Avalanches in Tip-Driven Interfaces in Random Media

Understand

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.