Modeling transport across the running-sandpile cellular automaton by means of fractional transport equations

dc.affiliation.dptoUC3M. Departamento de Ingeniería Telemáticaes
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Aplicaciones y Servicios Telemáticos (GAST)es
dc.contributor.authorSánchez Fernández, Luis Raúl
dc.contributor.authorNewman, D.E.
dc.contributor.authorMier Maza, Jose Angel
dc.contributor.funderEuropean Commissionen
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.contributor.funderUniversidad Carlos III de Madrides
dc.description.abstractFractional transport equations are used to build an effective model for transport across the running sandpile cellular automaton [Hwa et al., Phys. Rev. A 45, 7002 (1992)]. It is shown that both temporal and spatial fractional derivatives must be considered to properly reproduce the sandpile transport features, which are governed by self-organized criticality, at least over sufficiently long or large scales. In contrast to previous applications of fractional transport equations to other systems, the specifics of sand motion require in this case that the spatial fractional derivatives used for the running sandpile must be of the completely asymmetrical Riesz-Feller type. Appropriate values for the fractional exponents that define these derivatives in the case of the running sandpile are obtained numerically.en
dc.description.sponsorshipThis research has been sponsored in part by Ministerio de Economía y Competitividad of Spain under Projects No. ENE2015-68265-P and No. ENE2015-66444-R. Research was also supported in part by DOE-OFES Grant No. DE-FG02- 04ER5741 at University of Alaska. This work has also been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under Grant No. 633053 for the project WP17-ER/ENEA-10. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Sandpile automata simulations have been run in Uranus, a supercomputer cluster at Universidad Carlos III de Madrid (Spain) that has been funded by the Spanish Government via the national projects UNC313-4E-2361, ENE2009-12213-C03-03, ENE2012-33219, and ENE2012- 31753. Fruitful interactions with members of the ABIGMAP research network, funded by the Spanish Project MAT2015- 69777-REDT, are also acknowledged.en
dc.identifier.bibliographicCitationSánchez, R., Newman, D. E., & Mier, J. A. (2018). Modeling transport across the running-sandpile cellular automaton by means of fractional transport equations. In Physical Review E, 97(5), 052123-052133en
dc.identifier.publicationtitlePhysical review E, covering statistical, nonlinear, biological, and soft matter physicsen
dc.publisherAmerican Physical Society (APS)en
dc.relation.projectIDGobierno de España. ENE2009-12213-C03-03es
dc.relation.projectIDGobierno de España. ENE2012-33219es
dc.relation.projectIDGobierno de España. ENE2012-31753es
dc.relation.projectIDIndefinido. UNC313-4E-2361es
dc.relation.projectIDGobierno de España. ENE2015-68265-Pes
dc.relation.projectIDGobierno de España. ENE2015-66444-Res
dc.rights©2018 American Physical Societyen
dc.rights.accessRightsopen accessen
dc.titleModeling transport across the running-sandpile cellular automaton by means of fractional transport equationsen
dc.typeresearch article*
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