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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/4787

Title: Motion of a random walker in a quenched power law correlated velocity field
Authors: ROY, S
DAS, D
Keywords: anomalous diffusion
enhanced diffusion
disordered media
spin chains
dynamics
superdiffusion
flows
Issue Date: 2006
Publisher: AMERICAN PHYSICAL SOC
Citation: PHYSICAL REVIEW E, 73(2), -
Abstract: We 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 model, with long-range velocity correlation. For a velocity correlation function, dependent on transverse coordinates y as 1/(a+parallel to y(1)-y(2)parallel to)(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 behavior. We present results of simulations which support our analytical calculation.
URI: http://dx.doi.org/10.1103/PhysRevE.73.026106
http://dspace.library.iitb.ac.in/xmlui/handle/10054/4787
http://hdl.handle.net/10054/4787
ISSN: 1539-3755
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