Sliding blocks with random friction and absorbing random walks

Abstract

With the purpose of explaining recent experimental findings, we study the distribution $A(\lambda )$ of distances $\lambda$ traversed by a block that slides on an inclined plane and stops due to friction. A simple model in which the friction coefficient $\mu$ is a random function of position is considered. The problem of finding $A(\lambda )$ is equivalent to a First-Passage-Time problem for a one-dimensional random walk with nonzero drift, whose exact solution is well-known. From the exact solution of this problem we conclude that: a) for inclination angles $\theta$ less than $θ_c=\tan(\avμ)$ the average traversed distance $\avλ$ is finite, and diverges when $\theta \to {\theta }_c^{-}$ as $\avλ \sim (θ_c-θ)^{-1}$; b) at the critical angle a power-law distribution of slidings is obtained: $A(\lambda )\sim {\lambda }^{-3/2}$. Our analytical results are confirmed by numerical simulation, and are in partial agreement with the reported experimental results. We discuss the possible reasons for the remaining discrepancies.

8 pages, 8 figures, submitted to Phys. Rev. E

References in corpus (5)

• Directed Percolation with a Wall or Edge
• Dynamics of Dry Friction: A Numerical Investigation
• Acoustic radiation controls friction: Evidence from a spring-block experiment
• Sliding Objects with Random Friction
• Sliding Blocks Revisited: A simulational Study

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