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Exact and efficient discrete random walk method for time-dependent two-dimensional environments

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Asikainen, J.
dc.contributor.author Heinonen, J.
dc.contributor.author Ala-Nissilä, Tapio
dc.date.accessioned 2015-04-28T09:44:24Z
dc.date.available 2015-04-28T09:44:24Z
dc.date.issued 2002
dc.identifier.citation Asikainen, J. & Heinonen, J. & Ala-Nissilä, Tapio. 2002. Exact and efficient discrete random walk method for time-dependent two-dimensional environments. Physical Review E. Volume 66, Issue 6. P. 066706/1-10. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.66.066706. en
dc.identifier.issn 1539-3755 (printed)
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/15796
dc.description.abstract We present an exact method for speeding up random walk in two-dimensional complicated lattice environments. To this end, we derive the discrete two-dimensional probability distribution function for a diffusing particle starting at the center of a square of linear size s. This is used to propagate random walkers from the center of the square to sites which are nearest neighbors to its perimeter sites, thus saving O(s2) steps in numerical simulations. We discuss in detail how this method can be implemented efficiently. We examine its performance in the diffusion limited aggregation model which produces fractal structures, and in a one-sided step-growth model producing compact, fingerlike structures. We show that in both cases, the square propagator method reduces the computational effort by a factor proportional to the linear system size as compared to standard random walk. en
dc.format.extent 066706/1-10
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher American Physical Society (APS) en
dc.relation.ispartofseries Physical Review E en
dc.relation.ispartofseries Volume 66, Issue 6
dc.rights © 2002 American Physical Society (APS). http://www.aps.org en
dc.subject.other Physics en
dc.title Exact and efficient discrete random walk method for time-dependent two-dimensional environments en
dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi
dc.description.version Peer reviewed en
dc.rights.holder American Physical Society (APS)
dc.contributor.school Perustieteiden korkeakoulu fi
dc.contributor.school School of Science en
dc.contributor.department Teknillisen fysiikan laitos fi
dc.contributor.department Department of Applied Physics en
dc.subject.keyword two-dimensional lattices en
dc.subject.keyword numerical simulations en
dc.identifier.urn URN:NBN:fi:aalto-201504282457
dc.type.dcmitype text en
dc.identifier.doi 10.1103/physreve.66.066706
dc.type.version Final published version en

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