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.
- 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
- E-Print:
- Physical Review E 85, 011145 (2012) [5 pages]