484 research outputs found
Diffusion in Fluctuating Media: The Resonant Activation Problem
We present a one-dimensional model for diffusion in a fluctuating lattice;
that is a lattice which can be in two or more states. Transitions between the
lattice states are induced by a combination of two processes: one periodic
deterministic and the other stochastic. We study the dynamics of a system of
particles moving in that medium, and characterize the problem from different
points of view: mean first passage time (MFPT), probability of return to a
given site (), and the total length displacement or number of visited
lattice sites (). We observe a double {\it resonant activation}-like
phenomenon when we plot the MFPT and as functions of the intensity of
the transition rate stochastic component.Comment: RevTex, 15 pgs, 8 figures, submitted to Eur.Phys.J.
Noise effects in extended chaotic system: study on the Lorenz'96 model
We investigate the effects of a time-correlated noise on an extended chaotic
system. The chosen model is the Lorenz'96, a kind of toy model used for climate
studies. The system is subjected to both temporal and spatiotemporal
perturbations. Through the analysis of the system's time evolution and its time
correlations, we have obtained numerical evidence for two stochastic
resonance-like behaviors. Such behavior is seen when a generalized
signal-to-noise ratio function are depicted as a function of the external noise
intensity or as function of the system size. The underlying mechanism seems to
be associated to a noise-induced chaos reduction. The possible relevance of
those findings for an optimal climate prediction are discussed, using an
analysis of the noise effects on the evolution of finite perturbations and
errors.Comment: To appear in Statistical Mechanics Research Focus, Special volume
(Nova Science Pub., NY, in press) (LaTex, 16 pgs, 14 figures
Bulk Mediated Surface Diffusion: Non Markovian Desorption with Finite First Moment
Here we address a fundamental issue in surface physics: the dynamics of
adsorbed molecules. We study this problem when the particle's desorption is
characterized by a non Markovian process, while the particle's adsorption and
its motion in the bulk are governed by a Markovian dynamics. We study the
diffusion of particles in a semi-infinite cubic lattice, and focus on the
effective diffusion process at the interface . We calculate analytically
the conditional probability to find the particle on the plane as well as
the surface dispersion as functions of time. The comparison of these results
with Monte Carlo simulations show an excellent agreement.Comment: 16 pages, 7 figs. European Physical Journal B (in press
Bulk Mediated Surface Diffusion: The Infinite System Case
An analytical soluble model based on a Continuous Time Random Walk (CTRW)
scheme for the adsorption-desorption processes at interfaces, called
bulk-mediated surface diffusion, is presented. The time evolution of the
effective probability distribution width on the surface is calculated and
analyzed within an anomalous diffusion framework. The asymptotic behavior for
large times shows a sub-diffusive regime for the effective surface diffusion
but, depending on the observed range of time, other regimes may be obtained.
Montecarlo simulations show excellent agreement with analytical results. As an
important byproduct of the indicated approach, we present the evaluation of the
time for the first visit to the surface.Comment: 15 pages, 7 figure
Bulk Mediated Surface Diffusion: Finite System Case
We address the dynamics of adsorbed molecules (a fundamental issue in surface
physics) within the framework of a Master Equation scheme, and study the
diffusion of particles in a finite cubic lattice whose boundaries are at the
and the planes where , while the and
directions are unbounded. As we are interested in the effective diffusion
process at the interface , we calculate analytically the conditional
probability for finding the system on the plane as well as the surface
dispersion as a function of time and compare these results with Monte Carlo
simulations finding an excellent agreement.Comment: 19 pages, 8 figure
Invited review: KPZ. Recent developments via a variational formulation
Recently, a variational approach has been introduced for the paradigmatic
Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together
with the functional Taylor expansion that the KPZ nonequilibrium potential
(NEP) admits. Such expansion becomes naturally truncated at third order, giving
rise to a nonlinear stochastic partial differential equation to be regarded as
a gradient-flow counterpart to the KPZ equation. A dynamic renormalization
group analysis at one-loop order of this new mesoscopic model yields the KPZ
scaling relation alpha+z=2, as a consequence of the exact cancelation of the
different contributions to vertex renormalization. This result is quite
remarkable, considering the lower degree of symmetry of this equation, which is
in particular not Galilean invariant. In addition, this scheme is exploited to
inquire about the dynamical behavior of the KPZ equation through a
path-integral approach. Each of these aspects offers novel points of view and
sheds light on particular aspects of the dynamics of the KPZ equation.Comment: 16 pages, 2 figure
Variational Formulation for the KPZ and Related Kinetic Equations
We present a variational formulation for the Kardar-Parisi-Zhang (KPZ)
equation that leads to a thermodynamic-like potential for the KPZ as well as
for other related kinetic equations. For the KPZ case, with the knowledge of
such a potential we prove some global shift invariance properties previously
conjectured by other authors. We also show a few results about the form of the
stationary probability distribution function for arbitrary dimensions. The
procedure used for KPZ was extended in order to derive more general forms of
such a functional leading to other nonlinear kinetic equations, as well as
cases with density dependent surface tension.Comment: RevTex, 8pgs, double colum
The Use of Rank Histograms and MVL Diagrams to Characterize Ensemble Evolution in Weather Forecasting
13 páginas, 9 figuras.-- El pdf del artÃculo es la versión pre-print.Rank Histograms are suitable tools to assess the quality of ensembles within an ensemble prediction system or framework. By counting the rank of a given variable in the ensemble, we are basically making a sample analysis, which does not allow us to distinguish if the origin of its variability is external noise or comes from chaotic sources. The recently introduced Mean to Variance Logarithmic (MVL) Diagram accounts for the spatial variability, being very sensitive to the spatial localization produced by infinitesimal perturbations of spatiotemporal chaotic systems. By using as a benchmark a simple model subject to noise, we show the distinct information given by Rank Histograms and MVL Diagrams. Hence, the main effects of the external noise can be visualized in a graphic. From the MVL diagram we clearly observe a reduction of the amplitude growth rate and of the spatial localization (chaos suppression), while from the Rank Histogram we observe changes in the reliability of the ensemble. We conclude that in a complex framework including spatiotemporal chaos and noise, both provide a more complete forecasting picture.We acknowledge financial support
from MEC, Spain, through Grant No. CGL2007-
64387/CLI, and also thank the AECID, Spain, for support
through projects A/013666/07 and A/018685/08. JAR
thanks the MEC, Spain, for the award of a Juan de la
Cierva fellowship. HSW thanks to the European Commission
for the award of a Marie Curie Chair during part of
the development of this work.Peer reviewe
Discretization-related issues in the KPZ equation: Consistency, Galilean-invariance violation, and fluctuation--dissipation relation
In order to perform numerical simulations of the KPZ equation, in any
dimensionality, a spatial discretization scheme must be prescribed. The known
fact that the KPZ equation can be obtained as a result of a Hopf--Cole
transformation applied to a diffusion equation (with \emph{multiplicative}
noise) is shown here to strongly restrict the arbitrariness in the choice of
spatial discretization schemes. On one hand, the discretization prescriptions
for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen.
On the other hand, since the discretization is an operation performed on
\emph{space} and the Hopf--Cole transformation is \emph{local} both in space
and time, the former should be the same regardless of the field to which it is
applied. It is shown that whereas some discretization schemes pass both
consistency tests, known examples in the literature do not. The requirement of
consistency for the discretization of Lyapunov functionals is argued to be a
natural and safe starting point in choosing spatial discretization schemes. We
also analyze the relation between real-space and pseudo-spectral discrete
representations. In addition we discuss the relevance of the Galilean
invariance violation in these consistent discretization schemes, and the
alleged conflict of standard discretization with the fluctuation--dissipation
theorem, peculiar of 1D.Comment: RevTex, 23pgs, 2 figures, submitted to Phys. Rev.
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