Self-Organized Dynamical Equilibrium in the Corrosion of Random Solids

TL;DR

This paper models the corrosion process in random solids, showing how it self-organizes into a critical state with power law cluster size distribution through roughening and anti-percolation transitions.

Contribution

It introduces a dynamical system model for corrosion that self-organizes to a critical state without characteristic size, highlighting the roles of roughening and anti-percolation transitions.

Findings

System reaches a critical state with power law cluster size distribution.

Corrosion dynamics involve roughening and anti-percolation transitions.

Final state characterized by constant chemical potential and average cluster size.

Abstract

Self-organized criticality is characterized by power law correlations in the non-equilibrium steady state of externally driven systems. A dynamical system proposed here self-organizes itself to a critical state with no characteristic size at ``dynamical equilibrium''. The system is a random solid in contact with an aqueous solution and the dynamics is the chemical reaction of corrosion or dissolution of the solid in the solution. The initial difference in chemical potential at the solid-liquid interface provides the driving force. During time evolution, the system undergoes two transitions, roughening and anti-percolation. Finally, the system evolves to a dynamical equilibrium state characterized by constant chemical potential and average cluster size. The cluster size distribution exhibits power law at the final equilibrium state.