Sliding blocks with random friction and absorbing random walks

Details Sliding blocks with random friction and absorbing random walks Sliding blocks with random friction and absorbing random walks

1999-09-29

arxiv.org/abs/cond-mat/9909436v1

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.61.2267

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 $\theta_c=\tan(\av{\mu})$ the average traversed distance $\av{\lambda}$ is finite, and diverges when $\theta \to \theta_c^{-}$ as $\av{\lambda} \sim (\theta_c-\theta)^{-1}$; 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.

Affiliated with

Also associated with

No associations

Rating

Sliding blocks with random friction and absorbing random walks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sliding blocks with random friction and absorbing random walks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sliding blocks with random friction and absorbing random walks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-548338