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arXiv · 1002.1450

Dynamics of heterogeneous hard spheres in a file

Ophir Flomenbom
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Abstract

Normal dynamics in a quasi-one-dimensional channel of length L (\to\infty) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W D^(-{\gamma}), for small D, where 0\leq{\gamma}<1. The initial spheres' density {\rho} is non-uniform and scales with the distance (from the origin) l as, {\rho} l^(-a), 0\leqa\leq1. An approximation for the N-particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys, ~t^(1-{\gamma})/(2c-{\gamma}), where c=1/(1+a). The PDF of the tagged particle is Gaussian in position. Generalizations of these results are considered.

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Ophir Flomenbom. 2010-02-07. Dynamics of heterogeneous hard spheres in a file. https://doi.org/10.1103/physreve.82.031126

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