title: Effect of Coulombic friction on spatial displacement statistics.
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.
authors.affiliation: Department 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
authors.forename: Andreas M
authors.initials: AM
authors.lastname: Menzel
authors.forename: Nigel
authors.initials: N
authors.lastname: Goldenfeld
mesh_terms: D000465:Algorithms; D004058:Diffusion; D017276:Friction; D015233:Models, Statistical; D016011:Normal Distribution; D009991:Oscillometry; D010825:Physics / Q000379:methods*; D011336:Probability; D011789:Quantum Theory; D013269:Stochastic Processes