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dc.contributor.authorCasals, Blai
dc.contributor.authorSalje, Ekhard
dc.date.accessioned2021-12-04T00:30:23Z
dc.date.available2021-12-04T00:30:23Z
dc.date.issued2021-11
dc.identifier.issn2470-0045
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/331229
dc.description.abstractA simple numerical model to simulate athermal avalanches is presented. The model is inspired by the "porous collapse" process where the compression of porous materials generates collapse cascades, leading to power law distributed avalanches. The energy (E), amplitude (A_{max}), and size (S) exponents are derived by computer simulation in two approximations. Time-dependent "jerk" spectra are calculated in a single avalanche model where each avalanche is simulated separately from other avalanches. The average avalanche profile is parabolic, the scaling between energy and amplitude follows E∼A_{max}^{2}, and the energy exponent is ε = 1.33. Adding a general noise term in a continuous event model generates infinite avalanche sequences which allow the evaluation of waiting time distributions and pattern formation. We find the validity of the Omori law and the same exponents as in the single avalanche model. We then add spatial correlations by stipulating the ratio G/N between growth processes G (linked to a previous event location) and nucleation processes N (with new, randomly chosen nucleation sites). We found, in good approximation, a power law correlation between the energy exponent ε and the Hausdorff dimension H_{D} of the resulting collapse pattern H_{D}-1∼ɛ^{-3}. The evolving patterns depend strongly on G/N with the distribution of collapse sites equally power law distributed. Its exponent ɛ_{topo} would be linked to the dynamical exponent ε if each collapse carried an energy equivalent to the size of the collapse. A complex correlation between ɛ,ɛ_{topo}, and H_{D} emerges, depending strongly on the relative occupancy of the collapse sites in the simulation box.
dc.publisherAmerican Physical Society (APS)
dc.rightsAll rights reserved
dc.rights.urihttp://www.rioxx.net/licenses/all-rights-reserved
dc.titleEnergy exponents of avalanches and Hausdorff dimensions of collapse patterns.
dc.typeArticle
dc.publisher.departmentDepartment of Earth Sciences
dc.date.updated2021-12-03T12:10:43Z
prism.issueIdentifier5
prism.number054138
prism.publicationNamePhys Rev E
prism.volume104
dc.identifier.doi10.17863/CAM.78675
dcterms.dateAccepted2021-11-05
rioxxterms.versionofrecord10.1103/PhysRevE.104.054138
rioxxterms.versionVoR
dc.contributor.orcidSalje, Ekhard [0000-0002-8781-6154]
dc.identifier.eissn2470-0053
rioxxterms.typeJournal Article/Review
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/P024904/1)
cam.issuedOnline2021-11-29
cam.depositDate2021-12-03
pubs.licence-identifierapollo-deposit-licence-2-1
pubs.licence-display-nameApollo Repository Deposit Licence Agreement


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