Simulation of a Casimir-like effect in a granular pile with avalanches

Abstract

Using a modified Bak-Tang-Wiesenfeld model for sand piles, we simulate a Casimir-like effect in a granular pile with avalanches. Results obtained in the simulation are in good agreement with results previously acquired experimentally: two parallel walls are attracted to each other at small separation distances, with a force decreasing with increasing distance. In the simulation only, at medium distances a weak repulsion exists. Additionally, with the aim of avalanche prevention, the possibility of suppressing self-organized criticality with an array of walls placed on the slope of the pile is investigated, but the prevention effect is found to be negligible.

Localisation and universal fluctuations in ultraslow diffusion processes

“…The MSD is given by x 2 (t) ∼ δx 2 /Ψ(t) [33], where δx 2 is the variance of jump lengths [36]. The specific form (8) recovers the MSD (1) with diffusivity K γ = δx 2 /[2 ln γ (τ 0 )] [26,27,29,37], i.e., for γ = 4, we find a Sinai-like diffusion. Fig.…”

“…In a biophysical context, due to the inherently quenched heterogeneity of biomolecules Sinai-type models are used to describe mechanical DNA unzipping [13], translocation of biomolecules through nanopores [14,15], and molecular motor motion [15]. Ultraslow diffusion with mean squared displacement (MSD)in fact has a much broader scope in highly disordered low-dimensional systems: inter alia, in vacancy induced motion [16, 17], biased motion in exclusion processes [18], motion in aging environments [19], compactification of paper [20] or grain [21], dynamics in glassy systems [22], record statistics [23], the ABC model [24], diffusion with exponential position dependence of the diffusivity [25], or dynamics in non-linear maps [26].Here we report a comparative study of Sinai diffusion and ultraslow continuous time random walks (CTRWs) with super heavy-tailed waiting times [26][27][28][29]. Previous work focused on ensemble averaged observables.…”

“…Here we report a comparative study of Sinai diffusion and ultraslow continuous time random walks (CTRWs) with super heavy-tailed waiting times [26][27][28][29]. Previous work focused on ensemble averaged observables.…”

“…It would therefore be desirable to have a process, that captures the essential features of the Sinai diffusion. We show that such a process is given by a renewal CTRW on a one-dimensional lattice with the asymptotic form ψ(τ ) ∼ h(τ )/τ of the distribution of waiting times τ elapsing between successive jumps [29]. Here h(τ ) is a slowly varying function [35].…”

“…Jumps to left and right are equally likely, and the probability that no jump occurs until time t is Ψ(t) = ∞ t ψ(τ )dτ , in terms of which we express our results. A typical example is the logarithmic form [26][27][28][29]…”