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Rigidity for sticky disks
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dc.contributor.author | Connelly, Robert | |
dc.contributor.author | Gortler, Steven J. | |
dc.contributor.author | Theran, Louis Simon | |
dc.date.accessioned | 2019-01-17T16:30:08Z | |
dc.date.available | 2019-01-17T16:30:08Z | |
dc.date.issued | 2019-02-28 | |
dc.identifier | 257381998 | |
dc.identifier | 7e5e4c40-41bd-40b1-b706-1afef5ad6ede | |
dc.identifier | 85062725181 | |
dc.identifier | 000465426300012 | |
dc.identifier.citation | Connelly , R , Gortler , S J & Theran , L S 2019 , ' Rigidity for sticky disks ' , Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences , vol. 475 , no. 2222 , 20180773 . https://doi.org/10.1098/rspa.2018.0773 | en |
dc.identifier.issn | 1364-5021 | |
dc.identifier.other | ORCID: /0000-0001-5282-4800/work/73701816 | |
dc.identifier.uri | https://hdl.handle.net/10023/16892 | |
dc.description.abstract | We study the combinatorial and rigidity properties of disc packings with generic radii. We show that a packing of n discs in the plane with generic radii cannot have more than 2n − 3 pairs of discs in contact. The allowed motions of a packing preserve the disjointness of the disc interiors and tangency between pairs already in contact (modelling a collection of sticky discs). We show that if a packing has generic radii, then the allowed motions are all rigid body motions if and only if the packing has exactly 2n − 3 contacts. Our approach is to study the space of packings with a fixed contact graph. The main technical step is to show that this space is a smooth manifold, which is done via a connection to the Cauchy–Alexandrov stress lemma. Our methods also apply to jamming problems, in which contacts are allowed to break during a motion. We give a simple proof of a finite variant of a recent result of Connelly et al. (Connelly et al. 2018 (http://arxiv.org/abs/1702.08442)) on the number of contacts in a jammed packing of discs with generic radii. | |
dc.format.extent | 16 | |
dc.format.extent | 522744 | |
dc.language.iso | eng | |
dc.relation.ispartof | Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences | en |
dc.subject | Rigidity | en |
dc.subject | Circle packings | en |
dc.subject | Jamming | en |
dc.subject | QA Mathematics | en |
dc.subject | T-DAS | en |
dc.subject | BDC | en |
dc.subject.lcc | QA | en |
dc.title | Rigidity for sticky disks | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1098/rspa.2018.0773 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/1809.02006 | en |
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