Density and Polarization of Active Brownian Particles in Curved Activity Landscapes

TL;DR

This paper investigates how the curvature of activity landscapes influences density and polarization patterns in active Brownian particles, revealing that interface curvature affects key state functions like swim pressure.

Contribution

It generalizes the understanding of density and polarization patterns to curved activity landscapes, extending previous planar landscape results to arbitrary radially symmetric geometries.

Findings

Density and polarization depend on interface curvature.

Analytical results match numerical calculations.

Curvature influences swim pressure and polarization patterns.

Abstract

Suspensions of motile active particles with space dependent activity form characteristic polarization and density patterns. Recent single-particle studies for planar activity landscapes identified several quantities associated with emergent density-polarization patterns, including swim pressure, that are solely determined by bulk variables and thus constitute state functions. We show that for radially symmetric activity steps these variables depend on the curvature of the active-passive interface. In the specific case of total polarization and swim pressure, we generalize this result for arbitrary radially symmetric activity landscapes. Our exact as well as approximate analytical results agree with exact numerical calculations. We expect qualitatively the same results to hold for arbitrarily curved activity landscapes.