Effect of Coulombic friction on spatial displacement statistics

Andreas M. Menzel, Nigel Goldenfeld

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number011122
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
StatePublished - Jul 18 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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