Dynamic weakening and trained memory in avalanche dynamics from high-entropy alloys to neurons and spin systems

Avalanche dynamics—the abrupt, collective release of stored energy under slow external driving—arise in systems ranging from earthquakes and crystalline solids to neuronal networks and spin models. Despite differences in microscopic mechanisms, these systems share universal features such as broad event-size distributions and scale-invariant critical phenomena. A simple depinning theory provides a unifying framework for these behaviors, yet many systems deviate from pure criticality, exhibiting system-spanning runaways, characteristic length scales, and quasi-periodicity. Such deviations highlight the role of additional mechanisms, particularly dynamic weakening and healing, which temporarily modify local thresholds during and after avalanches. This thesis investigates how weakening and healing govern avalanche dynamics in materials and biological systems, and how avalanche analysis reveals underlying critical points and scaling laws in non-equilibrium complex systems. In crystalline solids, I analyze slip statistics in high-entropy alloys and construct phase diagrams that capture the influence of strain rate and temperature. Extending mean-field theory to finite healing rates, I derive analytical conditions for transitions from stochastic fluctuations to quasi-periodic and aperiodic runaways, providing an avalanche-based interpretation of the Portevin-Le Chatelier effect. In neuronal systems, I adapt a dual-species mean-field model with dynamic thresholds to explain post-stimulus silencing effect. Short-term weakening drives widespread activation, while slow healing process induces silent periods. The model reproduces experimental results from rat cortical slice recordings and human transcranial magnetic stimulation data, offering a candidate mechanism to explain both post-stimulus silent periods and quasi-periodic aftershocks observed in neural activity. Finally, I investigate avalanche statistics and limit-cycle dynamics in a non-equilibrium random-bond Ising model as a minimal theoretical framework for memory formation. Under cyclic driving, trained memory emerges through avalanche dynamics, with finite-size scaling revealing universal critical exponents for both avalanche and memory formation. I further show that partial driving enables local memory storage, as undriven spins act as a reservoir for the trained memory of driven spins. Together, these studies demonstrate that avalanche analysis provides a powerful diagnostic for criticality in non-equilibrium systems. By bridging statistical physics, materials science, and neuroscience, this work advances a coherent framework for criticality and memory effect in complex dynamical systems.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Liu, Ming-Wei

Contributors dc:contributor

• Dahmen, Karin
• Chemla, Yann
• Weaver, Richard
• Beggs, John

• Avalanche Dynamics
• Critical Phenomena
• Power-Law Statistics
• Non-Equilibrium Systems
• Mean-Field Theory
• Trained Memory

Statement dc:rights

• Copyright 2025 Ming-Wei Liu

Language dc:language

en

Handle dc:identifier

https://hdl.handle.net/2142/132666

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/132666