Analytical Investigations into Anomalous Diffusion Driven by Stress Redistribution Events: Consequences of Lévy Flights

Simple item page
dc.citation.issue18
dc.citation.volume10
dc.contributor.authorCleland JD
dc.contributor.authorWilliams MAK
dc.contributor.editorLopes AM
dc.contributor.editorAlfi A
dc.contributor.editorChen L
dc.contributor.editorDavid SA
dc.date.accessioned2024-01-16T02:07:41Z
dc.date.accessioned2024-07-25T06:47:55Z
dc.date.available2022-09-06
dc.date.available2024-01-16T02:07:41Z
dc.date.available2024-07-25T06:47:55Z
dc.date.issued2022-09-06
dc.description.abstractThis research is concerned with developing a generalised diffusion equation capable of describing diffusion processes driven by underlying stress-redistributing type events. The work utilises the development of an appropriate continuous time random walk framework as a foundation to consider a new generalised diffusion equation. While previous work has explored the resulting generalised diffusion equation for jump-timings motivated by stick-slip physics, here non-Gaussian probability distributions of the jump displacements are also considered, specifically Lévy flights. This work illuminates several features of the analytic solution to such a generalised diffusion equation using several known properties of the Fox H function. Specifically demonstrated are the temporal behaviour of the resulting position probability density function, and its normalisation. The reduction of the proposed form to expected known solutions upon the insertion of simplifying parameter values, as well as a demonstration of asymptotic behaviours, is undertaken to add confidence to the validity of this equation. This work describes the analytical solution of such a generalised diffusion equation for the first time, and additionally demonstrates the capacity of the Fox H function and its properties in solving and studying generalised Fokker–Planck equations.
dc.description.confidentialfalse
dc.edition.editionSeptember 2022
dc.identifier.citationCleland JD, Williams MAK. (2022). Analytical Investigations into Anomalous Diffusion Driven by Stress Redistribution Events: Consequences of Lévy Flights. Mathematics. 10. 18.
dc.identifier.doi10.3390/math10183235
dc.identifier.eissn2227-7390
dc.identifier.elements-typejournal-article
dc.identifier.number3235
dc.identifier.urihttps://mro.massey.ac.nz/handle/10179/70900
dc.languageEnglish
dc.publisherMDPI (Basel, Switzerland)
dc.publisher.urihttps://www.mdpi.com/2227-7390/10/18/3235
dc.relation.isPartOfMathematics
dc.rights(c) 2022 The Author/s
dc.rightsCC BY 4.0
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectgeneralized
dc.subjectfractional
dc.subjectdiffusion
dc.subjectFokker–Planck
dc.titleAnalytical Investigations into Anomalous Diffusion Driven by Stress Redistribution Events: Consequences of Lévy Flights
dc.typeJournal article
pubs.elements-id457164
pubs.organisational-groupOther
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