arXiv subjects

I. Grosse

Publications and source records attributed to I. Grosse.

3 recordsLinked to original sources

arXiv2001

Stable Distributions in Stochastic Fragmentation

We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail. Furthermore, the entire range of acceptable values of decay exponent consistent with the length conservation can be realized. We show that the stochastic fragmentation process is non-self-averaging as moments exhibit significant sample-to-sample fluctuations. Additionally, we find that the distributions of the moments and of extremal characteristics possess an infinite set of progressively weaker singularities.

cond-mat.stat-mech↗

arXiv1999

Scale Invariance and Lack of Self-Averaging in Fragmentation

We derive exact statistical properties of a class of recursive fragmentation processes. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution in one dimension, P(x) ~ x^{-2p}. In d dimensions, the volume distribution diverges algebraically in the small fragment limit, P(V)\sim V^{-γ} with γ=2p^{1/d}. Hence, the entire range of exponents allowed by mass conservation is realized. We demonstrate that this fragmentation process is non-self-averaging. Specifically, the moments Y_α=\sum_i x_i^α exhibit significant fluctuations even in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv1999

Sliding blocks with random friction and absorbing random walks

With the purpose of explaining recent experimental findings, we study the distribution $A(λ)$ of distances $λ$ traversed by a block that slides on an inclined plane and stops due to friction. A simple model in which the friction coefficient $μ$ is a random function of position is considered. The problem of finding $A(λ)$ 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 $θ$ less than $θ_c=\tan(\avμ)$ the average traversed distance $\avλ$ is finite, and diverges when $θ\to θ_c^{-}$ as $\avλ \sim (θ_c-θ)^{-1}$; b) at the critical angle a power-law distribution of slidings is obtained: $A(λ) \sim λ^{-3/2}$. 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.

cond-mat.stat-mech↗