Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/xmlui/handle/10054/4799
Title: Persistence of randomly coupled fluctuating interfaces
Authors: MAJUMDAR, SN
DAS, D
Keywords: Zero-Temperature Dynamics
Random Velocity-Fields
Parisi-Zhang Equation
Anomalous Diffusion
Gaussian-Processes
Disordered Media
Random-Walks
Random Flows
Spin Chains
Shear-Flow
Issue Date: 2005
Publisher: AMERICAN PHYSICAL SOC
Citation: PHYSICAL REVIEW E, 71(3), -
Abstract: 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.
URI: 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
ISSN: 1063-651X
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