Active Brownian and inertial particles in disordered environments: short-time expansion of the mean-square displacement

Abstract

We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behaviour adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is $\alpha =3$ and $\alpha =4$. We confirm our theoretical predictions by computer simulations. Moreover they are verifiable in experiments on self-propelled colloids in random environments.

10 page, 4 figures

References in corpus (17)

• Self-motile colloidal particles: from directed propulsion to random walk
• Accurate sampling using Langevin dynamics
• Phototaxis of synthetic microswimmers in optical landscapes
• Inertial effects of self-propelled particles: from active Brownian to active Langevin motion
• Distortion and destruction of colloidal flocks in disordered environments
• Speckle Optical Tweezers: Micromanipulation with Random Light Fields
• Dynamic Phases of Active Matter Systems with Quenched Disorder
• Symmetry properties of the large-deviation function of the velocity of a self-propelled polar particle
• Self-Polarizing Microswimmers in Active Density Waves
• Escape of a passive particle from activity-induced energy landscape: Emergence of slow and fast effective diffusion
• Translational and rotational dynamics of a self-propelled Janus probe in crowded environments
• Crowding-Enhanced Diffusion: An Exact Theory for Highly Entangled Self-Propelled Stiff Filaments
• Experimental creation and characterization of random potential energy landscapes exploiting speckle patterns
• Deflection of phototactic microswimmers through obstacle arrays
• Random motion of a circle microswimmer in a random environment
• Colloids Exposed to Random Potential Energy Landscapes: from Particle Number Density to Particle-Potential and Particle-Particle Interactions
• Colloidal Brazil nut effect in microswimmer mixtures induced by motility contrast

Cited by in corpus (17)

• Active Ornstein-Uhlenbeck model for self-propelled particles with inertia
• Time-dependent inertia of self-propelled particles: the Langevin rocket
• The Parental Active Model: a unifying stochastic description of self-propulsion
• Role of rotational inertia for collective phenomena in active matter
• Dynamics of active particles with space-dependent swim velocity
• Dynamics of active particles with translational and rotational inertia
• Active noise-driven particles under space-dependent friction in one dimension
• Active Matter Shepherding and Clustering in Inhomogeneous Environments
• Inertial self-propelled particles in anisotropic environments
• The Many Faces of Fluctuation-Dissipation Relations Out of Equilibrium
• Inertial Dynamics of Run-and-Tumble Particle
• Time-dependent properties of run-and-tumble particles: Density relaxation
• Harmonically trapped inertial run-and-tumble particle in one dimension
• AMEP: The Active Matter Evaluation Package for Python
• Confined active particles with spatially dependent Lorentz force: an odd twist to the "best Fokker-Planck approximation"
• Noise-cancellation algorithm for simulations of Brownian particles
• Correlated escape of active particles across a potential barrier