal field. Most of this energy is stored within the center of the active region in the low corona, below 30 Mm. After four days, the buildup of free energy is 10% that of the corresponding potential field. This energy buildup is sufficient to explain the radiative losses at coronal temperatures within the active region. Smallscale convective motions therefore play an integral part in the energy balance of the corona. This new technique has wide ranging applications with the new highresolution, highcadence observations from the SDO:HMI and SDO:AIA instruments.

The effects of lineofsight integration on multistrand coronal loop oscillations
http://hdl.handle.net/10023/4752
Description: IDM acknowledges support of a Royal Society University Research Fellowship.
Fri, 10 Feb 2012 00:00:00 GMT
http://hdl.handle.net/10023/4752
20120210T00:00:00Z
De Moortel, Ineke
Pascoe, David James

Standing kink modes in threedimensional coronal loops
http://hdl.handle.net/10023/4745
Abstract: So far, the straight flux tube model proposed by Edwin & Roberts is the most commonly used tool in practical coronal seismology, in particular, to infer values of the (coronal) magnetic field from observed, standing kink mode oscillations. In this paper, we compare the period predicted by this basic model with threedimensional (3D) numerical simulations of standing kink mode oscillations, as the period is a crucial parameter in the seismological inversion to determine the magnetic field. We perform numerical simulations of standing kink modes in both straight and curved 3D coronal loops and consider excitation by internal and external drivers. The period of oscillation for the displacement of dense coronal loops is determined by the loop length and the kink speed, in agreement with the estimate based on analytical theory for straight flux tubes. For curved coronal loops embedded in a magnetic arcade and excited by an external driver, a secondary mode with a period determined by the loop length and external Alfvén speed is also present. When a low number of oscillations is considered, these two periods can result in a single, nonresolved (broad) peak in the power spectrum, particularly for low values of the density contrast for which the two periods will be relatively similar. In that case (and for this particular geometry), the presence of this additional mode would lead to ambiguous seismological estimates of the magnetic field strength.
Description: I.D.M. acknowledges support from a Royal Society University Research Fellowship. The computational work for this paper was carried out at the joint STFC and SFC (SRIF)fundedclusterattheUniversityofStAndrews(UK). The research leading to these results has also received funding from the European Commissions Seventh Framework Programme (FP7/20072013) under the grant agreement SOLSPANET (project No. 269299;www.solspanet.eu/solspanet).
Tue, 11 Mar 2014 00:00:00 GMT
http://hdl.handle.net/10023/4745
20140311T00:00:00Z
De Moortel, Ineke
Pascoe, David James
So far, the straight flux tube model proposed by Edwin & Roberts is the most commonly used tool in practical coronal seismology, in particular, to infer values of the (coronal) magnetic field from observed, standing kink mode oscillations. In this paper, we compare the period predicted by this basic model with threedimensional (3D) numerical simulations of standing kink mode oscillations, as the period is a crucial parameter in the seismological inversion to determine the magnetic field. We perform numerical simulations of standing kink modes in both straight and curved 3D coronal loops and consider excitation by internal and external drivers. The period of oscillation for the displacement of dense coronal loops is determined by the loop length and the kink speed, in agreement with the estimate based on analytical theory for straight flux tubes. For curved coronal loops embedded in a magnetic arcade and excited by an external driver, a secondary mode with a period determined by the loop length and external Alfvén speed is also present. When a low number of oscillations is considered, these two periods can result in a single, nonresolved (broad) peak in the power spectrum, particularly for low values of the density contrast for which the two periods will be relatively similar. In that case (and for this particular geometry), the presence of this additional mode would lead to ambiguous seismological estimates of the magnetic field strength.

Simulating the "Sliding Doors" Effect Through Magnetic Flux Emergence
http://hdl.handle.net/10023/4742
Abstract: Recent Hinode photospheric vector magnetogram observations have shown that the opposite polarities of a long arcade structure move apart and then come together. In addition to this "sliding doors" effect, orientations of horizontal magnetic fields along the polarity inversion line on the photosphere evolve from a normalpolarity configuration to an inverse one. To explain this behavior, a simple model by Okamoto et al. suggested that it is the result of the emergence of a twisted flux rope. Here, we model this scenario using a threedimensional megnatohydrodynamic simulation of a twisted flux rope emerging into a preexisting overlying arcade. We construct magnetograms from the simulation and compare them with the observations. The model produces the two signatures mentioned above. However, the cause of the "sliding doors" effect differs from the previous model.
Description: D.M. acknowledges financial assistance from STFC. The computational work for this Letter was carried out on the joint STFC and SFC (SRIF) funded cluster at the University of St. Andrews. D.M. and A.W.H. acknowledge financial support form the European Commission through the SOLAIRE Network (MTRNCT2006035484).
Fri, 04 Jun 2010 00:00:00 GMT
http://hdl.handle.net/10023/4742
20100604T00:00:00Z
MacTaggart, David
Hood, Alan William
Recent Hinode photospheric vector magnetogram observations have shown that the opposite polarities of a long arcade structure move apart and then come together. In addition to this "sliding doors" effect, orientations of horizontal magnetic fields along the polarity inversion line on the photosphere evolve from a normalpolarity configuration to an inverse one. To explain this behavior, a simple model by Okamoto et al. suggested that it is the result of the emergence of a twisted flux rope. Here, we model this scenario using a threedimensional megnatohydrodynamic simulation of a twisted flux rope emerging into a preexisting overlying arcade. We construct magnetograms from the simulation and compare them with the observations. The model produces the two signatures mentioned above. However, the cause of the "sliding doors" effect differs from the previous model.

The storage and dissipation of magnetic energy in the quiet sun corona determined from SDO/HMI magnetograms
http://hdl.handle.net/10023/4741
Abstract: In recent years, higher cadence, higher resolution observations have revealed the quietSun photosphere to be complex and rapidly evolving. Since magnetic fields anchored in the photosphere extend up into the solar corona, it is expected that the smallscale coronal magnetic field exhibits similar complexity. For the first time, the quietSun coronal magnetic field is continuously evolved through a series of nonpotential, quasistatic equilibria, deduced from magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, where the photospheric boundary condition which drives the coronal evolution exactly reproduces the observed magnetograms. The buildup, storage, and dissipation of magnetic energy within the simulations is studied. We find that the free magnetic energy built up and stored within the field is sufficient to explain smallscale, impulsive events such as nanoflares. On comparing with coronal images of the same region, the energy storage and dissipation visually reproduces many of the observed features. The results indicate that the complex smallscale magnetic evolution of a large number of magnetic features is a key element in explaining the nature of the solar corona.
Description: 2013ApJ...770L..18M
Thu, 30 May 2013 00:00:00 GMT
http://hdl.handle.net/10023/4741
20130530T00:00:00Z
Meyer, Karen Alison
Sabol, Juraj
Mackay, Duncan Hendry
van Ballegooijen, Aad
In recent years, higher cadence, higher resolution observations have revealed the quietSun photosphere to be complex and rapidly evolving. Since magnetic fields anchored in the photosphere extend up into the solar corona, it is expected that the smallscale coronal magnetic field exhibits similar complexity. For the first time, the quietSun coronal magnetic field is continuously evolved through a series of nonpotential, quasistatic equilibria, deduced from magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, where the photospheric boundary condition which drives the coronal evolution exactly reproduces the observed magnetograms. The buildup, storage, and dissipation of magnetic energy within the simulations is studied. We find that the free magnetic energy built up and stored within the field is sufficient to explain smallscale, impulsive events such as nanoflares. On comparing with coronal images of the same region, the energy storage and dissipation visually reproduces many of the observed features. The results indicate that the complex smallscale magnetic evolution of a large number of magnetic features is a key element in explaining the nature of the solar corona.

Potential Evidence for the Onset of Alfvénic Turbulence in Transequatorial Coronal Loops
http://hdl.handle.net/10023/4740
Abstract: This study investigates Coronal Multichannel Polarimeter Dopplershift observations of a large, offlimb, transequatorial loop system observed on 2012 April 1011. Dopplershift oscillations with a broad range of frequencies are found to propagate along the loop with a speed of about 500 km s–1. The power spectrum of perturbations travelling up from both loop footpoints is remarkably symmetric, probably due to the almost perfect northsouth alignment of the loop system. Compared to the power spectrum at the footpoints of the loop, the Fourier power at the apex appears to be higher in the highfrequency part of the spectrum than expected from theoretical models. We suggest this excess highfrequency power could be tentative evidence for the onset of a cascade of the lowtomid frequency waves into (Alfvénic) turbulence.
Mon, 10 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/4740
20140210T00:00:00Z
De Moortel, Ineke
McIntosh, Scott
Threlfall, James William
Bethge, Christian
Liu, J
This study investigates Coronal Multichannel Polarimeter Dopplershift observations of a large, offlimb, transequatorial loop system observed on 2012 April 1011. Dopplershift oscillations with a broad range of frequencies are found to propagate along the loop with a speed of about 500 km s–1. The power spectrum of perturbations travelling up from both loop footpoints is remarkably symmetric, probably due to the almost perfect northsouth alignment of the loop system. Compared to the power spectrum at the footpoints of the loop, the Fourier power at the apex appears to be higher in the highfrequency part of the spectrum than expected from theoretical models. We suggest this excess highfrequency power could be tentative evidence for the onset of a cascade of the lowtomid frequency waves into (Alfvénic) turbulence.

The detection of numerous magnetic separators in a threedimensional magnetohydrodynamic model of solar emerging flux
http://hdl.handle.net/10023/4739
Abstract: Magnetic separators in threedimensional (3D) magnetic fields are believed to be often associated with locations of magnetic reconnection. In this preliminary study, we investigate this relationship using data from a numerical resistive 3D MHD experiment of a solar flux emergence event. For the first time separators are detected in complex magnetic fields resulting from a 3D resistive MHD model of flux emergence. Two snapshots of the model, taken from different stages of its evolution, are analyzed. Numerous separators are found in both snapshots, and their properties, including their geometry, length, relationship to the magnetic null points, and integrated parallel electric field are studied. The separators reside at the junctions between the emerging flux, the overlying field, and two other flux domains that are newly formed by reconnection. The long separators, which connect clusters of nulls that lie either side of the emerging flux, pass through spatially localized regions of high parallel electric field and correspond to local maxima in integrated parallel electric field. These factors indicate that strong magnetic reconnection takes place along many of the separators, and that separators play a key role during the interaction of emerging and overlying flux.
Mon, 20 Dec 2010 00:00:00 GMT
http://hdl.handle.net/10023/4739
20101220T00:00:00Z
Parnell, Clare Elizabeth
Maclean, Rhona Claire
Haynes, Andrew Lewis
Magnetic separators in threedimensional (3D) magnetic fields are believed to be often associated with locations of magnetic reconnection. In this preliminary study, we investigate this relationship using data from a numerical resistive 3D MHD experiment of a solar flux emergence event. For the first time separators are detected in complex magnetic fields resulting from a 3D resistive MHD model of flux emergence. Two snapshots of the model, taken from different stages of its evolution, are analyzed. Numerous separators are found in both snapshots, and their properties, including their geometry, length, relationship to the magnetic null points, and integrated parallel electric field are studied. The separators reside at the junctions between the emerging flux, the overlying field, and two other flux domains that are newly formed by reconnection. The long separators, which connect clusters of nulls that lie either side of the emerging flux, pass through spatially localized regions of high parallel electric field and correspond to local maxima in integrated parallel electric field. These factors indicate that strong magnetic reconnection takes place along many of the separators, and that separators play a key role during the interaction of emerging and overlying flux.

Globalscale consequences of magnetichelicity injection and condensation on the sun
http://hdl.handle.net/10023/4735
Abstract: In the recent paper of Antiochos, a new concept for the injection of magnetic helicity into the solar corona by smallscale convective motions and its condensation onto polarity inversion lines (PILs) has been developed. We investigate this concept through global simulations of the Sun’s photospheric and coronal magnetic fields, and compare the results with the hemispheric pattern of solar filaments. Assuming that the vorticity of the cells is predominately counterclockwise/clockwise in the northern/southern hemisphere, the convective motions inject negative/positive helicity into each hemisphere. The simulations show that: (1) on a north–south oriented PIL, both differential rotation and convective motions inject the same sign of helicity, which matches that required to reproduce the hemispheric pattern of filaments. (2) On a highlatitude east–west oriented polar crown or subpolar crown PIL, the vorticity of the cells has to be approximately 2–3 times greater than the local differentialrotation gradient in order to overcome the incorrect sign of helicity injection from differential rotation. (3) In the declining phase of the cycle, as a bipole interacts with the polar field, in some cases, helicity condensation can reverse the effect of differential rotation along the east–west lead arm but not in all cases. The results show that this newly developed concept of magnetic helicity injection and condensation, in conjunction with the mechanisms used in Yeates et al., is a viable explanation for the hemispheric pattern of filaments. Future observational studies should focus on examining the vorticity component within convective motions to determine both its magnitude and latitudinal variation relative to the differentialrotation gradient on the Sun.
Tue, 01 Apr 2014 00:00:00 GMT
http://hdl.handle.net/10023/4735
20140401T00:00:00Z
Mackay, Duncan Hendry
DeVore, Rick
Antiochos, Spiro
In the recent paper of Antiochos, a new concept for the injection of magnetic helicity into the solar corona by smallscale convective motions and its condensation onto polarity inversion lines (PILs) has been developed. We investigate this concept through global simulations of the Sun’s photospheric and coronal magnetic fields, and compare the results with the hemispheric pattern of solar filaments. Assuming that the vorticity of the cells is predominately counterclockwise/clockwise in the northern/southern hemisphere, the convective motions inject negative/positive helicity into each hemisphere. The simulations show that: (1) on a north–south oriented PIL, both differential rotation and convective motions inject the same sign of helicity, which matches that required to reproduce the hemispheric pattern of filaments. (2) On a highlatitude east–west oriented polar crown or subpolar crown PIL, the vorticity of the cells has to be approximately 2–3 times greater than the local differentialrotation gradient in order to overcome the incorrect sign of helicity injection from differential rotation. (3) In the declining phase of the cycle, as a bipole interacts with the polar field, in some cases, helicity condensation can reverse the effect of differential rotation along the east–west lead arm but not in all cases. The results show that this newly developed concept of magnetic helicity injection and condensation, in conjunction with the mechanisms used in Yeates et al., is a viable explanation for the hemispheric pattern of filaments. Future observational studies should focus on examining the vorticity component within convective motions to determine both its magnitude and latitudinal variation relative to the differentialrotation gradient on the Sun.

On the commutator lengths of certain classes of finitely presented groups
http://hdl.handle.net/10023/4719
Abstract: For a finite group G = 〈X〉 (X ≠ G), the least positive integer ML(G) is called the maximum length of G with respect to the generating set X if every element of G maybe represented as a product of at most ML(G) elements of X. The maximum length of G, denoted by ML (G), is defined to be the minimum of {ML(G) G = 〈X〉, X ≠ G, X ≠ G  {1}}. The wellknown commutator length of a group G, denoted by c (G), satisfies the inequality c (G) ≤ ML(G′), where G′ is the derived subgroup of G. In this paper we study the properties of ML (G) and by using this inequality we give upper bounds for the commutator lengths of certain classes of finite groups. In some cases these upper bounds involve the interesting sequences of Fibonacci and Lucas numbers.
Sun, 01 Jan 2006 00:00:00 GMT
http://hdl.handle.net/10023/4719
20060101T00:00:00Z
Doostie, H.
Campbell, P.P.
For a finite group G = 〈X〉 (X ≠ G), the least positive integer ML(G) is called the maximum length of G with respect to the generating set X if every element of G maybe represented as a product of at most ML(G) elements of X. The maximum length of G, denoted by ML (G), is defined to be the minimum of {ML(G) G = 〈X〉, X ≠ G, X ≠ G  {1}}. The wellknown commutator length of a group G, denoted by c (G), satisfies the inequality c (G) ≤ ML(G′), where G′ is the derived subgroup of G. In this paper we study the properties of ML (G) and by using this inequality we give upper bounds for the commutator lengths of certain classes of finite groups. In some cases these upper bounds involve the interesting sequences of Fibonacci and Lucas numbers.

The Sun's global photospheric and coronal magnetic fields : observations and models
http://hdl.handle.net/10023/4714
Abstract: In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the largescale properties of photospheric magnetic fields are described, along with recent advances in photospheric magnetic flux transport models. Following this, the wide variety of theoretical models used to simulate global coronal magnetic fields are described. From this, the combined application of both magnetic flux transport simulations and coronal modeling techniques to describe the phenomena of coronal holes, the Sun's open magnetic flux and the hemispheric pattern of solar filaments is discussed. Finally, recent advances in noneruptive global MHD models are described. While the review focuses mainly on solar magnetic fields, recent advances in measuring and modeling stellar magnetic fields are described where appropriate. In the final section key areas of future research are identified.
Description: 2012LRSP....9....6M Funding: STFC, the Leverhulme Trust and European Commission’s Seventh Framework Programme (FP7/20072013) under the grant agreement SWIFF (project no. 263340, http://www.swiff.eu).
Thu, 01 Nov 2012 00:00:00 GMT
http://hdl.handle.net/10023/4714
20121101T00:00:00Z
Mackay, Duncan Hendry
Yeates, Anthony Robinson
In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the largescale properties of photospheric magnetic fields are described, along with recent advances in photospheric magnetic flux transport models. Following this, the wide variety of theoretical models used to simulate global coronal magnetic fields are described. From this, the combined application of both magnetic flux transport simulations and coronal modeling techniques to describe the phenomena of coronal holes, the Sun's open magnetic flux and the hemispheric pattern of solar filaments is discussed. Finally, recent advances in noneruptive global MHD models are described. While the review focuses mainly on solar magnetic fields, recent advances in measuring and modeling stellar magnetic fields are described where appropriate. In the final section key areas of future research are identified.

An approximate Bayesian method applied to estimating the trajectories of four British grey seal (Halichoerus grypus) populations from pup counts.
http://hdl.handle.net/10023/4688
Abstract: 1. For British grey seals, as with many pinniped species, population monitoring is implemented by aerial surveys of pups at breeding colonies. Scaling pup counts up to population estimates requires assumptions about population structure; this is straightforward when populations are growing exponentially, but not when growth slows, since it is unclear whether density dependence affects pup survival or fecundity. 2. We present an approximate Bayesian method for fitting pup trajectories, estimating adult population size and investigating alternative biological models. The method is equivalent to fitting a density dependent Leslie matrix model, within a Bayesian framework, but with the forms of the density dependent effects as outputs rather than assumptions. 3. This approach requires fewer assumptions than the state space models currently used, and produces similar estimates. The simplifications made the models easier to fit, reducing their computational intensity and allowing regional differences in demographic parameters to be considered. 4. The approach is not restricted to situations where only a single component of the population is observable, but, particularly in those cases, provides a practical method for extracting information from limited datasets. 5. We discuss the potential and limitations of the method and suggest that this approach provides a useful tool for at least the preliminary analysis of similar datasets.
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10023/4688
20110101T00:00:00Z
Lonergan, Michael Edward
Thompson, David
Thomas, Leonard Joseph
Duck, Callan David
1. For British grey seals, as with many pinniped species, population monitoring is implemented by aerial surveys of pups at breeding colonies. Scaling pup counts up to population estimates requires assumptions about population structure; this is straightforward when populations are growing exponentially, but not when growth slows, since it is unclear whether density dependence affects pup survival or fecundity. 2. We present an approximate Bayesian method for fitting pup trajectories, estimating adult population size and investigating alternative biological models. The method is equivalent to fitting a density dependent Leslie matrix model, within a Bayesian framework, but with the forms of the density dependent effects as outputs rather than assumptions. 3. This approach requires fewer assumptions than the state space models currently used, and produces similar estimates. The simplifications made the models easier to fit, reducing their computational intensity and allowing regional differences in demographic parameters to be considered. 4. The approach is not restricted to situations where only a single component of the population is observable, but, particularly in those cases, provides a practical method for extracting information from limited datasets. 5. We discuss the potential and limitations of the method and suggest that this approach provides a useful tool for at least the preliminary analysis of similar datasets.

On the probability of generating a monolithic group
http://hdl.handle.net/10023/4626
Abstract: A group L is primitive monolithic if L has a unique minimal normal subgroup, N , and trivial Frattini subgroup. By PL,N(k) we denote the conditional probability that k randomly chosen elements of L generate L , given that they project onto generators for L/N. In this article we show that PL,N(k) is controlled by PY,S(2), where N≅Sr and Y is a 2generated almost simple group with socle S that is contained in the normalizer in L of the first direct factor of N . Information aboutPL,N(k) for L primitive monolithic yields various types of information about the generation of arbitrary finite and profinite groups.
Description: This research was supported through EPSRC grant EP/I03582X/1. The APC was paid through RCUK open access block grant funds.
Sun, 01 Jun 2014 00:00:00 GMT
http://hdl.handle.net/10023/4626
20140601T00:00:00Z
Detomi, Eloisa
Lucchini, Andrea
RoneyDougal, Colva Mary
A group L is primitive monolithic if L has a unique minimal normal subgroup, N , and trivial Frattini subgroup. By PL,N(k) we denote the conditional probability that k randomly chosen elements of L generate L , given that they project onto generators for L/N. In this article we show that PL,N(k) is controlled by PY,S(2), where N≅Sr and Y is a 2generated almost simple group with socle S that is contained in the normalizer in L of the first direct factor of N . Information aboutPL,N(k) for L primitive monolithic yields various types of information about the generation of arbitrary finite and profinite groups.

Modelling group dynamic animal movement
http://hdl.handle.net/10023/4555
Abstract: 1). Group dynamics are a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognized, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However, to date, practical statistical methods, which can include group dynamics in animal movement models, have been lacking. 2). We consider a flexible modelling framework that distinguishes a grouplevel model, describing the movement of the group's centre, and an individuallevel model, such that each individual makes its movement decisions relative to the group centroid. The basic idea is framed within the flexible class of hidden Markov models, extending previous work on modelling animal movement by means of multistate random walks. 3). While in simulation experiments parameter estimators exhibit some bias in nonideal scenarios, we show that generally the estimation of models of this type is both feasible and ecologically informative. 4). We illustrate the approach using real movement data from 11 reindeer (Rangifer tarandus). Results indicate a directional bias towards a group centroid for reindeer in an encamped state. Though the attraction to the group centroid is relatively weak, our model successfully captures groupinfluenced movement dynamics. Specifically, as compared to a regular mixture of correlated random walks, the group dynamic model more accurately predicts the nondiffusive behaviour of a cohesive mobile group. 5). As technology continues to develop, it will become easier and less expensive to tag multiple individuals within a group in order to follow their movements. Our work provides a first inferential framework for understanding the relative influences of individual versus grouplevel movement decisions. This framework can be extended to include covariates corresponding to environmental influences or body condition. As such, this framework allows for a broader understanding of the many internal and external factors that can influence an individual's movement.
Sat, 01 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/4555
20140201T00:00:00Z
Langrock, Roland
Hopcraft, Grant
Blackwell, Paul
Goodall, Victoria
King, Ruth
Niu, Mu
Patterson, Toby
Pedersen, Martin
Skarin, Anna
Schick, Robert Schilling
1). Group dynamics are a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognized, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However, to date, practical statistical methods, which can include group dynamics in animal movement models, have been lacking. 2). We consider a flexible modelling framework that distinguishes a grouplevel model, describing the movement of the group's centre, and an individuallevel model, such that each individual makes its movement decisions relative to the group centroid. The basic idea is framed within the flexible class of hidden Markov models, extending previous work on modelling animal movement by means of multistate random walks. 3). While in simulation experiments parameter estimators exhibit some bias in nonideal scenarios, we show that generally the estimation of models of this type is both feasible and ecologically informative. 4). We illustrate the approach using real movement data from 11 reindeer (Rangifer tarandus). Results indicate a directional bias towards a group centroid for reindeer in an encamped state. Though the attraction to the group centroid is relatively weak, our model successfully captures groupinfluenced movement dynamics. Specifically, as compared to a regular mixture of correlated random walks, the group dynamic model more accurately predicts the nondiffusive behaviour of a cohesive mobile group. 5). As technology continues to develop, it will become easier and less expensive to tag multiple individuals within a group in order to follow their movements. Our work provides a first inferential framework for understanding the relative influences of individual versus grouplevel movement decisions. This framework can be extended to include covariates corresponding to environmental influences or body condition. As such, this framework allows for a broader understanding of the many internal and external factors that can influence an individual's movement.

Living on the edge : Roe deer (Capreolus capreolus) density in the margins of Its geographical range
http://hdl.handle.net/10023/4523
Abstract: Over the last decades roe deer (Capreolus capreolus) populations have increased in number and distribution throughout Europe. Such increases have profound impacts on ecosystems, both positive and negative. Therefore monitoring roe deer populations is essential for the appropriate management of this species, in order to achieve a balance between conservation and mitigation of the negative impacts. Despite being required for an effective management plan, the study of roe deer ecology in Portugal is at an early stage, and hence there is still a complete lack of knowledge of roe deer density within its known range. Distance sampling of pellet groups coupled with production and decay rates for pellet groups provided density estimates for roe deer in northeastern Portugal (Lombada National Hunting Area  LNHA, Serra de Montesinho – SM and Serra da Nogueira – SN; LNHA and SM located in Montesinho Natural Park). The estimated roe deer density using a stratified detection function was 1.23/100 ha for LNHA, 4.87/100 ha for SM and 4.25/100 ha in SN, with 95% confidence intervals (CI) of 0.68 to 2.21, 3.08 to 7.71 and 2.25 to 8.03, respectively. For the entire area, the estimated density was about 3.51/100 ha (95% CI  2.26–5.45). This method can provide estimates of roe deer density, which will ultimately support management decisions. However, effective monitoring should be based on longterm studies that are able to detect population fluctuations. This study represents the initial phase of roe deer monitoring at the edge of its European range and intends to fill the gap in this species ecology, as the gathering of similar data over a number of years will provide the basis for stronger inferences. Monitoring should be continued, although the study area should be increased to evaluate the accuracy of estimates and assess the impact of management actions.
Sat, 01 Feb 2014 00:00:00 GMT
http://hdl.handle.net/10023/4523
20140201T00:00:00Z
Valente, Ana M.
Fonseca, Carlos
Marques, Tiago A.
Santos, João P.
Rodrigues, Rogério
Torres, Rita Tinoco
Over the last decades roe deer (Capreolus capreolus) populations have increased in number and distribution throughout Europe. Such increases have profound impacts on ecosystems, both positive and negative. Therefore monitoring roe deer populations is essential for the appropriate management of this species, in order to achieve a balance between conservation and mitigation of the negative impacts. Despite being required for an effective management plan, the study of roe deer ecology in Portugal is at an early stage, and hence there is still a complete lack of knowledge of roe deer density within its known range. Distance sampling of pellet groups coupled with production and decay rates for pellet groups provided density estimates for roe deer in northeastern Portugal (Lombada National Hunting Area  LNHA, Serra de Montesinho – SM and Serra da Nogueira – SN; LNHA and SM located in Montesinho Natural Park). The estimated roe deer density using a stratified detection function was 1.23/100 ha for LNHA, 4.87/100 ha for SM and 4.25/100 ha in SN, with 95% confidence intervals (CI) of 0.68 to 2.21, 3.08 to 7.71 and 2.25 to 8.03, respectively. For the entire area, the estimated density was about 3.51/100 ha (95% CI  2.26–5.45). This method can provide estimates of roe deer density, which will ultimately support management decisions. However, effective monitoring should be based on longterm studies that are able to detect population fluctuations. This study represents the initial phase of roe deer monitoring at the edge of its European range and intends to fill the gap in this species ecology, as the gathering of similar data over a number of years will provide the basis for stronger inferences. Monitoring should be continued, although the study area should be increased to evaluate the accuracy of estimates and assess the impact of management actions.

A risk function for behavioral disruption of Blainville’s beaked whales (Mesoplodon densirostris) from midfrequency active sonar
http://hdl.handle.net/10023/4522
Abstract: There is increasing concern about the potential effects of noise pollution on marine life in the world’s oceans. For marine mammals, anthropogenic sounds may cause behavioral disruption, and this can be quantified using a risk function that relates sound exposure to a measured behavioral response. Beaked whales are a taxon of deep diving whales that may be particularly susceptible to naval sonar as the species has been associated with sonarrelated mass stranding events. Here we derive the first empirical risk function for Blainville’s beaked whales (Mesoplodon densirostris) by combining in situ data from passive acoustic monitoring of animal vocalizations and navy sonar operations with precise ship tracks and sound field modeling. The hydrophone array at the Atlantic Undersea Test and Evaluation Center, Bahamas, was used to locate vocalizing groups of Blainville’s beaked whales and identify sonar transmissions before, during, and after MidFrequency Active (MFA) sonar operations. Sonar transmission times and source levels were combined with ship tracks using a sound propagation model to estimate the received level (RL) at each hydrophone. A generalized additive model was fitted to data to model the presence or absence of the start of foraging dives in 30minute periods as a function of the corresponding sonar RL at the hydrophone closest to the center of each group. This model was then used to construct a risk function that can be used to estimate the probability of a behavioral change (cessation of foraging) the individual members of a Blainville’s beaked whale population might experience as a function of sonar RL. The function predicts a 0.5 probability of disturbance at a RL of 150dBrms re µPa (CI: 144 to 155) This is 15dB lower than the level used historically by the US Navy in their risk assessments but 10 dB higher than the current 140 dB stepfunction
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10023/4522
20140101T00:00:00Z
Moretti, David
Thomas, Len
Marques, Tiago A.
Harwood, John
Dilley, Ashley
Neales, Bert
Shaffer, Jessica
Mccarthy, E
New, Leslie Frances
Jarvis, S
Morrissey, Ron
There is increasing concern about the potential effects of noise pollution on marine life in the world’s oceans. For marine mammals, anthropogenic sounds may cause behavioral disruption, and this can be quantified using a risk function that relates sound exposure to a measured behavioral response. Beaked whales are a taxon of deep diving whales that may be particularly susceptible to naval sonar as the species has been associated with sonarrelated mass stranding events. Here we derive the first empirical risk function for Blainville’s beaked whales (Mesoplodon densirostris) by combining in situ data from passive acoustic monitoring of animal vocalizations and navy sonar operations with precise ship tracks and sound field modeling. The hydrophone array at the Atlantic Undersea Test and Evaluation Center, Bahamas, was used to locate vocalizing groups of Blainville’s beaked whales and identify sonar transmissions before, during, and after MidFrequency Active (MFA) sonar operations. Sonar transmission times and source levels were combined with ship tracks using a sound propagation model to estimate the received level (RL) at each hydrophone. A generalized additive model was fitted to data to model the presence or absence of the start of foraging dives in 30minute periods as a function of the corresponding sonar RL at the hydrophone closest to the center of each group. This model was then used to construct a risk function that can be used to estimate the probability of a behavioral change (cessation of foraging) the individual members of a Blainville’s beaked whale population might experience as a function of sonar RL. The function predicts a 0.5 probability of disturbance at a RL of 150dBrms re µPa (CI: 144 to 155) This is 15dB lower than the level used historically by the US Navy in their risk assessments but 10 dB higher than the current 140 dB stepfunction

Optimizing sampling design to deal with mistnet avoidance in Amazonian birds and bats
http://hdl.handle.net/10023/4520
Abstract: Mist netting is a widely used technique to sample bird and bat assemblages. However, captures often decline with time because animals learn and avoid the locations of nets. This avoidance or net shyness can substantially decrease sampling efficiency. We quantified the daytoday decline in captures of Amazonian birds and bats with mist nets set at the same location for four consecutive days. We also evaluated how net avoidance influences the efficiency of surveys under different logistic scenarios using resampling techniques. Net avoidance caused substantial declines in bird and bat captures, although more accentuated in the latter. Most of the decline occurred between the first and second days of netting: 28% in birds and 47% in bats. Captures of commoner species were more affected. The numbers of species detected also declined. Moving nets daily to minimize the avoidance effect increased captures by 30% in birds and 70% in bats. However, moving the location of nets may cause a reduction in netting time and captures. When moving the nets caused the loss of one netting day it was no longer advantageous to move the nets frequently. In bird surveys that could even decrease the number of individuals captured and species detected. Net avoidance can greatly affect sampling efficiency but adjustments in survey design can minimize this. Whenever nets can be moved without losing netting time and the objective is to capture many individuals, they should be moved daily. If the main objective is to survey species present then nets should still be moved for bats, but not for birds. However, if relocating nets causes a significant loss of netting time, moving them to reduce effects of shyness will not improve sampling efficiency in either group. Overall, our findings can improve the design of mist netting sampling strategies in other tropical areas.
Wed, 18 Sep 2013 00:00:00 GMT
http://hdl.handle.net/10023/4520
20130918T00:00:00Z
Marques, Joao Tiago
Ramos Pereira, Maria J.
Marques, Tiago A.
Santos, Carlos David
Santana, Joana
Beja, Pedro
Palmeirim, Jorge M.
Mist netting is a widely used technique to sample bird and bat assemblages. However, captures often decline with time because animals learn and avoid the locations of nets. This avoidance or net shyness can substantially decrease sampling efficiency. We quantified the daytoday decline in captures of Amazonian birds and bats with mist nets set at the same location for four consecutive days. We also evaluated how net avoidance influences the efficiency of surveys under different logistic scenarios using resampling techniques. Net avoidance caused substantial declines in bird and bat captures, although more accentuated in the latter. Most of the decline occurred between the first and second days of netting: 28% in birds and 47% in bats. Captures of commoner species were more affected. The numbers of species detected also declined. Moving nets daily to minimize the avoidance effect increased captures by 30% in birds and 70% in bats. However, moving the location of nets may cause a reduction in netting time and captures. When moving the nets caused the loss of one netting day it was no longer advantageous to move the nets frequently. In bird surveys that could even decrease the number of individuals captured and species detected. Net avoidance can greatly affect sampling efficiency but adjustments in survey design can minimize this. Whenever nets can be moved without losing netting time and the objective is to capture many individuals, they should be moved daily. If the main objective is to survey species present then nets should still be moved for bats, but not for birds. However, if relocating nets causes a significant loss of netting time, moving them to reduce effects of shyness will not improve sampling efficiency in either group. Overall, our findings can improve the design of mist netting sampling strategies in other tropical areas.

Novel methods for species distribution mapping including spatial models in complex regions
http://hdl.handle.net/10023/4514
Abstract: Species Distribution Modelling (SDM) plays a key role in a number of biological applications: assessment of temporal trends in distribution, environmental impact assessment and spatial conservation planning. From a statistical perspective, this thesis develops two methods for increasing the accuracy and reliability of maps of density surfaces and provides a solution to the problem of how to collate multiple density maps of the same region, obtained from differing sources. From a biological perspective, these statistical methods are used to analyse two marine mammal datasets to produce accurate maps for use in spatial conservation planning and temporal trend assessment.
The first new method, Complex Region Spatial Smoother [CReSS; ScottHayward et al., 2013], improves smoothing in areas where the real distance an animal must travel (`as the animal swims') between two points may be greater than the straight line distance between them, a problem that occurs in complex domains with coastline or islands. CReSS uses estimates of the geodesic distance between points, model averaging and local radial smoothing. Simulation is used to compare its performance with other traditional and recentlydeveloped smoothing techniques: Thin Plate Splines (TPS, Harder and Desmarais [1972]), Geodesic Low rank TPS (GLTPS; Wang and Ranalli [2007]) and the Soap lm smoother (SOAP; Wood et al. [2008]). GLTPS cannot be used in areas with islands and SOAP can be very hard to parametrise. CReSS outperforms all of the other methods on a range of simulations, based on their fit to the underlying function as measured by mean squared error, particularly for sparse data sets.
Smoothing functions need to be flexible when they are used to model density surfaces that are highly heterogeneous, in order to avoid biases due to under or overfitting. This issue was addressed using an adaptation of a Spatially Adaptive Local Smoothing Algorithm (SALSA, Walker et al. [2010]) in combination with the CReSS method (CReSSSALSA2D). Unlike traditional methods, such as Generalised Additive Modelling, the adaptive knot selection approach used in SALSA2D naturally accommodates local changes in the smoothness of the density surface that is being modelled. At the time of writing, there are no other methods available to deal with this issue in topographically complex regions. Simulation results show that CReSSSALSA2D performs better than CReSS (based on MSE scores), except at very high noise levels where there is an issue with overfitting.
There is an increasing need for a facility to combine multiple density surface maps of individual species in order to make best use of metadatabases, to maintain existing maps, and to extend their geographical coverage. This thesis develops a framework and methods for combining species distribution maps as new information becomes available. The methods use Bayes Theorem to combine density surfaces, taking account of the levels of precision associated with the different sets of estimates, and kernel smoothing to alleviate artefacts that may be created where pairs of surfaces join. The methods were used as part of an algorithm (the Dynamic Cetacean Abundance Predictor) designed for BAE Systems to aid in risk mitigation for naval exercises.
Two case studies show the capabilities of CReSS and CReSSSALSA2D when applied to real ecological data. In the first case study, CReSS was used in a Generalised Estimating Equation framework to identify a candidate Marine Protected Area for the Southern Resident Killer Whale population to the south of San Juan Island, off the Pacific coast of the United States. In the second case study, changes in the spatial and temporal distribution of harbour porpoise and minke whale in northwestern European waters over a period of 17 years (19942010) were modelled. CReSS and CReSSSALSA2D performed well in a large, topographically complex study area. Based on simulation results, maps produced using these methods are more accurate than if a traditional GAMbased method is used. The resulting maps identified particularly high densities of both harbour porpoise and minke whale in an area off the west coast of Scotland in 2010, that might be a candidate for inclusion into the
Scottish network of Nature Conservation Marine Protected Areas.
Tue, 05 Nov 2013 00:00:00 GMT
http://hdl.handle.net/10023/4514
20131105T00:00:00Z
ScottHayward, Lindesay Alexandra Sarah
Species Distribution Modelling (SDM) plays a key role in a number of biological applications: assessment of temporal trends in distribution, environmental impact assessment and spatial conservation planning. From a statistical perspective, this thesis develops two methods for increasing the accuracy and reliability of maps of density surfaces and provides a solution to the problem of how to collate multiple density maps of the same region, obtained from differing sources. From a biological perspective, these statistical methods are used to analyse two marine mammal datasets to produce accurate maps for use in spatial conservation planning and temporal trend assessment.
The first new method, Complex Region Spatial Smoother [CReSS; ScottHayward et al., 2013], improves smoothing in areas where the real distance an animal must travel (`as the animal swims') between two points may be greater than the straight line distance between them, a problem that occurs in complex domains with coastline or islands. CReSS uses estimates of the geodesic distance between points, model averaging and local radial smoothing. Simulation is used to compare its performance with other traditional and recentlydeveloped smoothing techniques: Thin Plate Splines (TPS, Harder and Desmarais [1972]), Geodesic Low rank TPS (GLTPS; Wang and Ranalli [2007]) and the Soap lm smoother (SOAP; Wood et al. [2008]). GLTPS cannot be used in areas with islands and SOAP can be very hard to parametrise. CReSS outperforms all of the other methods on a range of simulations, based on their fit to the underlying function as measured by mean squared error, particularly for sparse data sets.
Smoothing functions need to be flexible when they are used to model density surfaces that are highly heterogeneous, in order to avoid biases due to under or overfitting. This issue was addressed using an adaptation of a Spatially Adaptive Local Smoothing Algorithm (SALSA, Walker et al. [2010]) in combination with the CReSS method (CReSSSALSA2D). Unlike traditional methods, such as Generalised Additive Modelling, the adaptive knot selection approach used in SALSA2D naturally accommodates local changes in the smoothness of the density surface that is being modelled. At the time of writing, there are no other methods available to deal with this issue in topographically complex regions. Simulation results show that CReSSSALSA2D performs better than CReSS (based on MSE scores), except at very high noise levels where there is an issue with overfitting.
There is an increasing need for a facility to combine multiple density surface maps of individual species in order to make best use of metadatabases, to maintain existing maps, and to extend their geographical coverage. This thesis develops a framework and methods for combining species distribution maps as new information becomes available. The methods use Bayes Theorem to combine density surfaces, taking account of the levels of precision associated with the different sets of estimates, and kernel smoothing to alleviate artefacts that may be created where pairs of surfaces join. The methods were used as part of an algorithm (the Dynamic Cetacean Abundance Predictor) designed for BAE Systems to aid in risk mitigation for naval exercises.
Two case studies show the capabilities of CReSS and CReSSSALSA2D when applied to real ecological data. In the first case study, CReSS was used in a Generalised Estimating Equation framework to identify a candidate Marine Protected Area for the Southern Resident Killer Whale population to the south of San Juan Island, off the Pacific coast of the United States. In the second case study, changes in the spatial and temporal distribution of harbour porpoise and minke whale in northwestern European waters over a period of 17 years (19942010) were modelled. CReSS and CReSSSALSA2D performed well in a large, topographically complex study area. Based on simulation results, maps produced using these methods are more accurate than if a traditional GAMbased method is used. The resulting maps identified particularly high densities of both harbour porpoise and minke whale in an area off the west coast of Scotland in 2010, that might be a candidate for inclusion into the
Scottish network of Nature Conservation Marine Protected Areas.

Laboratory astrophysics : investigation of planetary and astrophysical maser emission
http://hdl.handle.net/10023/4494
Abstract: This paper describes a model for cyclotron maser emission applicable to planetary auroral radio emission, the stars UV Ceti and CU Virginus, blazar jets and astrophysical shocks. These emissions may be attributed to energetic electrons moving into convergent magnetic fields that are typically found in association with dipole like planetary magnetospheres or shocks. It is found that magnetic compression leads to the formation of a velocity distribution having a horseshoe shape as a result of conservation of the electron magnetic moment. Under certain plasma conditions where the local electron plasma frequency ωpe is much less than the cyclotron frequency ωce the distribution is found to be unstable to maser type radiation emission. We have established a laboratorybased facility that has verified many of the details of our original theoretical description and agrees well with numerical simulations. The experiment has demonstrated that the horseshoe distribution produces cyclotron emission at a frequency just below the local electron cyclotron frequency, with polarisation close to Xmode and propagating nearly perpendicularly to the electron beam motion. We discuss recent developments in the theory and simulation of the instability including addressing radiation escape problems, and relate these to the laboratory, space, and astrophysical observations. The experiments showed strong narrow band EM emissions at frequencies just below the coldplasma cyclotron frequency as predicted by the theory. Measurements of the conversion efficiency, mode and spectral content were in close agreement with the predictions of numerical simulations undertaken using a particleincell code and also with satellite observations confirming the horseshoe maser as an important emission mechanism in geophysical/astrophysical plasmas. In each case we address how the radiation can escape the plasma without suffering strong absorption at the second harmonic layer.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/4494
20130101T00:00:00Z
Speirs, David
Cairns, R Alan
Kellett, Barry
Vorgul, Irena
McConville, Sandra
Cross, Adrian
Phelps, Alan
Ronald, Kevin
Bingham, Robert
This paper describes a model for cyclotron maser emission applicable to planetary auroral radio emission, the stars UV Ceti and CU Virginus, blazar jets and astrophysical shocks. These emissions may be attributed to energetic electrons moving into convergent magnetic fields that are typically found in association with dipole like planetary magnetospheres or shocks. It is found that magnetic compression leads to the formation of a velocity distribution having a horseshoe shape as a result of conservation of the electron magnetic moment. Under certain plasma conditions where the local electron plasma frequency ωpe is much less than the cyclotron frequency ωce the distribution is found to be unstable to maser type radiation emission. We have established a laboratorybased facility that has verified many of the details of our original theoretical description and agrees well with numerical simulations. The experiment has demonstrated that the horseshoe distribution produces cyclotron emission at a frequency just below the local electron cyclotron frequency, with polarisation close to Xmode and propagating nearly perpendicularly to the electron beam motion. We discuss recent developments in the theory and simulation of the instability including addressing radiation escape problems, and relate these to the laboratory, space, and astrophysical observations. The experiments showed strong narrow band EM emissions at frequencies just below the coldplasma cyclotron frequency as predicted by the theory. Measurements of the conversion efficiency, mode and spectral content were in close agreement with the predictions of numerical simulations undertaken using a particleincell code and also with satellite observations confirming the horseshoe maser as an important emission mechanism in geophysical/astrophysical plasmas. In each case we address how the radiation can escape the plasma without suffering strong absorption at the second harmonic layer.

Modelling catch sampling uncertainty in fisheries stock assessment : the AtlanticIberian sardine case
http://hdl.handle.net/10023/4474
Abstract: The statistical assessment of harvested fish populations, such as the AtlanticIberian sardine (AIS)
stock, needs to deal with uncertainties inherent in fisheries systems. Uncertainties arising from
sampling errors and stochasticity in stock dynamics must be incorporated in stock assessment
models so that management decisions are based on realistic evaluation of the uncertainty about
the status of the stock. The main goal of this study is to develop a stock assessment framework
that accounts for some of the uncertainties associated with the AIS stock that are currently not
integrated into stock assessment models. In particular, it focuses on accounting for the uncertainty
arising from the catch data sampling process.
The central innovation the thesis is the development of a Bayesian integrated stock assessment
(ISA) model, in which an observation model explicitly links stock dynamics parameters
with statistical models for the various types of data observed from catches of the AIS stock.
This allows for systematic and statistically consistent propagation of the uncertainty inherent in
the catch sampling process across the whole stock assessment model, through to estimates of
biomass and stock parameters. The method is tested by simulations and found to provide reliable
and accurate estimates of stock parameters and associated uncertainty, while also outperforming
existing designedbased and modelbased estimation approaches.
The method is computationally very demanding and this is an obstacle to its adoption
by fisheries bodies. Once this obstacle is overcame, the ISA modelling framework developed
and presented in this thesis could provide an important contribution to the improvement in the
evaluation of uncertainty in fisheries stock assessments, not only of the AIS stock, but of any other
fish stock with similar data and dynamics structure. Furthermore, the models developed in this
study establish a solid conceptual platform to allow future development of more complex models
of fish population dynamics.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10023/4474
20130101T00:00:00Z
Caneco, Bruno
The statistical assessment of harvested fish populations, such as the AtlanticIberian sardine (AIS)
stock, needs to deal with uncertainties inherent in fisheries systems. Uncertainties arising from
sampling errors and stochasticity in stock dynamics must be incorporated in stock assessment
models so that management decisions are based on realistic evaluation of the uncertainty about
the status of the stock. The main goal of this study is to develop a stock assessment framework
that accounts for some of the uncertainties associated with the AIS stock that are currently not
integrated into stock assessment models. In particular, it focuses on accounting for the uncertainty
arising from the catch data sampling process.
The central innovation the thesis is the development of a Bayesian integrated stock assessment
(ISA) model, in which an observation model explicitly links stock dynamics parameters
with statistical models for the various types of data observed from catches of the AIS stock.
This allows for systematic and statistically consistent propagation of the uncertainty inherent in
the catch sampling process across the whole stock assessment model, through to estimates of
biomass and stock parameters. The method is tested by simulations and found to provide reliable
and accurate estimates of stock parameters and associated uncertainty, while also outperforming
existing designedbased and modelbased estimation approaches.
The method is computationally very demanding and this is an obstacle to its adoption
by fisheries bodies. Once this obstacle is overcame, the ISA modelling framework developed
and presented in this thesis could provide an important contribution to the improvement in the
evaluation of uncertainty in fisheries stock assessments, not only of the AIS stock, but of any other
fish stock with similar data and dynamics structure. Furthermore, the models developed in this
study establish a solid conceptual platform to allow future development of more complex models
of fish population dynamics.

Incomplete contingency tables with censored cells with application to estimating the number of people who inject drugs in Scotland
http://hdl.handle.net/10023/4433
Abstract: Estimating the size of hidden or difficult to reach populations is often of interest for economic, sociological or public health reasons. In order to estimate such populations, administrative data lists are often collated to form multilist crosscounts and displayed in the form of an incomplete contingency table. Loglinear models are typically fitted to such data to obtain an estimate of the total population size by estimating the number of individuals not observed by any of the datasources. This approach has been taken to estimate the current number of people who inject drugs (PWID) in Scotland, with the Hepatitis C virus (HCV) diagnosis database used as one of the datasources to identify PWID. However, the HCV diagnosis datasource does not distinguish between current and former PWID, which, if ignored, will lead to overestimation of the total population size of current PWID. We extend the standard modelfitting approach to allow for a datasource which contains a mixture of target and nontarget individuals (i.e. in this case; current and former PWID). We apply the proposed approach to data for PWID in Scotland in 2003, 2006 and 2009 and compare to the results from standard loglinear models.
Wed, 30 Apr 2014 00:00:00 GMT
http://hdl.handle.net/10023/4433
20140430T00:00:00Z
Overstall, Antony
King, Ruth
Bird, Sheila
Hutchinson, Sharon
Hay, Gordon
Estimating the size of hidden or difficult to reach populations is often of interest for economic, sociological or public health reasons. In order to estimate such populations, administrative data lists are often collated to form multilist crosscounts and displayed in the form of an incomplete contingency table. Loglinear models are typically fitted to such data to obtain an estimate of the total population size by estimating the number of individuals not observed by any of the datasources. This approach has been taken to estimate the current number of people who inject drugs (PWID) in Scotland, with the Hepatitis C virus (HCV) diagnosis database used as one of the datasources to identify PWID. However, the HCV diagnosis datasource does not distinguish between current and former PWID, which, if ignored, will lead to overestimation of the total population size of current PWID. We extend the standard modelfitting approach to allow for a datasource which contains a mixture of target and nontarget individuals (i.e. in this case; current and former PWID). We apply the proposed approach to data for PWID in Scotland in 2003, 2006 and 2009 and compare to the results from standard loglinear models.

Magnetohydrodynamics dynamical relaxation of coronal magnetic fields : I. Parallel untwisted magnetic fields in 2D
http://hdl.handle.net/10023/4378
Abstract: Context. For the last thirty years, most of the studies on the relaxation of stressed magnetic fields in the solar environment have only considered the Lorentz force, neglecting plasma contributions, and therefore, limiting every equilibrium to that of a forcefree field. Aims: Here we begin a study of the nonresistive evolution of finite beta plasmas and their relaxation to magnetohydrostatic states, where magnetic forces are balanced by plasmapressure gradients, by using a simple 2D scenario involving a hydromagnetic disturbance to a uniform magnetic field. The final equilibrium state is predicted as a function of the initial disturbances, with aims to demonstrate what happens to the plasma during the relaxation process and to see what effects it has on the final equilibrium state. Methods: A set of numerical experiments are run using a full MHD code, with the relaxation driven by magnetoacoustic waves damped by viscous effects. The numerical results are compared with analytical calculations made within the linear regime, in which the whole process must remain adiabatic. Particular attention is paid to the thermodynamic behaviour of the plasma during the relaxation. Results: The analytical predictions for the final non forcefree equilibrium depend only on the initial perturbations and the total pressure of the system. It is found that these predictions hold surprisingly well even for amplitudes of the perturbation far outside the linear regime. Conclusions: Including the effects of a finite plasma beta in relaxation experiments leads to significant differences from the forcefree case.
Sat, 01 May 2010 00:00:00 GMT
http://hdl.handle.net/10023/4378
20100501T00:00:00Z
Fuentes Fernandez, Jorge
Parnell, Clare Elizabeth
Hood, Alan William
Context. For the last thirty years, most of the studies on the relaxation of stressed magnetic fields in the solar environment have only considered the Lorentz force, neglecting plasma contributions, and therefore, limiting every equilibrium to that of a forcefree field. Aims: Here we begin a study of the nonresistive evolution of finite beta plasmas and their relaxation to magnetohydrostatic states, where magnetic forces are balanced by plasmapressure gradients, by using a simple 2D scenario involving a hydromagnetic disturbance to a uniform magnetic field. The final equilibrium state is predicted as a function of the initial disturbances, with aims to demonstrate what happens to the plasma during the relaxation process and to see what effects it has on the final equilibrium state. Methods: A set of numerical experiments are run using a full MHD code, with the relaxation driven by magnetoacoustic waves damped by viscous effects. The numerical results are compared with analytical calculations made within the linear regime, in which the whole process must remain adiabatic. Particular attention is paid to the thermodynamic behaviour of the plasma during the relaxation. Results: The analytical predictions for the final non forcefree equilibrium depend only on the initial perturbations and the total pressure of the system. It is found that these predictions hold surprisingly well even for amplitudes of the perturbation far outside the linear regime. Conclusions: Including the effects of a finite plasma beta in relaxation experiments leads to significant differences from the forcefree case.

Flux emergence and coronal eruption
http://hdl.handle.net/10023/4376
Abstract: Aims. Our aim is to study the photospheric flux distribution of a twisted flux tube that emerges from the solar interior. We also report on the eruption of a new flux rope when the emerging tube rises into a preexisting magnetic field in the corona. Methods. To study the evolution, we use 3D numerical simulations by solving the timedependent and resistive MHD equations. We qualitatively compare our numerical results with MDI magnetograms of emerging flux at the solar surface. Results. We find that the photospheric magnetic flux distribution consists of two regions of opposite polarities and elongated magnetic tails on the two sides of the polarity inversion line (PIL), depending on the azimuthal nature of the emerging field lines and the initial field strength of the rising tube. Their shape is progressively deformed due to plasma motions towards the PIL. Our results are in qualitative agreement with observational studies of magnetic flux emergence in active regions (ARs). Moreover, if the initial twist of the emerging tube is small, the photospheric magnetic field develops an undulating shape and does not possess tails. In all cases, we find that a new flux rope is formed above the original axis of the emerging tube that may erupt into the corona, depending on the strength of the ambient field.
Sat, 01 May 2010 00:00:00 GMT
http://hdl.handle.net/10023/4376
20100501T00:00:00Z
Archontis, Vasilis
Hood, Alan William
Aims. Our aim is to study the photospheric flux distribution of a twisted flux tube that emerges from the solar interior. We also report on the eruption of a new flux rope when the emerging tube rises into a preexisting magnetic field in the corona. Methods. To study the evolution, we use 3D numerical simulations by solving the timedependent and resistive MHD equations. We qualitatively compare our numerical results with MDI magnetograms of emerging flux at the solar surface. Results. We find that the photospheric magnetic flux distribution consists of two regions of opposite polarities and elongated magnetic tails on the two sides of the polarity inversion line (PIL), depending on the azimuthal nature of the emerging field lines and the initial field strength of the rising tube. Their shape is progressively deformed due to plasma motions towards the PIL. Our results are in qualitative agreement with observational studies of magnetic flux emergence in active regions (ARs). Moreover, if the initial twist of the emerging tube is small, the photospheric magnetic field develops an undulating shape and does not possess tails. In all cases, we find that a new flux rope is formed above the original axis of the emerging tube that may erupt into the corona, depending on the strength of the ambient field.

Magnetohydrodynamic kink waves in twodimensional nonuniform prominence threads
http://hdl.handle.net/10023/4374
Abstract: Aims. We analyse the oscillatory properties of resonantly damped transverse kink oscillations in twodimensional prominence threads. Methods. The fine structures are modelled as cylindrically symmetric magnetic flux tubes with a dense central part with prominence plasma properties and an evacuated part, both surrounded by coronal plasma. The equilibrium density is allowed to vary nonuniformly in both the transverse and the longitudinal directions. We examine the influence of longitudinal density structuring on periods, damping times, and damping rates for transverse kink modes computed by numerically solving the linear resistive magnetohydrodynamic (MHD) equations. Results. The relevant parameters are the length of the thread and the density in the evacuated part of the tube, two quantities that are difficult to directly estimate from observations. We find that both of them strongly influence the oscillatory periods and damping times, and to a lesser extent the damping ratios. The analysis of the spatial distribution of perturbations and of the energy flux into the resonances allows us to explain the obtained damping times. Conclusions. Implications for prominence seismology, the physics of resonantly damped kink modes in twodimensional magnetic flux tubes, and the heating of prominence plasmas are discussed.
Thu, 01 Sep 2011 00:00:00 GMT
http://hdl.handle.net/10023/4374
20110901T00:00:00Z
Arregui, I
Soler, R
Ballester, J.
Wright, Andrew Nicholas
Aims. We analyse the oscillatory properties of resonantly damped transverse kink oscillations in twodimensional prominence threads. Methods. The fine structures are modelled as cylindrically symmetric magnetic flux tubes with a dense central part with prominence plasma properties and an evacuated part, both surrounded by coronal plasma. The equilibrium density is allowed to vary nonuniformly in both the transverse and the longitudinal directions. We examine the influence of longitudinal density structuring on periods, damping times, and damping rates for transverse kink modes computed by numerically solving the linear resistive magnetohydrodynamic (MHD) equations. Results. The relevant parameters are the length of the thread and the density in the evacuated part of the tube, two quantities that are difficult to directly estimate from observations. We find that both of them strongly influence the oscillatory periods and damping times, and to a lesser extent the damping ratios. The analysis of the spatial distribution of perturbations and of the energy flux into the resonances allows us to explain the obtained damping times. Conclusions. Implications for prominence seismology, the physics of resonantly damped kink modes in twodimensional magnetic flux tubes, and the heating of prominence plasmas are discussed.

Thermal conduction effects on the kink instability in coronal loops
http://hdl.handle.net/10023/4373
Abstract: Context. Heating of the solar corona by nanoflares, which are small transient events in which stored magnetic energy is dissipated by magnetic reconnection, may occur as the result of the nonlinear phase of the kink instability (Hood et al. 2009). Because of the high temperatures reached through these reconnection events, thermal conduction cannot be ignored in the evolution of the kink instability. Aims. To study the effect of thermal conduction on the nonlinear evolution of the kink instability of a coronal loop. To assess the efficiency of loop heating and the role of thermal conduction, both during the kink instability and for the long time evolution of the loop. Methods. Numerically solve the 3D nonlinear magnetohydrodynamic equations to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The initial state has zero net current. A comparison is made of the time evolution of the loop with thermal conduction and without thermal conduction. Results. Thermal conduction along magnetic field lines reduces the local temperature. This leads to temperatures that are an order of magnitude lower than those obtained in the absence of thermal conductivity. Consequently, different spectral lines are activated with and without the inclusion of thermal conduction, which have consequences for observations of solar corona loops. The conduction process is also important on the timescale of the fast magnetohydrodynamic phenomena. It reduces the kinetic energy released by an order of magnitude. Conclusions. Thermal conduction plays an essential role in the kink instability of coronal loops and cannot be ignored in the forward modelling of such loops.
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10023/4373
20110101T00:00:00Z
Botha, G. J. J.
Arber, T. D.
Hood, A. W.
Context. Heating of the solar corona by nanoflares, which are small transient events in which stored magnetic energy is dissipated by magnetic reconnection, may occur as the result of the nonlinear phase of the kink instability (Hood et al. 2009). Because of the high temperatures reached through these reconnection events, thermal conduction cannot be ignored in the evolution of the kink instability. Aims. To study the effect of thermal conduction on the nonlinear evolution of the kink instability of a coronal loop. To assess the efficiency of loop heating and the role of thermal conduction, both during the kink instability and for the long time evolution of the loop. Methods. Numerically solve the 3D nonlinear magnetohydrodynamic equations to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The initial state has zero net current. A comparison is made of the time evolution of the loop with thermal conduction and without thermal conduction. Results. Thermal conduction along magnetic field lines reduces the local temperature. This leads to temperatures that are an order of magnitude lower than those obtained in the absence of thermal conductivity. Consequently, different spectral lines are activated with and without the inclusion of thermal conduction, which have consequences for observations of solar corona loops. The conduction process is also important on the timescale of the fast magnetohydrodynamic phenomena. It reduces the kinetic energy released by an order of magnitude. Conclusions. Thermal conduction plays an essential role in the kink instability of coronal loops and cannot be ignored in the forward modelling of such loops.

Alfven wave phasemixing and damping in the ion cyclotron range of frequencies
http://hdl.handle.net/10023/4372
Abstract: Aims. We determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfven waves in the ion cyclotron range of frequencies in uniform and nonuniform equilibrium plasmas. Methods. Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient. Results. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in k(2)delta(2)(i) where k is wavenumber and delta(i) is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit k(2)delta(2)(i) >> 1. In a nonuniform plasma it is found that the spatiallyintegrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispersion, tends to zero in both the weak and strong phase mixing limits.
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10023/4372
20110101T00:00:00Z
Threlfall, J.
McClements, K. G.
De Moortel, I.
Aims. We determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfven waves in the ion cyclotron range of frequencies in uniform and nonuniform equilibrium plasmas. Methods. Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient. Results. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in k(2)delta(2)(i) where k is wavenumber and delta(i) is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit k(2)delta(2)(i) >> 1. In a nonuniform plasma it is found that the spatiallyintegrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispersion, tends to zero in both the weak and strong phase mixing limits.

Nonlinear wave propagation and reconnection at magnetic Xpoints in the Hall MHD regime
http://hdl.handle.net/10023/4368
Abstract: Context: The highly dynamical, complex nature of the solar atmosphere naturally implies the presence of waves in a topologically varied magnetic environment. Here, the interaction of waves with topological features such as null points is inevitable and potentially important for energetics. The low resistivity of the solar coronal plasma implies that nonmagnetohydrodynamic (MHD) effects should be considered in studies of magnetic energy release in this environment. Aims: This paper investigates the role of the Hall term in the propagation and dissipation of waves, their interaction with 2D magnetic Xpoints and the nature of the resulting reconnection. Methods: A Lagrangian remap shockcapturing code (Lare2d) was used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth (δi) in resistive Hall MHD. A magnetic nullpoint finding algorithm was also used to locate and track the evolution of the multiple nullpoints that are formed in the system. Results: Depending on the ratio of ion skin depth to system size, our model demonstrates that Hall effects can play a key role in the wavenull interaction. In particular, the initial fastwave pulse now consists of whistler and ioncyclotron components; the dispersive nature of the whistler wave leads to (i) earlier interaction with the null; (ii) the creation of multiple additional, transient nulls and, hence, an increased number of energy release sites. In the Hall regime, the relevant timescales (such as the onset of reconnection and the period of the oscillatory relaxation) of the system are reduced significantly, and the reconnection rate is enhanced.
Sun, 01 Jul 2012 00:00:00 GMT
http://hdl.handle.net/10023/4368
20120701T00:00:00Z
Threlfall, James William
Parnell, Clare Elizabeth
De Moortel, Ineke
McClements, Ken
Arber, Tony D.
Context: The highly dynamical, complex nature of the solar atmosphere naturally implies the presence of waves in a topologically varied magnetic environment. Here, the interaction of waves with topological features such as null points is inevitable and potentially important for energetics. The low resistivity of the solar coronal plasma implies that nonmagnetohydrodynamic (MHD) effects should be considered in studies of magnetic energy release in this environment. Aims: This paper investigates the role of the Hall term in the propagation and dissipation of waves, their interaction with 2D magnetic Xpoints and the nature of the resulting reconnection. Methods: A Lagrangian remap shockcapturing code (Lare2d) was used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth (δi) in resistive Hall MHD. A magnetic nullpoint finding algorithm was also used to locate and track the evolution of the multiple nullpoints that are formed in the system. Results: Depending on the ratio of ion skin depth to system size, our model demonstrates that Hall effects can play a key role in the wavenull interaction. In particular, the initial fastwave pulse now consists of whistler and ioncyclotron components; the dispersive nature of the whistler wave leads to (i) earlier interaction with the null; (ii) the creation of multiple additional, transient nulls and, hence, an increased number of energy release sites. In the Hall regime, the relevant timescales (such as the onset of reconnection and the period of the oscillatory relaxation) of the system are reduced significantly, and the reconnection rate is enhanced.