Asymptotic analysis of the energy for a ferroelectric nematic

TL;DR

This paper analyzes the asymptotic behavior of the energy functional for ferroelectric nematics, showing its convergence to a nematic energy model under high elastic anisotropy conditions.

Contribution

It establishes the $$-convergence of the ferroelectric nematic energy to a nematic energy model, highlighting differences in physical regimes.

Findings

The ferroelectric nematic energy functional $$-converges to a nematic energy model.

The models operate in fundamentally different parameter regimes.

The analysis reveals the asymptotic relationship between ferroelectric and nematic energies.

Abstract

The variational model for a ferroelectric nematic bears close resemblance to the well-known energy model for micromagnetics. Despite this similarity, the two models operate in fundamentally distinct parameter regimes describing different physics. In this paper we establish that the ferroelectric nematic energy functional $\Gamma$-converges to the energy of a nematic with high elastic anisotropy.