English

Spontaneous Breaking of Rotational Symmetry with Arbitrary Defects and a Rigidity Estimate

Probability 2015-06-23 v3 Differential Geometry

Abstract

The goal of this paper is twofold. First we prove a rigidity estimate, which generalises the theorem on geometric rigidity of Friesecke, James and M\"uller to 1-forms with non-vanishing exterior derivative. Second we use this estimate to prove a kind of spontaneous breaking of rotational symmetry for some models of crystals, which allow almost all kinds of defects, including unbounded defects as well as edge, screw and mixed dislocations, i.e. defects with Burgers vectors.

Keywords

Cite

@article{arxiv.1408.5375,
  title  = {Spontaneous Breaking of Rotational Symmetry with Arbitrary Defects and a Rigidity Estimate},
  author = {Simon Aumann},
  journal= {arXiv preprint arXiv:1408.5375},
  year   = {2015}
}

Comments

40 pages, 6 figures, minor changes