2016/01/31 by Thimothée Thiery, Pierre Le Doussal
Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Critical exponent #Cryospheric studies and observations #Cusp (singularity) #Geometry #Landslides and related hazards #Mathematical physics #Mathematics #Mean field theory #Observable #Physics #Quantum mechanics #Renormalization group #Scaling #Singularity #Statistical physics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1209/0295-5075/114/36003
published as Core of the manuscript (letter) published as Thimothée Thiery and Pierre Le Doussal 2016 EPL 114 36003 · 6 pages + 15 pages of Supplemental Material, 13 figures. Minor corrections added, typos corrected. Core of the manuscript (letter) now matches published version
openalex publication_date 2016/05/01 · arxiv created 2016/06/06 · arxiv updated 2016/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantifying the universality of avalanche observables beyond critical exponents is of current great interest in theory and experiments. Here, we compute the spatial shape of avalanches in the universality class of the depinning of elastic interfaces in random media. We provide for the first time an analytically tractable definition of the spatial shape, accessible in experiments, and study the mean spatial shape of avalanches at fixed size centered around their starting point (seed) . We calculate the associated universal scaling functions, both in a mean-field model and beyond. Notably, they are predicted to exhibit a cusp singularity near the seed. The results are in good agreement with a numerical simulation of an elastic line.