Computing with non-orientable defects: nematics, smectics and natural patterns
| Autor: | Amit Acharya, Chiqun Zhang, Alan C. Newell, Shankar C. Venkataramani |
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| Rok vydání: | 2020 |
| Předmět: |
Physics
Condensed Matter - Materials Science Computation Numerical analysis Physical system Pattern formation Materials Science (cond-mat.mtrl-sci) FOS: Physical sciences Statistical and Nonlinear Physics Pattern Formation and Solitons (nlin.PS) Condensed Matter - Soft Condensed Matter Condensed Matter Physics 01 natural sciences Nonlinear Sciences - Pattern Formation and Solitons Symmetry (physics) 010305 fluids & plasmas Liquid crystal 0103 physical sciences Soft Condensed Matter (cond-mat.soft) Gravitational singularity Statistical physics 010306 general physics Translational symmetry |
| DOI: | 10.48550/arxiv.2001.11534 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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