IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i7p1269-1278.html
   My bibliography  Save this article

A damage model based on failure threshold weakening

Author

Listed:
  • Gran, Joseph D.
  • Rundle, John B.
  • Turcotte, Donald L.
  • Holliday, James R.
  • Klein, William

Abstract

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long-range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size L is increased for fixed R. We also examine the effect of the weakening parameter on the frequency–magnitude scaling relationship and the ergodic behavior of the model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:7:p:1269-1278
    DOI: 10.1016/j.physa.2010.12.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110010150
    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.2010.12.004?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. Pride, Steven R & Toussaint, Renaud, 2002. "Thermodynamics of fiber bundles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 159-171.
    2. Raymond D. Mountain & D. Thirumalai, 1990. "Ergodic Convergence In Liquids And Glasses," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 77-89.
    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. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    Full references (including those not matched with items on IDEAS)

    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. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    2. Juan C. Henao-Londono & Sebastian M. Krause & Thomas Guhr, 2021. "Price response functions and spread impact in correlated financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(4), pages 1-20, April.
    3. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    4. Giorgio Fagiolo & Mauro Napoletano & Andrea Roventini, 2008. "Are output growth-rate distributions fat-tailed? some evidence from OECD countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 639-669.
    5. Peng Yue & Qing Cai & Wanfeng Yan & Wei-Xing Zhou, 2020. "Information flow networks of Chinese stock market sectors," Papers 2004.08759, arXiv.org.
    6. Jørgen Vitting Andersen & Ioannis Vrontos & Petros Dellaportas & Serge Galam, 2014. "Communication impacting financial markets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00982959, HAL.
    7. Nobi, Ashadun & Maeng, Seong Eun & Ha, Gyeong Gyun & Lee, Jae Woo, 2014. "Effects of global financial crisis on network structure in a local stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 135-143.
    8. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2013. "How efficiency shapes market impact," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1743-1758, November.
    9. Changtai Li & Weihong Huang & Wei-Siang Wang & Wai-Mun Chia, 2023. "Price Change and Trading Volume: Behavioral Heterogeneity in Stock Market," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 677-713, February.
    10. Andrew Balthrop, 2016. "Power laws in oil and natural gas production," Empirical Economics, Springer, vol. 51(4), pages 1521-1539, December.
    11. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 49-100.
    12. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross‐Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
    13. Hokky Situngkir & Yohanes Surya, 2004. "Stylized Statistical Facts of Indonesian Financial Data: Empirical Study of Several Stock Indexes in Indonesia," Papers cond-mat/0403465, arXiv.org.
    14. Marcus Berliant & Hiroki Watanabe, 2015. "Explaining the size distribution of cities: Extreme economies," Quantitative Economics, Econometric Society, vol. 6(1), pages 153-187, March.
    15. Louis Saddier & Matteo Marsili, 2023. "A Bayesian theory of market impact," Papers 2303.08867, arXiv.org, revised Feb 2024.
    16. 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.
    17. 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.
    18. Zhang, Yali & Shang, Pengjian, 2019. "Multivariate multiscale distribution entropy of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 72-80.
    19. Payzan-LeNestour, Elise & Woodford, Michael, 2022. "Outlier blindness: A neurobiological foundation for neglect of financial risk," Journal of Financial Economics, Elsevier, vol. 143(3), pages 1316-1343.
    20. 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.

    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:390:y:2011:i:7:p:1269-1278. 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.