In this thesis we generalise the rigidity estimates of Friesecke et al. [2002] and Müller et al. [2014] to vector fields whose properties are constrained by both conditions on the support of their curl and the underlying discrete symmetries of the lattice Z2. These analytical estimates and other considerations are applied to a statistical model of a crystal containing defects based on work by Aumann [2015]. It is demonstrated in this thesis that we allow a finite density of defects. The main result is that regardless of crystal size, the ordering of the crystal, expressed via the L2-distance of a random vector field from the rotations, can be made arbitrarily small for sufficiently low temperature β-1.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:752454 |
| Date | January 2017 |
| Creators | Williams, Luke D. |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/105569/ |
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