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Persistence of randomly coupled fluctuating interfaces

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Title Persistence of randomly coupled fluctuating interfaces
 
Creator MAJUMDAR, SN
DAS, D
 
Subject zero-temperature dynamics
random velocity-fields
parisi-zhang equation
anomalous diffusion
gaussian-processes
disordered media
random-walks
random flows
spin chains
shear-flow
 
Description We study the persistence properties in a simple model of two coupled interfaces characterized by heights h(1) and h(2), respectively, each growing over a d-dimensional substrate. The first interface evolves independently of the second and can correspond to any generic growing interface, e.g., of the Edwards-Wilkinson or of the Kardar-Parisi-Zhang variety. The evolution of h(2), however, is coupled to h(1) via a quenched random velocity field. In the limit d -> 0, our model reduces to the Matheron-de Marsily model in two dimensions. For d=1, our model describes a Rouse polymer chain in two dimensions advected by a transverse velocity field. We show analytically that after a long waiting time t(0)->infinity, the stochastic process h(2), at a fixed point in space but as a function of time, becomes a fractional Brownian motion with a Hurst exponent, H-2=1-beta(1)/2, where beta(1) is the growth exponent characterizing the first interface. The associated persistence exponent is shown to be theta(s)(2)=1-H-2=beta(1)/2. These analytical results are verified by numerical simulations.
 
Publisher AMERICAN PHYSICAL SOC
 
Date 2011-07-17T17:57:07Z
2011-12-26T12:50:26Z
2011-12-27T05:34:57Z
2011-07-17T17:57:07Z
2011-12-26T12:50:26Z
2011-12-27T05:34:57Z
2005
 
Type Article
 
Identifier PHYSICAL REVIEW E, 71(3), -
1063-651X
http://dx.doi.org/10.1103/PhysRevE.71.036129
http://dspace.library.iitb.ac.in/xmlui/handle/10054/4799
http://hdl.handle.net/10054/4799
 
Language en