### 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 language | English |
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Article number | 011145 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 85 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Jan 27 |

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### ASJC Scopus subject areas

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

### Cite this

**Power-law behavior in a cascade process with stopping events : A solvable model.** / Yamamoto, Ken; Yamazaki, Yoshihiro.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Power-law behavior in a cascade process with stopping events

T2 - A solvable model

AU - Yamamoto, Ken

AU - Yamazaki, Yoshihiro

PY - 2012/1/27

Y1 - 2012/1/27

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84863416395&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863416395&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.85.011145

DO - 10.1103/PhysRevE.85.011145

M3 - Article

VL - 85

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 1

M1 - 011145

ER -