title: Power-law behavior in a cascade process with stopping events: a solvable model.
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.
authors.affiliation: Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo, Japan.
authors.forename: Ken
authors.initials: K
authors.lastname: Yamamoto
authors.forename: Yoshihiro
authors.initials: Y
authors.lastname: Yamazaki
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D015233:Models, Statistical; D013269:Stochastic Processes