Stretched-Exponential Aging Governs Nonequilibrium Precipitate Patterns

TL;DR

This study reveals that nonequilibrium precipitate patterns are governed by stretched-exponential aging laws, with failure probability depending on material history, leading to scale-free behavior near critical points.

Contribution

It introduces a novel aging law for failure in driven materials and demonstrates how aging controls pattern formation through experiments and cellular automaton modeling.

Findings

Failure probability follows a stretched-exponential aging law.

Approaching critical concentration causes a transition to power-law behavior.

A stochastic automaton reproduces filament patterns and thickening.

Abstract

Localized growth in driven materials is often governed by intermittent failure, yet how a material's history biases failure sites remains poorly understood. Using pause-restart experiments on chemical precipitate membranes, we quantify the probability of age-dependent breaching. We show that the kinetics follow a stretched-exponential aging law with parameters that obey one-parameter scaling. As the system approaches a critical concentration, the stretching exponent $\beta$ tends to zero, signaling a crossover to scale-free, power-law behavior. A stochastic cellular automaton based on this aging rule reproduces the emergent filaments and their concentration-dependent thickening. Our findings identify aging-controlled failure with long-lived but decaying memory as a general route to pattern formation in far-from-equilibrium systems.