Two-dimensional active motion

Abstract

The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of scattered angles of the swimming direction, which encompasses the pattern of motion of particles that move at constant speed. An exact analytical expression for the marginal probability density of finding a particle on a given position at a given instant, independently of its direction of motion, is provided; and a connection with a generalized diffusion equation is unveiled. Exact analytical expressions for the time dependence of the mean-square displacement and of the kurtosis of the distribution of the particle positions are presented. For this, it is shown that only the first trigonometric moments of the distribution of the scattered direction of motion are needed. The effects of persistence and of circular motion are discussed for different families of distributions of the scattered direction of motion.

arXiv comment17 pages, 8 figures (published version)

References in corpus (30)

• Active Particles in Complex and Crowded Environments
• Swimming in circles: Motion of bacteria near solid boundaries
• Lévy walks
• How far from equilibrium is active matter?
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Circular motion of asymmetric self-propelling particles
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• A self-propelled particle in an external potential: is there an effective temperature?
• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Dynamics of a Brownian circle swimmer
• Effective Interactions in Active Brownian Suspensions
• Multidimensional Stationary Probability Distribution for Interacting Active Particles
• Dynamics of self-propelled Janus particles in viscoelastic fluids
• Deformable self-propelled particles
• Memory-induced transition from a persistent random walk to circular motion for achiral microswimmers
• Probing the spatiotemporal dynamics of catalytic Janus particles with single-particle tracking and differential dynamic microscopy
• A self-driven phase transition drives Myxococcus xanthus fruiting body formation
• Intermediate scattering function of an anisotropic active Brownian particle
• Steering chiral swimmers along noisy helical paths
• The self-propelled Brownian spinning top: dynamics of a biaxial swimmer at low Reynolds numbers
• Diffusion of active chiral particles
• Smoluchowski Diffusion Equation for Active Brownian Swimmers
• Diffusion properties of active particles with directional reversal
• Generalized Ornstein-Uhlenbeck Model for Active Motion
• Intermediate scattering function of an anisotropic Brownian circle swimmer
• Active motion assisted by correlated stochastic torques
• Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order
• Critical Phenomena in Active Matter
• Non-Gaussian normal diffusion induced by delocalization
• Effect of reorientation statistics on torque response of self propelled particles

Cited by in corpus (13)

• Run-and-tumble particles in two-dimensions : Marginal position distributions
• Dynamics of switching processes: general results and applications to intermittent active motion
• Self-propulsion with speed and orientation fluctuation: exact computation of moments and dynamical bistabilities in displacement
• Chiral run-and-tumble walker: transport and optimizing search
• Magnetized granular particles running and tumbling on $S^1$
• Anisotropic run-and-tumble-turn dynamics
• Generalized persistence dynamics for active motion
• Persistence of an active asymmetric rigid Brownian particle in two dimensions
• Tagged particle behavior in a harmonic chain of direction reversing active Brownian particles
• Experimental Modeling of Chiral Active Robots and a Minimal Model of Non-Gaussian Displacements
• First-Passage-Time Asymmetry for Biased Run-and-Tumble Processes
• Orthogonal run-and-tumble walks
• The Memory Function of the Generalized Diffusion Equation of Active Motion