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 -