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 |
|---|---|
| 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.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 85, No. 1, 011145, 27.01.2012.Research output: Contribution to journal › Article
}
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
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 -