Towards deterministic equations for Levy walks: the fractional material derivative

Details Towards deterministic equations for Levy walks: the fractional material derivative Towards deterministic equations for Levy walks: the fractional material derivative

2002-10-17

arxiv.org/abs/cond-mat/0210373v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.67.010101

Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We derive a generalized dynamical formulation for Levy walks in which the fractional equivalent of the material derivative occurs. Our approach will be useful for the dynamical formulation of Levy walks in an external force field or in phase space for which the description in terms of the continuous time random walk or its corresponding generalized master equation are less well suited.

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