TY - JOUR
T1 - Computing with non-orientable defects
T2 - Nematics, smectics and natural patterns
AU - Zhang, Chiqun
AU - Acharya, Amit
AU - Newell, Alan C.
AU - Venkataramani, Shankar C.
N1 - Funding Information:
AA, SCV, and ACN were supported by the NSF Growing Convergence Research award 2021019. SCV is partially supported by the Simons Foundation, United States through award 524875 and by the National Science Foundation, United States through award DMR 1923922 . This work was initiated during a visit by AA to the Dept. of Mathematics at the University of Arizona; their hospitality is much appreciated. Portions of this work were carried out when SCV was visiting the Center for Nonlinear Analysis at Carnegie Mellon University, and their hospitality is gratefully acknowledged.
PY - 2021/3
Y1 - 2021/3
N2 - 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.
AB - 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.
KW - Computation of defects
KW - Defects in materials
KW - Effective theories
KW - Liquid crystals
KW - Non-orientability
KW - Pattern formation
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U2 - 10.1016/j.physd.2020.132828
DO - 10.1016/j.physd.2020.132828
M3 - Article
AN - SCOPUS:85099267039
VL - 417
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
M1 - 132828
ER -