Dynamics of a collection of active particles on a two-dimensional periodic undulated surface

TL;DR

This study investigates how active particles move on a two-dimensional undulated surface, revealing different dynamical regimes and conditions under which effective equilibrium behavior emerges.

Contribution

It introduces a model for active particles on undulated surfaces and characterizes their dynamics across various activity levels and surface undulations.

Findings

Particles can be confined, subdiffusive, or superdiffusive depending on activity and surface undulation.

Green-Kubo relation holds for small undulations, indicating effective equilibrium.

Deviations increase with surface undulation amplitude.

Abstract

We study the dynamics of circular active particles (AP) on a two dimensional periodic undulated surface. Each particle has an internal energy mechanism which is modeled by an active friction force and it is controlled by an activity parameter $v_0$. It acts as negative friction if the speed of the particle is smaller than $v_0$ and normal friction otherwise. Surface undulation is modeled by the periodic undulation of fixed amplitude and wavelength and is measured in terms of a dimensionless ratio of amplitude and wavelength, $\bar{h}$. The dynamics of the particle is studied for different activities, $v_0$ and surface undulations (SU), $\bar{h}$. Three types of particle dynamics are observed on varying activity and SU. For small $v_0 \lesssim 0.1$ and $\bar{h}$ $\gtrsim 0.8$, particles remain confined in a surface minimum, for moderate $v_0 \lesssim \bar{h}$, dynamics of particle shows an intermediate subdiffusion to late time diffusion and for large $v_0 \gtrsim \bar{h}$, it shows initial superdiffusion to late time diffusion. For all $v_0$'s and $\bar{h} \lesssim 0.2$, the dynamics of particle, satisfies the Green-Kubo relation between the effective diffusivity and velocity auto-correlation function. Systematic deviation is found on increasing $\bar{h}$. Hence, an effective equilibrium can be established for a range of system parameters in this nonequilibirum system.