Kinematic matrix theory and universalities in self-propellers and active swimmers

TL;DR

This paper introduces a matrix-based kinematrix formalism that simplifies the analysis of self-propellers and active swimmers, revealing universal behaviors and emergent time scales across diverse systems.

Contribution

The paper presents a novel, efficient matrix formalism that unifies the study of various active particles and uncovers universal ensemble behaviors.

Findings

Unified matrix formalism for self-propellers

Revealed universal behaviors and emergent time scales

Expressed active fluctuations and hydrodynamics additively

Abstract

We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the "kinematrix", from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales. Active fluctuations and hydrodynamic interactions can be expressed as an additive composition of separate self-propellers.