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.

17 pages, 8 figures (published version)

References in corpus (11)

• Lévy walks
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• A self-propelled particle in an external potential: is there an effective temperature?
• Dynamics of a Brownian circle swimmer
• Effective Interactions in Active Brownian Suspensions
• Multidimensional Stationary Probability Distribution for Interacting Active Particles
• Intermediate scattering function of an anisotropic active Brownian particle
• Diffusion of active chiral particles
• Generalized Ornstein-Uhlenbeck Model for Active Motion
• Intermediate scattering function of an anisotropic Brownian circle swimmer

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