Anomalous diffusion driven by the redistribution of internal stresses

Cleland, Josiah D.; Williams, Martin A. K.

doi:10.1103/physreve.104.014123

Cited by 5 publications

(1 citation statement)

References 46 publications

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“…The next step for extending the RDA model is to introduce aftershocks following the Omori law into the system in order to investigate the waiting time distribution (compare [9]). From the other side, the form of the distribution [8] has been connected with the timing of stress-redistribution events and it leads to so-called anomalous diffusion-see [26,27] and references therein. Extending the RDA model, we aim at providing a mechanistic model connecting the above-mentioned ideas.…”

Section: Discussionmentioning

confidence: 99%

Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton

Białecki

Galka

Bagchi

et al. 2023

Entropy

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We develop the notion of Random Domino Automaton, a simple probabilistic cellular automaton model for earthquake statistics, in order to provide a mechanistic basis for the interrelation of Gutenberg–Richter law and Omori law with the waiting time distribution for earthquakes. In this work, we provide a general algebraic solution to the inverse problem for the model and apply the proposed procedure to seismic data recorded in the Legnica-Głogów Copper District in Poland, which demonstrate the adequacy of the method. The solution of the inverse problem enables adjustment of the model to localization-dependent seismic properties manifested by deviations from Gutenberg–Richter law.

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Section: Discussionmentioning

confidence: 99%

Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton

Białecki

Galka

Bagchi

et al. 2023

Entropy

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Oxidation resistance mechanism of copper wire regulated by nano-palladium coating

Li,

Su,

Song

et al. 2025

Applied Surface Science

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A generalised diffusion equation corresponding to continuous time random walks with coupling between the waiting time and jump length distributions

Cleland¹,

Williams²

2023

J. Phys. A: Math. Theor.

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This work outlines a transiently coupled continuous time random walk framework. The coupling is between the displacement probability density function and the elapsed waiting time, and is of the form 1 − exp (−αt) coupling of this kind generates larger displacements for longer waiting times, however, decouples on longer timescales. Such coupling is proposed to be physically relevant to systems in which diffusion is driven by the development of internal stresses which release and develop cyclically. This article outlines the associated generalised diffusion equation (GDE), which describes the time evolution of the position probability density function, P(x, t). The solution for P(x, t) is obtained using the properties of the Fox H function, both in terms of its transform properties but also its expansion theorems. The second moment and the asymptotic features of the solution are extracted. The relaxation of P(x, t) back to the solution of a decoupled-type GDE is highlighted.

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Anomalous diffusion driven by the redistribution of internal stresses

Cited by 5 publications

References 46 publications

Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton

Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton

Oxidation resistance mechanism of copper wire regulated by nano-palladium coating

A generalised diffusion equation corresponding to continuous time random walks with coupling between the waiting time and jump length distributions

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