Power-law behavior in a cascade process with stopping events: A solvable model

Ken Yamamoto*, Yoshihiro Yamazaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


The present paper proposes a stochastic model to be solved analytically, and a power-law-like distribution is derived. This model is formulated based on a cascade fracture with the additional effect that each fragment at each stage of a cascade ceases fracture with a certain probability. When the probability is constant, the exponent of the power-law cumulative distribution lies between -1 and 0, depending not only on the probability but the distribution of fracture points. Whereas, when the probability depends on the size of a fragment, the exponent is less than -1, irrespective of the distribution of fracture points. The applicability of our model is also discussed.

Original languageEnglish
Article number011145
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
Publication statusPublished - 2012 Jan 27

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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