Elastic properties of anisotropic domain wall lattices

TL;DR

This paper studies the elastic properties and stability of various anisotropic domain wall lattices in two and three dimensions, with implications for cosmological models like solid dark energy.

Contribution

It provides detailed calculations of rigidity coefficients and propagation velocities for different lattice geometries, including non-affine perturbations, to evaluate their stability.

Findings

Triangular, hexagonal, and square lattices analyzed in 2D.

Cubic symmetric lattices examined in 3D.

Stability criteria established for various lattice configurations.

Abstract

Interest in the elastic properties of regular lattices constructed from domain walls has recently been motivated by cosmological applications as solid dark energy. This work investigates the particularly simple examples of triangular, hexagonal and square lattices in two dimensions and a variety of more complicated lattices in three dimensions which have cubic symmetry. The relevant rigidity coefficients are computed taking into account non-affine perturbations where necessary, and these are used to evaluate the propagation velocity for any macroscopic scale perturbation mode. Using this information we assess the stability of the various configurations.