Mesoscopic theory for fluctuating active nematics

TL;DR

This paper develops a mesoscopic theoretical framework for active nematics, capturing key phenomena like anomalous fluctuations and long-range correlations through derived stochastic PDEs from a kinetic theory approach.

Contribution

It introduces a mesoscopic theory for active nematics derived from a kinetic model, including effective noise terms, and analyzes the resulting equations for instabilities and band solutions.

Findings

Recovered key terms responsible for anomalous fluctuations

Identified long-wavelength instability at nematic order onset

Derived a closed-form nonlinear density-segregated band solution

Abstract

The term active nematics designates systems in which apolar elongated particles spend energy to move randomly along their axis and interact by inelastic collisions in the presence of noise. Starting from a simple Vicsek-style model for active nematics, we derive a mesoscopic theory, complete with effective multiplicative noise terms, using a combination of kinetic theory and It\^o calculus approaches. The stochastic partial differential equations thus obtained are shown to recover the key terms argued in EPL \textbf{62} (2003) 196 to be at the origin of anomalous number fluctuations and long-range correlations. Their deterministic part is studied analytically, and is shown to give rise to the long-wavelength instability at onset of nematic order (see arXiv:1011.5408). The corresponding nonlinear density-segregated band solution is given in a closed form.