Levy Walk Dynamics in an External Constant Force Field in Non-Static Media

Based on the recognition of the huge change of the transport properties for diffusion particles in non-static media, we consider a Levy walk model subjected to an external constant force in non-static media. Since the physical and comoving coordinates of non-static media are related by scale factor, we equivalently transfer the process from physical coordinate into comoving coordinate and derive the master equation governing the probability density function of the position of the particles in comoving coordinate. Utilizing the Hermite orthogonal polynomial expansions, some statistical properties are obtained, including the asymptotic behaviors of the first two moments in both coordinates and kurtosis. For some representative types of non-static media and Levy walks, the striking and interesting phenomena originating from the interplay between non-static media, external force, and intrinsic stochastic motion are observed. The stationary distribution are also analyzed for some cases through numerical simulations.

Automated summary

Based on recognizing the changes in transport properties of diffusion particles in non-static media, this study investigates a Levy walk model subjected to a constant external force in non-static media. By transferring the process from physical to comoving coordinates and deriving the master equation, the probability density function of particle positions in comoving coordinates is obtained. The study observes interesting phenomena resulting from the interplay between non-static media, external force, and intrinsic stochastic motion.