Activity statistics, avalanche kinetics, and velocity correlations in surface growth

TL;DR

This paper develops a general scaling theory to analyze avalanche-driven surface growth, linking local activity, avalanche dynamics, and interface velocity correlations, with applications to imbibition fronts.

Contribution

It introduces a comprehensive scaling framework connecting local and global surface growth phenomena, applicable to various avalanche-driven systems.

Findings

Derived scaling relationships among critical exponents.

Validated theory with phase-field simulations of imbibition.

Established applicability to a broad class of interface growth systems.

Abstract

We investigate the complex spatio-temporal dynamics in avalanche driven surface growth by means of scaling theory. We study local activity statistics, avalanche kinetics, and temporal correlations in the global interface velocity, obtaining different scaling relationships among the involved critical exponents depending on how far from or close to a critical point the system is. Our scaling arguments are very general and connect local and global magnitudes through several scaling relationships. We expect our results to be applicable in a wide range of systems exhibiting interface kinetic roughening driven by avalanches of local activity, either critical or not. As an example we apply the scaling theory to analyze avalanches and roughening of forced-flow imbibition fronts in excellent agreement with phase-field numerical simulations.