Motion of a random walker in a quenched power law correlated velocity field

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dc.creatorRoy, Soumen
dc.creatorDas, Dibyendu
dc.date2005-11-01
dc.date2006-01-12
dc.date.accessioned2026-07-07T06:45:44Z
dc.date.available2026-07-07T06:45:44Z
dc.descriptionWe study the motion of a random walker in one longitudinal and d transverse dimensions with a quenched power law correlated velocity field in the longitudinal x-direction. The model is a modification of the Matheron-de Marsily (MdM) model, with long-range velocity correlation. For a velocity correlation function, dependent on transverse co-ordinates y as 1/(a+|{y_1 - y_2}|)^alpha, we analytically calculate the two-time correlation function of the x-coordinate. We find that the motion of the x-coordinate is a fractional Brownian motion (fBm), with a Hurst exponent H = max [1/2, (1- alpha/4), (1-d/4)]. From this and known properties of fBM, we calculate the disorder averaged persistence probability of x(t) up to time t. We also find the lines in the parameter space of d and alpha along which there is marginal behaviour. We present results of simulations which support our analytical calculation.
dc.description8 pages, 4 figures. To appear in Physical Review E
dc.identifierhttps://arxiv.org/abs/cond-mat/0511008
dc.identifierhttp://arxiv.org/abs/cond-mat/0511008
dc.identifierPhys. Rev. E 73, 026106 (2006)
dc.identifierdoi:10.1103/PhysRevE.73.026106
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103126
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.subjectSoft Condensed Matter
dc.titleMotion of a random walker in a quenched power law correlated velocity field
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