BPS Configurations in Smectics
C.D. Santangelo, Randall D. Kamien
TL;DR
This paper extends the exact solutions for elastic deformations in smectic liquid crystals to more complex configurations, revealing nonlinear effects and long-range interactions using BPS decomposition.
Contribution
It introduces a generalized approach for 1D deformations in smectics, including multiple dislocations, and analyzes nonlinear elastic interactions.
Findings
Enhanced long-range attractive interactions due to nonlinear elasticity.
Extension of exact solutions to complex dislocation configurations.
Approximate deformation profiles near spherical inclusions.
Abstract
It is typical in smectic liquid crystals to describe elastic deformations with a linear theory when the elastic strain is small. We extend the recent, exact solution of Brener and Marchenko to more general one-dimensional deformations, including multiple edge dislocations by relying on the Bogomol'nyi, Prasad and Sommerfield (BPS) decomposition. We introduce an approximation for the deformation profile far from a spherical inclusion and find an enhanced attractive interaction at long distances due to the nonlinear elasticity.
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