Fluctuations and symmetries in two-dimensional active gels

TL;DR

This paper develops effective 2D hydrodynamic equations for active gels with polar or nematic symmetry, analyzing their instabilities, correlations, and particle diffusion influenced by activity, inspired by biological cytoskeletal systems.

Contribution

It derives and analyzes effective 2D hydrodynamic equations for active gels with different symmetries based on 3D models, highlighting how boundary conditions affect their behavior.

Findings

Identified linear instabilities in active gels.

Calculated correlation functions and diffusion constants.

Showed dependence of properties on activity levels.

Abstract

Motivated by the unique physical properties of {\em biological active matter}, e.g., cytoskeletal dynamics in eukaryotic cells, we set up {\em effective} two-dimensional (2d) coarse-grained hydrodynamic equations for the dynamics of thin {\em active gels} with polar or nematic symmetries. We use the well-known three-dimensional (3d) descriptions [K. Kruse {\em et al}, {\em Eur. Phys. J E}, {\bf 16}, 5 (2005); A. Basu {\em et al}, {\em Eur. Phys. J E}, {\bf 27}, 149 (2008)] for thin active gel samples confined between parallel plates with appropriate boundary conditions to derive the effective 2d constitutive relations between appropriate thermodynamic fluxes and generalised forces for small deviations from equilibrium. We consider three distinct cases, characterised by spatial symmetries and boundary conditions, and show how such considerations dictate the structure of the constitutive relations. We use these to study the linear instabilities, calculate the correlation functions and the diffusion constant of a small tagged particle, and elucidate their dependences on the {\em activity} or nonequilibrium drive.