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  • Open Access

Stretched-exponential aging governs nonequilibrium precipitate patterns

Amari Z. Morris and Oliver Steinbock*

  • *Contact author: osteinbock@fsu.edu
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Phys. Rev. Research 8, 033025 – Published 6 July, 2026

DOI: https://doi.org/10.1103/t5gt-r6q2

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 β 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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Phys. Rev. Research 8, 033025– Published 6 July, 2026
  • Received 6 February 2026
  • Accepted 11 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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