2014/07/04 by Ka Sin Jamie Wong, Wong, Ka Sin Jamie
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.1407.1136
8 pages, 4 figures; a statement in the proof to Claim II.2 has been modified; Claim II.3 and its proof have been stated more carefully to ensure clarity
openalex publication_date 2014/07/04 · arxiv created 2014/07/08 · arxiv updated 2014/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a more general class of the Alessandro-Beatrice-Bertotti-Montorsi (AMMB) models with velocity-dependent dissipation. We obtain the Fokker-Planck equation describing the evolution of an arbitrary initial probability distribution, and from there the stationary distribution under constant driving. For this class of models, we show that the distribution of the size of an avalanche is the same as when the dissipation is velocity-independent. As for durations, we show that, under non-stationary driving known as "kicks", although no closed-form solution seems to be available for an arbitrary velocity-dependent dissipation, for large durations the distribution seems to demonstrate an exponential fall-off, while for small durations (under some extra conditions to be made clear in the paper) the distribution seems to show a characteristic power-law behaviour.