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Dynamic scaling for avalanches in disordered systems.

G P Zheng1, M Li

  • 1Department of Materials Science and Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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This study investigates dynamic scaling in fracture processes within disordered systems using a two-dimensional random field Ising model (RFIM). Researchers identified distinct short-time and late-time stages, revealing critical exponents and field strength at the critical point.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Disordered systems exhibit complex fracture and breakdown dynamics.
  • Understanding dynamic scaling is crucial for characterizing phase transitions in such systems.

Purpose of the Study:

  • To investigate dynamic scaling in fracture processes within a two-dimensional random field Ising model (RFIM).
  • To identify distinct stages of avalanche behavior and determine critical exponents.

Main Methods:

  • Utilized a two-dimensional random field Ising model (RFIM).
  • Analyzed avalanche size evolution over time, focusing on short-time and late-time regimes.
  • Applied dynamic scaling laws to determine critical parameters.

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Main Results:

  • Identified two distinct stages in the avalanche process: short-time power-law growth and late-time nucleation-growth.
  • Observed avalanche size obeying a dynamic scaling law at the critical point.
  • Determined critical exponents (beta, nu, z) and critical random field strength (D(c)).

Conclusions:

  • The fracture dynamics in the RFIM are characterized by distinct temporal regimes.
  • The findings support a nucleation theory for first-order phase transformations in disordered systems.