Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model

Rene Batac; Anthony Longjas; Christopher Monterola

doi:10.1016/j.physa.2011.08.032

Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model

Rene Batac, Anthony Longjas, Christopher Monterola

St. Anthony Falls Laboratory

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Sandpile-based models have successfully shed light on key features of nonlinear relaxational processes in nature, particularly the occurrence of fat-tailed magnitude distributions and exponential return times, from simple local stress redistributions. In this work, we extend the existing sandpile paradigm into an inter-sandpile cascade, wherein the avalanches emanating from a uniformly-driven sandpile (first layer) is used to trigger the next (second layer), and so on, in a successive fashion. Statistical characterizations reveal that avalanche size distributions evolve from a power-law p(S)≈S- ^1.3 for the first layer to gamma distributions p(S) ≈^Sαexp(-S^S0) for layers far away from the uniformly driven sandpile. The resulting avalanche size statistics is found to be associated with the corresponding waiting time distribution, as explained in an accompanying analytic formulation. Interestingly, both the numerical and analytic models show good agreement with actual inventories of non-uniformly driven events in nature.

Original language	English (US)
Pages (from-to)	616-624
Number of pages	9
Journal	Physica A: Statistical Mechanics and its Applications
Volume	391
Issue number	3
DOIs	https://doi.org/10.1016/j.physa.2011.08.032
State	Published - Feb 1 2012

Bibliographical note

Funding Information:
The authors would like to thank Prof. B.D. Malamud for the empirical landslide data and Prof. E. Piegari for the synthetic model results. We would also like to thank G.A. Esleta for his contributions in the early part of the work. The work is supported by the OVCRD—University of the Philippines Diliman and the National Research Council of the Philippines . RB and AL acknowledge the DOST-PCASTRD.

Keywords

Cellular automata
Inter-sandpile cascade model
Landslides

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title = "Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model",

abstract = "Sandpile-based models have successfully shed light on key features of nonlinear relaxational processes in nature, particularly the occurrence of fat-tailed magnitude distributions and exponential return times, from simple local stress redistributions. In this work, we extend the existing sandpile paradigm into an inter-sandpile cascade, wherein the avalanches emanating from a uniformly-driven sandpile (first layer) is used to trigger the next (second layer), and so on, in a successive fashion. Statistical characterizations reveal that avalanche size distributions evolve from a power-law p(S)≈S- 1.3 for the first layer to gamma distributions p(S) ≈Sαexp(-SS0) for layers far away from the uniformly driven sandpile. The resulting avalanche size statistics is found to be associated with the corresponding waiting time distribution, as explained in an accompanying analytic formulation. Interestingly, both the numerical and analytic models show good agreement with actual inventories of non-uniformly driven events in nature.",

keywords = "Cellular automata, Inter-sandpile cascade model, Landslides",

author = "Rene Batac and Anthony Longjas and Christopher Monterola",

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AU - Monterola, Christopher

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N2 - Sandpile-based models have successfully shed light on key features of nonlinear relaxational processes in nature, particularly the occurrence of fat-tailed magnitude distributions and exponential return times, from simple local stress redistributions. In this work, we extend the existing sandpile paradigm into an inter-sandpile cascade, wherein the avalanches emanating from a uniformly-driven sandpile (first layer) is used to trigger the next (second layer), and so on, in a successive fashion. Statistical characterizations reveal that avalanche size distributions evolve from a power-law p(S)≈S- 1.3 for the first layer to gamma distributions p(S) ≈Sαexp(-SS0) for layers far away from the uniformly driven sandpile. The resulting avalanche size statistics is found to be associated with the corresponding waiting time distribution, as explained in an accompanying analytic formulation. Interestingly, both the numerical and analytic models show good agreement with actual inventories of non-uniformly driven events in nature.

AB - Sandpile-based models have successfully shed light on key features of nonlinear relaxational processes in nature, particularly the occurrence of fat-tailed magnitude distributions and exponential return times, from simple local stress redistributions. In this work, we extend the existing sandpile paradigm into an inter-sandpile cascade, wherein the avalanches emanating from a uniformly-driven sandpile (first layer) is used to trigger the next (second layer), and so on, in a successive fashion. Statistical characterizations reveal that avalanche size distributions evolve from a power-law p(S)≈S- 1.3 for the first layer to gamma distributions p(S) ≈Sαexp(-SS0) for layers far away from the uniformly driven sandpile. The resulting avalanche size statistics is found to be associated with the corresponding waiting time distribution, as explained in an accompanying analytic formulation. Interestingly, both the numerical and analytic models show good agreement with actual inventories of non-uniformly driven events in nature.

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Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model

Abstract

Bibliographical note

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