3,642 research outputs found
Aspects of the Noisy Burgers Equation
The noisy Burgers equation describing for example the growth of an interface
subject to noise is one of the simplest model governing an intrinsically
nonequilibrium problem. In one dimension this equation is analyzed by means of
the Martin-Siggia-Rose technique. In a canonical formulation the morphology and
scaling behavior are accessed by a principle of least action in the weak noise
limit. The growth morphology is characterized by a dilute gas of nonlinear
soliton modes with gapless dispersion law with exponent z=3/2 and a superposed
gas of diffusive modes with a gap. The scaling exponents and a heuristic
expression for the scaling function follow from a spectral representation.Comment: 23 pages,LAMUPHYS LaTeX-file (Springer), 13 figures, and 1 table, to
appear in the Proceedings of the XI Max Born Symposium on "Anomalous
Diffusion: From Basics to Applications", May 20-24, 1998, Ladek Zdroj, Polan
Gaussian noise and time-reversal symmetry in non-equilibrium Langevin models
We show that in driven systems the Gaussian nature of the fluctuating force
and time-reversibility are equivalent properties. This result together with the
potential condition of the external force drastically restricts the form of the
probability distribution function, which can be shown to satisfy
time-independent relations. We have corroborated this feature by explicitly
analyzing a model for the stretching of a polymer and a model for a suspension
of non-interacting Brownian particles in steady flow.Comment: 6 pages, submitted to PR
About the parabolic relation existing between the skewness and the kurtosis in time series of experimental data
In this work we investigate the origin of the parabolic relation between
skewness and kurtosis often encountered in the analysis of experimental
time-series. We argue that the numerical values of the coefficients of the
curve may provide informations about the specific physics of the system
studied, whereas the analytical curve per se is a fairly general consequence of
a few constraints expected to hold for most systems.Comment: To appear in Physica Script
The Escape Problem for Irreversible Systems
The problem of noise-induced escape from a metastable state arises in
physics, chemistry, biology, systems engineering, and other areas. The problem
is well understood when the underlying dynamics of the system obey detailed
balance. When this assumption fails many of the results of classical
transition-rate theory no longer apply, and no general method exists for
computing the weak-noise asymptotics of fundamental quantities such as the mean
escape time. In this paper we present a general technique for analysing the
weak-noise limit of a wide range of stochastically perturbed continuous-time
nonlinear dynamical systems. We simplify the original problem, which involves
solving a partial differential equation, into one in which only ordinary
differential equations need be solved. This allows us to resolve some old
issues for the case when detailed balance holds. When it does not hold, we show
how the formula for the mean escape time asymptotics depends on the dynamics of
the system along the most probable escape path. We also present new results on
short-time behavior and discuss the possibility of focusing along the escape
path.Comment: 24 pages, APS revtex macros (version 2.1) now available from PBB via
`get oldrevtex.sty
Large deviations and Gallavotti-Cohen principle for dissipative PDE's with rough noise
We study a class of dissipative PDE's perturbed by an unbounded kick force.
Under some natural assumptions, the restrictions of solutions to integer times
form a homogeneous Markov process. Assuming that the noise is rough with
respect to the space variables and has a non-degenerate law, we prove that the
system in question satisfies a large deviation principle in tau-topology. Under
some additional hypotheses, we establish a Gallavotti-Cohen type symmetry for
the rate function of an entropy production functional and the strict positivity
and finiteness of the mean entropy production in the stationary regime. The
latter result is applicable to PDE's with strong nonlinear dissipation.Comment: 47 pages; to appear in Communications in Mathematical Physic
A modified semi--implict Euler-Maruyama Scheme for finite element discretization of SPDEs with additive noise
We consider the numerical approximation of a general second order
semi--linear parabolic stochastic partial differential equation (SPDE) driven
by additive space-time noise. We introduce a new modified scheme using a linear
functional of the noise with a semi--implicit Euler--Maruyama method in time
and in space we analyse a finite element method (although extension to finite
differences or finite volumes would be possible). We prove convergence in the
root mean square norm for a diffusion reaction equation and diffusion
advection reaction equation. We present numerical results for a linear reaction
diffusion equation in two dimensions as well as a nonlinear example of
two-dimensional stochastic advection diffusion reaction equation. We see from
both the analysis and numerics that the proposed scheme has better convergence
properties than the standard semi--implicit Euler--Maruyama method
Nonequilibrium dynamics of a growing interface
A growing interface subject to noise is described by the Kardar-Parisi-Zhang
equation or, equivalently, the noisy Burgers equation. In one dimension this
equation is analyzed by means of a weak noise canonical phase space approach
applied to the associated Fokker-Planck equation. The growth morphology is
characterized by a gas of nonlinear soliton modes with superimposed linear
diffusive modes. We also discuss the ensuing scaling properties.Comment: 14 pages, 11 figures, conference proceeding; a few corrections have
been adde
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