IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i3p616-624.html
   My bibliography  Save this article

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

Author

Listed:
  • Batac, Rene
  • Longjas, Anthony
  • Monterola, Christopher

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.

Suggested Citation

  • Batac, Rene & Longjas, Anthony & Monterola, Christopher, 2012. "Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 616-624.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:3:p:616-624
    DOI: 10.1016/j.physa.2011.08.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111006601
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2011.08.032?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. S. Santhanam & Holger Kantz, 2008. "Return interval distribution of extreme events and long term memory," Papers 0803.1706, arXiv.org.
    2. Batac, Rene & Pastor, Marissa & Arciaga, Marko & Bantang, Johnrob & Monterola, Christopher, 2009. "Kinks, logarithmic tails, and super-stability in bi-disperse granular media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3072-3082.
    3. Drossel, B. & Schwabl, F., 1992. "Self-organized criticality in a forest-fire model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 47-50.
    4. Bunde, Armin & F. Eichner, Jan & Havlin, Shlomo & W. Kantelhardt, Jan, 2004. "Return intervals of rare events in records with long-term persistence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 308-314.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tarun, Anjali B. & Paguirigan, Antonino A. & Batac, Rene C., 2015. "Spatiotemporal recurrences of sandpile avalanches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 293-300.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xie, Wen-Jie & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2014. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Economic Modelling, Elsevier, vol. 36(C), pages 8-17.
    2. de Benicio, Rosilda B. & Stošić, Tatijana & de Figueirêdo, P.H. & Stošić, Borko D., 2013. "Multifractal behavior of wild-land and forest fire time series in Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6367-6374.
    3. Satulovsky, Javier E., 1997. "On the synchronizing mechanism of a class of cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(1), pages 52-58.
    4. Kondor, Dániel & Mátray, Péter & Csabai, István & Vattay, Gábor, 2013. "Measuring the dimension of partially embedded networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4160-4171.
    5. Li, Wei-Zhen & Zhai, Jin-Rui & Jiang, Zhi-Qiang & Wang, Gang-Jin & Zhou, Wei-Xing, 2022. "Predicting tail events in a RIA-EVT-Copula framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    6. Bill McKelvey & Benyamin B. Lichtenstein & Pierpaolo Andriani, 2012. "When organisations and ecosystems interact: toward a law of requisite fractality in firms," International Journal of Complexity in Leadership and Management, Inderscience Enterprises Ltd, vol. 2(1/2), pages 104-136.
    7. Marzouk, Cyril, 2016. "Fires on large recursive trees," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 265-289.
    8. Benavent-Corai, J. & Rojo, C. & Suárez-Torres, J. & Velasco-García, L., 2007. "Scaling properties in forest fire sequences: The human role in the order of nature," Ecological Modelling, Elsevier, vol. 205(3), pages 336-342.
    9. Biton, Dionessa C. & Tarun, Anjali B. & Batac, Rene C., 2020. "Comparing spatio-temporal networks of intermittent avalanche events: Experiment, model, and empirical data," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    10. LaViolette, Randall A. & Glass, Kristin & Colbaugh, Richard, 2009. "Deep information from limited observation of robust yet fragile systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3283-3287.
    11. Czechowski, Zbigniew & Telesca, Luciano, 2024. "Effect of nonlinearity of discrete Langevin model on behavior of extremes in generated time series," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    12. Honecker, A. & Peschel, I., 1997. "Length scales and power laws in the two-dimensional forest-fire model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 239(4), pages 509-530.
    13. Zhi-Qiang Jiang & Gang-Jin Wang & Askery Canabarro & Boris Podobnik & Chi Xie & H. Eugene Stanley & Wei-Xing Zhou, 2018. "Short term prediction of extreme returns based on the recurrence interval analysis," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 353-370, March.
    14. Ren, Fei & Gu, Gao-Feng & Zhou, Wei-Xing, 2009. "Scaling and memory in the return intervals of realized volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4787-4796.
    15. Tang, Da-Hai & Han, Xiao-Pu & Wang, Bing-Hong, 2010. "Stretched exponential distribution of recurrent time of wars in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2637-2641.
    16. Gran, Joseph D. & Rundle, John B. & Turcotte, Donald L. & Holliday, James R. & Klein, William, 2011. "A damage model based on failure threshold weakening," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1269-1278.
    17. Chi Zhang & Zhengning Pu & Jiasha Fu, 2018. "The Recurrence Interval Difference of Power Load in Heavy/Light Industries of China," Energies, MDPI, vol. 11(1), pages 1-20, January.
    18. Karain, Wael I., 2019. "Investigating large-amplitude protein loop motions as extreme events using recurrence interval analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 1-10.
    19. Vittorio Zanon & Fátima Viveiros & Catarina Silva & Ana Hipólito & Teresa Ferreira, 2008. "Impact of lightning on organic matter-rich soils: influence of soil grain size and organic matter content on underground fires," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 45(1), pages 19-31, April.
    20. Bonabeau, Eric, 1994. "Self-reorganizations in a simple model of the immune system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(3), pages 336-350.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:391:y:2012:i:3:p:616-624. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.