Persistence of Randomly Coupled Fluctuating Interfaces

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\to 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\to \infty, 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-β_1/2, where β_1 is the growth exponent characterizing the first interface. The associated persistence exponent is shown to be θ_s^2=1-H_2=β_1/2. These analytical results are verified by numerical simulations.

15 pages, 3 .eps figures included

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• Local Persistence in the Directed Percolation Universality Class
• Persistence and survival in equilibrium step fluctuations
• Persistence of a Rouse polymer chain under transverse shear flow
• Passive advection of fractional Brownian motion by random layered flows
• Model of bound interface dynamics for coupled magnetic domain walls
• Persistence in Advection of Passive Scalar
• Motion of a random walker in a quenched power law correlated velocity field
• The effect of shear on persistence in coarsening systems