Nonextensive statistics in viscous fingering

Details Nonextensive statistics in viscous fingering Nonextensive statistics in viscous fingering

2005-01-18

arxiv.org/abs/cond-mat/0501417v1

Physics

Condensed Matter

Statistical Mechanics

8 pages including 3 figures; to appear in PHYSICA A

Scientific paper

10.1016/j.physa.2005.09.007

Measurements in turbulent flows have revealed that the velocity field in nonequilibrium systems exhibits $q$-exponential or power law distributions in agreement with theoretical arguments based on nonextensive statistical mechanics. Here we consider Hele-Shaw flow as simulated by the Lattice Boltzmann method and find similar behavior from the analysis of velocity field measurements. For the transverse velocity, we obtain a spatial $q$-Gaussian profile and a power law velocity distribution over all measured decades. To explain these results, we suggest theoretical arguments based on Darcy's law combined with the non-linear advection-diffusion equation for the concentration field. Power law and $q$-exponential distributions are the signature of nonequilibrium systems with long-range interactions and/or long-time correlations, and therefore provide insight to the mechanism of the onset of fingering processes.

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