Complex-tensor theory of simple smectics

TL;DR

This paper introduces a complex tensor-based theory for smectic materials that captures their unique order, defects, and local effects, simplifying numerical modeling of their complex dynamics.

Contribution

It presents a novel complex order parameter tensor framework that models smectic order, defects, and local effects, improving computational efficiency.

Findings

Successfully models dislocations and disclinations in smectics

Enables simulation of complex lamellar dynamics

Simplifies numerical analysis of smectic systems

Abstract

Smectic materials represent a unique state between fluids and solids, characterized by orientational and partial positional order, making them notoriously difficult to model, particularly in confining geometries. We propose a complex order parameter tensor to describe the local degree of lamellar ordering, layer displacement and orientation. The theory accounts for both dislocations and disclinations, as well as arrested configurations and colloid-induced local ordering. It considerably simplifies numerics, facilitating studies on the dynamics of topologically complex lamellar systems.