Effect of Correlations on the Exponents for the Power-Law Distributions in Self-Organized Criticality |
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Authors: | DENG Yong-Ju ZHENG Hua YANG Chun-Bin |
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Institution: | 1. School of Physics and Electronic Information, Hubei University of Education, Wuhan 430205, China;
2. Institute of Particle Physics, Central China Normal University, Wuhan 430079, China |
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Abstract: | The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-return random-walk process in a one-dimensional lattice. In order to understand the reason of variant exponents for the power-law distributions in different self-organized critical systems, we introduce the correlations among evolution steps. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. It is found that the longer the correlation length, the smaller values of the exponents for the power-law distributions. |
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Keywords: | power-law distribution correlation self-organized criticality random-walk |
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