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Published on: August 1, 2011
Tuning coupling: discrete changes in runaway avalanche sizes in disordered media
Braden A W Brinkman1, Karin A Dahmen
1Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street Urbana, Illinois 61801-3080, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
Understanding catastrophic runaway avalanches in hysteretic systems is crucial. This study reveals how interaction strength (J) critically influences avalanche size distribution, providing insights into system behavior near critical points.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Complex Systems
Background:
- Hysteretic systems can exhibit catastrophic runaway avalanches where many components change state simultaneously.
- The influence of interaction strength on the magnitude of these avalanches is not fully understood.
Purpose of the Study:
- To investigate the role of interaction strength (J) in determining the size distribution of runaway avalanches.
- To analyze how tuning J near a critical value J(c) affects avalanche dynamics using the random field Ising model.
Main Methods:
- Utilized the random field Ising model to simulate hysteretic system behavior.
- Calculated the distribution of runaway avalanche sizes, P(S), as J approached J(c).
- Analyzed scaling behavior and identified critical exponents (τ and σ) and a universal scaling function D(x).
Main Results:
- The avalanche size distribution P(S) exhibits scaling behavior: P(S)∼S(-τ)D(S(σ)(J/J(c)-1)).
- In mean field theory, critical exponents were found to be τ=3/2 and σ=1/2, with a specific scaling function D(x)=exp[-(3x)(1/σ)/2].
- Predicted values for three dimensions are τ=1.6 and σ=0.24, based on current findings and prior research.
Conclusions:
- Interaction strength is a key factor governing the size of catastrophic avalanches in hysteretic systems.
- The identified scaling laws and critical exponents provide a universal framework for understanding avalanche phenomena.
- This research offers valuable insights for predicting and controlling abrupt changes in complex systems.
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