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arXiv · 2602.07183

Stretched-Exponential Aging Governs Nonequilibrium Precipitate Patterns

Amari Morris·Oliver Steinbock
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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.

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Amari Morris, Oliver Steinbock. 2026-02-06. Stretched-Exponential Aging Governs Nonequilibrium Precipitate Patterns. https://arxiv.org/abs/2602.07183

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