First-passage time of Brownian motion with dry friction
arXiv:1312.0581 · doi:10.1103/PhysRevE.89.022103
Abstract
We provide an analytic solution to the first-passage time (FPT) problem of a piecewise-smooth stochastic model, namely Brownian motion with dry friction, using two different but closely related approaches which are based on eigenfunction decompositions on the one hand and on the backward Kolmogorov equation on the other. For the simple case containing only dry friction, a phase transition phenomenon in the spectrum is found which relates to the position of the exit point, and which affects the tail of the FPT distribution. For the model containing as well a driving force and viscous friction the impact of the corresponding stick-slip transition and of the transition to ballistic exit is evaluated quantitatively. The proposed model is one of the very few cases where FPT properties are accessible by analytical means.
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Cited by in corpus (5)
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- Nonequilibrium dynamics of a pure dry friction model subjected to coloured noise
- On large deviation properties of Brownian motion with dry friction
- Numerical solutions of Fokker-Planck equations with drift-admitting jumps
- Diffusion Properties of a Brownian Ratchet with Coulomb Friction