Levy walks with velocity fluctuations

Details Levy walks with velocity fluctuations Levy walks with velocity fluctuations

2012-02-03

arxiv.org/abs/1202.0683v1

Phys. Rev. E 85, 031148 (2012)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.85.031148

The standard Levy walk is performed by a particle that moves ballistically between randomly occurring collisions, when the intercollision time is a random variable governed by a power-law distribution. During instantaneous collision events the particle randomly changes the direction of motion but maintains the same constant speed. We generalize the standard model to incorporate velocity fluctuations into the process. Two types of models are considered, namely, (i) with a walker changing the direction and absolute value of its velocity during collisions only, and (ii) with a walker whose velocity continuously fluctuates. We present full analytic evaluation of both models and emphasize the importance of initial conditions. We show that the type of the underlying Levy walk process can be identified by looking at the ballistic regions of the diffusion profiles. Our analytical results are corroborated by numerical simulations.

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