Restricted diffusion and the return to the origin probability at intermediate and long times

Schwartz, L. M., Hürlimann, M. D., Dunn, K. J., Mitra, P. P., Bergman, D. J. (1997) Restricted diffusion and the return to the origin probability at intermediate and long times. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 55 (4). pp. 4225-4234. ISSN 1063651X (ISSN)

URL: http://journals.aps.org/pre/abstract/10.1103/PhysR...
DOI: 10.1103/PhysRevE.55.4225

Abstract

Pulsed field gradient spin echo magnetic resonance measurements on fluid saturated porous media provide a natural framework for the examination of a classic problem in mathematical physics. We examine the overall time dependence of the return to the origin probability (RTOP) with particular emphasis on the intermediate and long time behavior. In the long time limit this probability is related to the electrical conductivity. In periodic geometries we compare the results of eigenvalue expansions and numerical simulations. Here we find that, when the diffusion length is roughly equal to a pore diameter, the normalized PRTOP, Ps(t), shows a maximum. Thus, the approach to the long time limit is not monotonie. We show that the existence of this maximum can be predicted based on variational arguments. For disordered systems, simulations and experiments are found to be in agreement and again suggest that the behavoir of Ps(t) is not monotonie.

Item Type: Paper
Subjects: physics > biophysics
physics > fluid dynamics
Investigative techniques and equipment > magnetic resonance imaging
physics > biophysics > pore dynamics
CSHL Authors:
Communities: CSHL labs > Mitra lab
Depositing User: CSHL Librarian
Date: 1997
Date Deposited: 02 Apr 2012 20:32
Last Modified: 10 Feb 2017 17:18
URI: http://repository.cshl.edu/id/eprint/25876

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