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We present a new method to extract universal scaling functions and critical exponents from data, analyzing avalanche dynamics in driven quenched Kardar-Parisi-Zhang (qKPZ) simulations. This approach addresses distortions from limited fields of view in crackling noise experiments.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Computational Science

Background:

  • Avalanche dynamics and crackling noise are prevalent in various physical systems.
  • Extracting universal scaling functions and critical exponents from experimental data is challenging.
  • Limited field of view in imaging experiments often distorts observed distributions.

Purpose of the Study:

  • To introduce a systematic method for extracting multivariable universal scaling functions and critical exponents from data.
  • To analyze avalanche dynamics in simulations of the driven quenched Kardar-Parisi-Zhang (qKPZ) equation.
  • To resolve issues caused by limited field of view in crackling noise and avalanche dynamics experiments.

Main Methods:

  • Developed a systematic data analysis method for multivariable universal scaling functions and critical exponents.
  • Analyzed simulations of avalanches using the driven quenched Kardar-Parisi-Zhang (qKPZ) equation.
  • Employed artificially windowed data to model distortions from limited fields of view.
  • Utilized a novel software environment, SloppyScaling, for accurate parametrizations.

Main Results:

  • Fully characterized the spatial structure of avalanches, reporting universal scaling functions for size, height, and width distributions.
  • Demonstrated that windowed distributions and their multivariable scaling functions depend on window size and characteristic length scale.
  • Developed accurate parametrizations for universal scaling functions, including corrections to scaling and systematic error bars, for both full and windowed systems.

Conclusions:

  • The introduced method successfully extracts multivariable universal scaling functions and critical exponents from complex data.
  • The study provides a framework to understand and correct for field-of-view distortions in avalanche dynamics analysis.
  • The SloppyScaling software facilitates accurate analysis and parametrization of universal scaling functions in complex systems.