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Analysis of power-law exponents by maximum-likelihood maps.

Jordi Baró1, Eduard Vives

  • 1Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia, Spain. jordibaro@ecm.ub.es

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

Maximum-likelihood exponent maps enhance power-law exponent analysis for data with cutoffs. This method was applied to seismological, acoustic emission, and Ising model avalanche data, revealing insights into underlying physics.

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Area of Science:

  • Physics
  • Geophysics
  • Materials Science

Background:

  • Power-law distributions are common in natural and simulated systems.
  • Analyzing data with upper and lower cutoffs presents challenges for traditional methods.
  • Understanding the underlying physics requires accurate exponent fitting.

Purpose of the Study:

  • To evaluate maximum-likelihood exponent maps for analyzing power-law exponents.
  • To test the technique on diverse datasets including seismology, acoustic emissions, and simulations.
  • To investigate deviations in exponent maps and their physical implications.

Main Methods:

  • Application of maximum-likelihood exponent mapping.
  • Analysis of seismological data.
  • Analysis of acoustic emission data.
  • Numerical simulations of the three-dimensional random field Ising model.

Main Results:

  • Successful application of the technique to various complex datasets.
  • Identification and characterization of deviations in exponent maps.
  • Demonstration of the method's utility in understanding system physics.

Conclusions:

  • Maximum-likelihood exponent maps provide a robust tool for power-law analysis, especially with cutoffs.
  • Deviations in exponent maps offer valuable clues to the physical processes governing the systems.
  • The technique aids in interpreting complex phenomena across different scientific domains.