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Updated: May 7, 2026
11:51
Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Avalanche dynamics of elastic interfaces.
Pierre Le Doussal1, Kay Jörg Wiese
1CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 17, 2013
Summary
This study introduces a field-theoretic approach to understand intermittent avalanche motion in elastic interfaces. It reveals how interface dynamics simplify to particle motion in random forces, offering exact solutions and insights into velocity statistics.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Elastic interfaces exhibit intermittent motion via avalanches, crucial in phenomena like wetting and fracture.
- Understanding the space-time statistics of velocities within these avalanches is key to predicting material behavior.
Purpose of the Study:
- To develop a field-theoretic framework for calculating avalanche velocity statistics.
- To analyze the behavior of elastic interfaces at and above their upper critical dimensions.
Main Methods:
- Developed a field-theoretic treatment for elastic interface dynamics.
- Utilized exact solutions via tree graph summation and instanton equations.
- Applied mean-field theory (MFT) and loop corrections beyond MFT.
Main Results:
- Showed interface dynamics reduce to particle motion in random forces (ABBM and BFM models).
- Calculated velocity correlations, probability distribution functions (PDFs), and avalanche shapes.
- Found velocity correlations are time-asymmetric and reduced singularity in PDFs beyond MFT.
Conclusions:
- The field-theoretic approach provides a robust method for analyzing avalanche dynamics.
- Results offer insights into the statistical properties of intermittent motion in disordered systems.
- The study bridges theoretical models with observable quantities relevant to experimental systems.
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