A mean-field model for nematic alignment of self-propelled rods

TL;DR

This paper introduces a rigorous mean-field model for nematic alignment in self-propelled rods, deriving a Fokker-Planck equation from microscopic collision rules to study the emergence of nematic order.

Contribution

It develops a novel, microscopic-based mean-field model for nematic alignment, avoiding phenomenological assumptions and deriving the governing Fokker-Planck equation.

Findings

Nematic order emerges from the homogeneous steady-state.

The model accurately captures the transition to nematic alignment.

Analytical and numerical analysis validate the model's predictions.

Abstract

In this paper we develop a model for nematic alignment of self-propelled rods interacting through binary collisions. We avoid phenomenological descriptions of rod interaction in favor of rigorously using a set of microscopic-level rules. Under the assumption that each collision results in a small change to a rod's orientation, we derive the Fokker-Planck equation for the evolution of the kinetic density function. Using analytical and numerical methods, we study the emergence of the nematic order from a homogeneous, uniform steady-state of the mean-field equation.