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arXiv · 1904.08657

Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification

Alejandro B. Kolton·Pierre Le Doussal·Kay Joerg Wiese
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Abstract

We study several probability distributions relevant to the avalanche dynamics of elastic interfaces driven on a random substrate: The distribution of size, duration, lateral extension or area, as well as velocities. Results from the functional renormalization group and scaling relations involving two independent exponents, roughness $ζ$, and dynamics $z$, are confronted to high-precision numerical simulations of an elastic line with short-range elasticity, i.e. of internal dimension $d=1$. The latter are based on a novel stochastic algorithm which generates its disorder on the fly. Its precision grows linearly in the time-discretization step, and it is parallelizable. Our results show good agreement between theory and numerics, both for the critical exponents as for the scaling functions. In particular, the prediction ${\sf a} = 2 - \frac{2}{d+ ζ- z}$ for the velocity exponent is confirmed with good accuracy.

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Alejandro B. Kolton, Pierre Le Doussal, Kay Joerg Wiese. 2019-04-18. Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification. https://doi.org/10.1209/0295-5075%2F127%2F46001

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