Powerlaw 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 powerlawlike 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 powerlaw 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.
 Publication:

Physical Review E
 Pub Date:
 January 2012
 DOI:
 10.1103/PhysRevE.85.011145
 arXiv:
 arXiv:1106.1506
 Bibcode:
 2012PhRvE..85a1145Y
 Keywords:

 02.50.r;
 46.50.+a;
 05.40.a;
 Probability theory stochastic processes and statistics;
 Fracture mechanics fatigue and cracks;
 Fluctuation phenomena random processes noise and Brownian motion;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 Physical Review E 85, 011145 (2012) [5 pages]