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Disordered elastic systems advance in bursts called avalanches. This study analyzes avalanche spatial shapes and fluctuations, finding universal scaling behaviors confirmed by simulations.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Soft Matter Physics

Background:

  • Disordered elastic systems exhibit driven dynamics characterized by intermittent bursts known as avalanches.
  • These avalanches possess finite spatial and temporal extensions, with spatial movement confined to a portion of the system's interface.

Purpose of the Study:

  • To investigate the spatial shape and fluctuations of avalanches in disordered elastic systems.
  • To establish scaling relations governing avalanche behavior, particularly near boundaries.
  • To validate theoretical predictions with numerical simulations, considering discretization effects.

Main Methods:

  • Analytical study of avalanche spatial shape (⟨S(x)⟩_{ℓ}) and its fluctuations (⟨S^{2}(x)⟩_{ℓ}^{c}).
  • Derivation of scaling relations for boundary behavior.
  • Application of the Brownian force model with random walk disorder.
  • Numerical simulations to confirm analytical results and assess discretization effects.

Main Results:

  • Established scaling relations for avalanche spatial shape and fluctuations near boundaries.
  • Obtained analytic results for the Brownian force model.
  • Numerical simulations confirmed the universal shape and fluctuations, including amplitudes, in the scaling limit.

Conclusions:

  • The study successfully characterized the universal spatial properties of avalanches in disordered elastic systems.
  • Discretization effects were properly addressed, enabling the observation of scaling behavior in moderate-sized avalanches.
  • Excellent agreement between theoretical predictions and numerical simulations validates the findings.