Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties

dc.creatorComets, F
dc.creatorPopov, S
dc.creatorSchutz, GM
dc.creatorVachkovskaia, M
dc.date2010
dc.dateSEP
dc.date2014-11-16T03:37:17Z
dc.date2015-11-26T17:23:06Z
dc.date2014-11-16T03:37:17Z
dc.date2015-11-26T17:23:06Z
dc.date.accessioned2018-03-29T00:10:26Z
dc.date.available2018-03-29T00:10:26Z
dc.identifierJournal Of Statistical Physics. Springer, v. 140, n. 5, n. 948, n. 984, 2010.
dc.identifier0022-4715
dc.identifierWOS:000280816000007
dc.identifier10.1007/s10955-010-0023-8
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/61034
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/61034
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/61034
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1283749
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.descriptionWe consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate (the tube axis). Inside the random tube, which is stationary and ergodic, non-interacting particles move straight with constant speed. Upon hitting the tube walls, they are reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the cosine of the angle between this direction and the normal vector. Steady state transport is studied by introducing an open tube segment as follows: We cut out a large finite segment of the tube with segment boundaries perpendicular to the tube axis. Particles which leave this piece through the segment boundaries disappear from the system. Through stationary injection of particles at one boundary of the segment a steady state with non-vanishing stationary particle current is maintained. We prove (i) that in the thermodynamic limit of an infinite open piece the coarse-grained density profile inside the segment is linear, and (ii) that the transport diffusion coefficient obtained from the ratio of stationary current and effective boundary density gradient equals the diffusion coefficient of a tagged particle in an infinite tube. Thus we prove Fick's law and equality of transport diffusion and self-diffusion coefficients for quite generic rough (random) tubes. We also study some properties of the crossing time and compute the Milne extrapolation length in dependence on the shape of the random tube.
dc.description140
dc.description5
dc.description948
dc.description984
dc.descriptionCNRS [UMR 7599]
dc.descriptionANR Polintbio
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionDFG [SPP 1155]
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.descriptionCNRS [UMR 7599]
dc.descriptionCNPq [300886/2008-0, 304561/2006-1, 471925/2006-3, 472431/2009-9]
dc.descriptionDFG [SPP 1155]
dc.descriptionFAPESP [2009/52379-8]
dc.languageen
dc.publisherSpringer
dc.publisherNew York
dc.publisherEUA
dc.relationJournal Of Statistical Physics
dc.relationJ. Stat. Phys.
dc.rightsfechado
dc.rightshttp://www.springer.com/open+access/authors+rights?SGWID=0-176704-12-683201-0
dc.sourceWeb of Science
dc.subjectCosine law
dc.subjectKnudsen random walk
dc.subjectRandom medium
dc.subjectSelf-diffusion coefficient
dc.subjectTransport diffusion coefficient
dc.subjectRandom walk in random environment
dc.subjectSelf-diffusion
dc.subjectBilliards
dc.subjectLaw
dc.titleKnudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties
dc.typeArtículos de revistas


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