2017/08/03 by Zhaoxuan Zhu, Kay Jörg Wiese, Kay Joerg Wiese
Materials Science · Mathematics · Physics and Astronomy · #Amplitude #Ansatz #Brownian motion #Discretization #Geometry #Material Dynamics and Properties #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Random walk #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.96.062116
published as Phys. Rev. E 96, 062116 (2017) · 15 pages, 17 figures
arxiv created 2017/08/03 · openalex publication_date 2017/12/14 · arxiv updated 2017/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In disordered elastic systems, driven by displacing a parabolic confining potential adiabatically slowly, all advance of the system is in bursts, termed avalanches. Avalanches have a finite extension in time, which is much smaller than the waiting time between them. Avalanches also have a finite extension ℓ in space, i.e., only a part of the interface of size ℓ moves during an avalanche. Here we study their spatial shape 〈S(x)〉ℓ given ℓ, as well as its fluctuations encoded in the second cumulant 〈S2(x)〉ℓc. We establish scaling relations governing the behavior close to the boundary. We then give analytic results for the Brownian force model, in which the microscopic disorder for each degree of freedom is a random walk. Finally, we confirm these results with numerical simulations. To do this properly we elucidate the influence of discretization effects, which also confirms the assumptions entering into the scaling ansatz. This allows us to reach the scaling limit already for avalanches of moderate size. We find excellent agreement for the universal shape and its fluctuations, including all amplitudes.