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Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
Published on: August 5, 2016
Statistics of static avalanches in a random pinning landscape
Pierre Le Doussal1, A Alan Middleton, Kay Jörg Wiese
1Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, CNRS, 24 rue Lhomond, 75005 Paris, France.
Summary
We investigate how elastic interfaces in random potentials jump discretely, revealing the statistical distribution of these "static avalanches" through analytical and numerical methods.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Disordered Systems
Background:
- Elastic interfaces in random potentials exhibit complex behavior.
- The phenomenon of 'static avalanches' or discrete jumps in interface position is observed.
Purpose of the Study:
- To analytically determine the distribution of avalanche sizes and their cumulants.
- To compare analytical predictions with numerical simulations for interface energy minimization.
Main Methods:
- Analytical calculation using a d=4-epsilon expansion.
- Tree and one-loop resummation via functional renormalization group.
- Exact numerical minimization of interface energies for d=2 and d=3.
Main Results:
- The distribution of static avalanche sizes and their cumulants were derived analytically.
- Analytical results were compared with numerical findings for random-field disorder.
- The study provides insights into the statistical properties of interface deformations.
Conclusions:
- The study successfully characterized the statistical distribution of static avalanches.
- Analytical and numerical methods provide consistent insights into interface behavior in disordered systems.
- Connections between static and dynamic avalanches are suggested for future research.
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