Now showing items 1-6 of 6

    • The Assouad dimension of randomly generated fractals 

      Fraser, Jonathan MacDonald; Miao, Jun Jie; Troscheit, Sascha (2018-05) - Journal article
      We consider several dierent models for generating random fractals including random self-similar sets, random self-affine carpets, and Mandelbrot percolation. In each setting we compute either the almost sure or the Baire ...
    • The Assouad spectrum and the quasi-Assouad dimension : a tale of two spectra 

      Fraser, Jonathan MacDonald; Hare, Kathryn E.; Hare, Kevin G.; Troscheit, Sascha; Yu, Han (2019-01-17) - Journal article
      We consider the Assouad spectrum, introduced by Fraser and Yu, along with a natural variant that we call the 'upper Assouad spectrum'. These spectra are designed to interpolate between the upper box-counting and Assouad ...
    • Dimension theory of random self-similar and self-affine constructions 

      Troscheit, Sascha (University of St Andrews, 2017-06-23) - Thesis
      This thesis is structured as follows. Chapter 1 introduces fractal sets before recalling basic mathematical concepts from dynamical systems, measure theory, dimension theory and probability theory. In Chapter 2 we give ...
    • An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta 

      Allanson, Oliver Douglas; Neukirch, Thomas; Wilson, Fiona; Troscheit, Sascha (2015-10) - Journal article
      We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution ...
    • From one-dimensional fields to Vlasov equilibria : Theory and application of Hermite Polynomials 

      Allanson, Oliver Douglas; Neukirch, Thomas; Troscheit, Sascha; Wilson, Fiona (2016-06) - Journal article
      We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov-Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using ...
    • On the inverse problem for Channell collisionless plasma equilibria 

      Allanson, Oliver Douglas; Troscheit, Sascha; Neukirch, Thomas (2018-09-24) - Journal article
      Vlasov–Maxwell equilibria are described by the self-consistent solutions of the time-independent Maxwell equations for the real-space dynamics of electromagnetic fields and the Vlasov equation for the phase-space dynamics ...