Diffusion, super-diffusion and coalescence from single step

Details Diffusion, super-diffusion and coalescence from single step Diffusion, super-diffusion and coalescence from single step

2007-09-14

arxiv.org/abs/0709.2333v2

J. Stat. Mech. P10007 (2007)

Physics

Condensed Matter

Statistical Mechanics

RevTeX (iopstyle) 19 pages, 5 eps-figures

Scientific paper

10.1088/1742-5468/2007/10/P10007

From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to build a velocity field. First we show that spatially uncorrelated fields $\bu(\bx)$ lead to both standard and anomalous diffusion equation. When the field $\bu(\bx)$ is spatially correlated each particle performs a simple free Brownian motion, but the trajectories of different particles result to be mutually correlated. The two-point statistical properties of the field $\bu(\bx)$ induce two-point spatial correlations in the particle distribution satisfying a simple but non-trivial diffusion-like equation. These displacement-displacement correlations lead the system to three possible regimes: coalescence, simple clustering and a combination of the two. The existence of these different regimes, in the one-dimensional system, is shown through computer simulations and a simple theoretical argument.

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