Power-law behavior in a cascade process with stopping events

A solvable model

Ken Yamamoto, Yoshihiro Yamazaki

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    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
    Volume85
    Issue number1
    DOIs
    Publication statusPublished - 2012 Jan 27

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    Solvable Models
    stopping
    Cascade
    cascades
    Power Law
    Fragment
    Exponent
    fragments
    exponents
    Stochastic Model
    Model

    ASJC Scopus subject areas

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

    Cite this

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