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.

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U2 - 10.1103/PhysRevE.85.011145

DO - 10.1103/PhysRevE.85.011145

M3 - Article

C2 - 22400550

AN - SCOPUS:84863416395

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 -