Computing with non-orientable defects: Nematics, smectics and natural patterns

PHYSICA D-NONLINEAR PHENOMENA

卷:417

Article

Zhang, Chiqun¹  Acharya, Amit^2,3  Newell, Alan C.⁴  Venkataramani, Shankar C.⁴ 

[1] Microsoft, Irvine, CA USA

[2] Carnegie Mellon Univ, Dept Civil & Environm Engn, Pittsburgh, PA 15213 USA

[3] Carnegie Mellon Univ, Ctr Nonlinear Anal, Pittsburgh, PA 15213 USA

[4] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

关键词: Defects in materials;    Non-orientability;    Effective theories;    Liquid crystals;    Pattern formation;    Computation of defects;   

DOI  :  10.1016/j.physd.2020.132828

来源: Elsevier

【 摘 要 】

Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as 'unphysical' singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the 'micro-physics' to obtain thermodynamically consistent, well-set models that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials pectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations. (c) 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

【 授权许可】

Free