Boltzmann-Ginzburg-Landau theory for autochemotaxis of active rod-like particles

TL;DR

This paper develops a Boltzmann-Ginzburg-Landau theoretical framework to analyze how chemotaxis influences collective behavior in active rod-like particles, revealing contrasting effects of translational and rotational responses on stability.

Contribution

It introduces a novel BGL approach to derive dynamical equations for active rods with chemotaxis, linking microscopic responses to macroscopic collective phenomena.

Findings

Translational chemotaxis promotes instability in uniform states.

Rotational chemotaxis suppresses instability.

Theoretical analysis clarifies chemotaxis effects on collective dynamics.

Abstract

We investigate the interplay between chemotaxis and alignment interactions in active rod-like particles, such as E. coli and Janus rods. Starting from a discrete model of self-propelled rods with chemotactic responses, we employ a Boltzmann-Ginzburg-Landau (BGL) approach to derive coarse-grained dynamical equations for the density, polar and nematic orientational order parameters, and the concentration field of the chemoattractant. We perform a linear stability analysis for fluctuations around uniform steady states corresponding to isotropic and nematic phases. In both phases, we find that translational chemotactic response promotes instability, while rotational chemotactic response suppresses it, elucidating their contrasting effects on the onset of collective dynamics.