Avalanches in Tip-Driven Interfaces in Random Media

Abstract

We analyse by numerical simulations and scaling arguments the avalanche statistics of 1-dimensional elastic interfaces in random media driven at a single point. Both global and local avalanche sizes are power-law distributed, with universal exponents given by the depinning roughness exponent $\zeta$ and the interface dimension $d$, and distinct from their values in the uniformly driven case. A crossover appears between uniformly driven behaviour for small avalanches, and point driven behaviour for large avalanches. The scale of the crossover is controlled by the ratio between the stiffness of the pulling spring and the elasticity of the interface; it is visible both in the global and local avalanche-size distributions, as in the average spatial avalanche shape. Our results are relevant to model experiments involving locally driven elastic manifolds at low temperatures, such as magnetic domain walls or vortex lines in superconductors.

6 pages, 6 figures

References in corpus (3)

• An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media
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• Mapping the train model for earthquakes onto the stochastic sandpile model

Cited by in corpus (8)

• Driven interfaces: from flow to creep through model reduction
• The Spatial Shape of Avalanches
• Field Theory of Disordered Elastic Interfaces at 3-Loop Order: Critical Exponents and Scaling Functions
• On the critical region of long-range depinning transitions
• Universal correlations between shocks in the ground state of elastic interfaces in disordered media
• Correlations between avalanches in the depinning dynamics of elastic interfaces
• Depinning in the quenched Kardar-Parisi-Zhang class I: Mappings, simulations and algorithm
• Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification