Abstract
Using tools of nonequilibrium mechanics, we study a model of self-propelled hard rods ona substrate in two dimensions to quantify the interplay of self-propulsion andexcluded-volume effects. We derive a Smoluchowski equation for the configurationalprobability density of self-propelled rods that contains several modifications as compared tothe familiar Smoluchowski equation for thermal rods. As a side-product of our work, wealso present a purely dynamical derivation of the Onsager form of the mean-fieldexcluded-volume interaction among thermal hard rods.
Highlights
Self-propelled particles draw energy from internal or external sources and dissipate this energy by moving through the medium they inhabit
Before deriving the Smoluchwski equation for self-propelled hard rods, we show how this method can be implemented to provide a derivation of the Smoluchowski equation for thermal hard rods, with the well-known mean field Onsager excluded volume interaction
In this paper we have analyzed the microscopic dynamics and statistical mechanics of a collection of self-propelled particles modeled as long thin polar rods that move along one direction of their long axis
Summary
Self-propelled particles draw energy from internal or external sources and dissipate this energy by moving through the medium they inhabit. This is the simplest model for a “living nematic liquid crystal”, a terminology that has been used to describe the collective behavior of a variety of intrinsically self-propelled systems, from bacterial suspensions to monolayers of vibrated granular rods. The momentum exchanged by two rods upon collision is rendered highly anisotropic by self-propulsion This yields the additional collisional contributions to the excluded volume interaction described by the last terms in Eqs. This approximation, together with a low density closure of the Fokker-Planck hierarchy, allows us to derive the Smoluchowski equation.
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