478 research outputs found
Persistence and First-Passage Properties in Non-equilibrium Systems
In this review we discuss the persistence and the related first-passage
properties in extended many-body nonequilibrium systems. Starting with simple
systems with one or few degrees of freedom, such as random walk and random
acceleration problems, we progressively discuss the persistence properties in
systems with many degrees of freedom. These systems include spins models
undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces
etc. Persistence properties are nontrivial in these systems as the effective
underlying stochastic process is non-Markovian. Several exact and approximate
methods have been developed to compute the persistence of such non-Markov
processes over the last two decades, as reviewed in this article. We also
discuss various generalisations of the local site persistence probability.
Persistence in systems with quenched disorder is discussed briefly. Although
the main emphasis of this review is on the theoretical developments on
persistence, we briefly touch upon various experimental systems as well.Comment: Review article submitted to Advances in Physics: 149 pages, 21
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Interface Fluctuations, Burgers Equations, and Coarsening under Shear
We consider the interplay of thermal fluctuations and shear on the surface of
the domains in various systems coarsening under an imposed shear flow. These
include systems with nonconserved and conserved dynamics, and a conserved order
parameter advected by a fluid whose velocity field satisfies the Navier-Stokes
equation. In each case the equation of motion for the interface height reduces
to an anisotropic Burgers equation. The scaling exponents that describe the
growth and coarsening of the interface are calculated exactly in any dimension
in the case of conserved and nonconserved dynamics. For a fluid-advected
conserved order parameter we determine the exponents, but we are unable to
build a consistent perturbative expansion to support their validity.Comment: 10 RevTeX pages, 2 eps figure
Survival of a diffusing particle in an expanding cage
We consider a Brownian particle, with diffusion constant D, moving inside an
expanding d-dimensional sphere whose surface is an absorbing boundary for the
particle. The sphere has initial radius L_0 and expands at a constant rate c.
We calculate the joint probability density, p(r,t|r_0), that the particle
survives until time t, and is at a distance r from the centre of the sphere,
given that it started at a distance r_0 from the centre.Comment: 5 page
Geometric properties of two-dimensional coarsening with weak disorder
The domain morphology of weakly disordered ferromagnets, quenched from the
high-temperature phase to the low-temperature phase, is studied using numerical
simulations. We find that the geometrical properties of the coarsening domain
structure, e.g., the distributions of hull enclosed areas and domain perimeter
lengths, are described by a scaling phenomenology in which the growing domain
scale R(t) is the only relevant parameter. Furthermore, the scaling functions
have forms identical to those of the corresponding pure system, extending the
'super-universality' property previously noted for the pair correlation
function.Comment: 6 pages, 6 figure
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