2020/01/31 by Chiqun Zhang, Amit Acharya, Alan C. Newell +1 · 10 citations
Chemistry · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Algorithm #Chemistry #Computation #Computer science #Condensed matter physics #Geometry #Gravitational singularity #Integrable system #Liquid Crystal Research Advancements #Liquid crystal #Mathematics #Physics #Quantum mechanics #Statistical physics #Symmetry (geometry) #Theoretical and Computational Physics #Theoretical physics #Topological defect #Topology (electrical circuits) #Translation (biology) #Translational symmetry #cond-mat.mtrl-sci #cond-mat.soft #nlin.PS
paper · pdf · open access · doi:10.1016/j.physd.2020.132828
published in Physica D Nonlinear Phenomena 417, 132828 (Elsevier BV)
arxiv created 2020/12/22 · openalex publication_date 2020/12/24 · openalex created_date 2021/01/05 · arxiv updated 2021/02/24 · openalex updated_date 2026/08/05
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 spectrum. 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.