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Effect of Coulombic friction on spatial displacement statistics
Andreas M Menzel1, Nigel Goldenfeld
1Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801, USA. menzel@mpip-mainz.mpg.de
Abstract:
The phenomenon of Coulombic friction enters the stochastic description of dry friction between two solids and the statistic characterization of vibrating granular media. Here we analyze the corresponding Fokker-Planck equation including both velocity and spatial components, exhibiting a formal connection to a quantum mechanical harmonic oscillator in the presence of a delta potential. Numerical solutions for the resulting spatial displacement statistics show a crossover from exponential to Gaussian displacement statistics. We identify a transient intermediate regime that exhibits multiscaling properties arising from the contribution of Coulombic friction. The possible role of these effects during observations in diffusion experiments is briefly discussed.
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