2,009 research outputs found
Flux reversal in a simple random walk model on a fluctuating symmetric lattice
A rather simple random walk model on a one-dimensional lattice is put
forward. The lattice as a whole switches randomly between two possible states
which are spatially symmetric. Both lattice states are identical, but
translated by one site with respect to each other, and consist of infinite
arrays of absorbing sites separated by two non-absorbing sites. Exact explicit
expressions for the long-time velocity and the effective diffusion coefficient
are obtained and discussed. In particular, it is shown that the direction of
the steady motion can be reversed by conveniently varying the values of either
the mean residence times in the lattice states or the transition rates to the
absorbing and non-absorbing sites.Comment: 6 pages, 3 Figures, (to appear in Physical Review E
Stochastic resonance with weak monochromatic driving: gains above unity induced by high-frequency signals
We study the effects of a high-frequency (HF) signal on the response of a
noisy bistable system to a low-frequency subthreshold sinusoidal signal. We
show that, by conveniently choosing the ratio of the amplitude of the HF signal
to its frequency, stochastic resonance gains greater than unity can be measured
at the low-frequency value. Thus, the addition of the HF signal can entail an
improvement in the detection of weak monochromatic signals. The results are
explained in terms of an effective model and illustrated by means of numerical
simulations.Comment: 5 pages, 2 figure
Statistical Mechanics of finite arrays of coupled bistable elements
We discuss the equilibrium of a single collective variable characterizing a
finite set of coupled, noisy, bistable systems as the noise strength, the size
and the coupling parameter are varied. We identify distinct regions in
parameter space. The results obtained in prior works in the asymptotic infinite
size limit are significantly different from the finite size results. A
procedure to construct approximate 1-dimensional Langevin equation is adopted.
This equation provides a useful tool to understand the collective behavior even
in the presence of an external driving force
Checking the validity of truncating the cumulant hierarchy description of a small system
We analyze the behavior of the first few cumulant in an array with a small
number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf
19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global
coupling and derived an infinite hierarchy of differential equations for the
cumulant moments. They focused on the behavior of infinite size systems using a
strategy based on truncating the hierarchy. In this work we explore the
reliability of such an approach to describe systems with a small number of
elements. We carry out an extensive numerical analysis of the truncated
hierarchy as well as numerical simulations of the full set of Langevin
equations governing the dynamics. We find that the results provided by the
truncated hierarchy for finite systems are at variance with those of the
Langevin simulations for large regions of parameter space. The truncation of
the hierarchy leads to a dependence on initial conditions and to the
coexistence of states which are not consistent with the theoretical
expectations based on the multidimensional linear Fokker-Planck equation for
finite arrays
High-frequency effects in the FitzHugh-Nagumo neuron model
The effect of a high-frequency signal on the FitzHugh-Nagumo excitable model
is analyzed. We show that the firing rate is diminished as the ratio of the
high-frequency amplitude to its frequency is increased. Moreover, it is
demonstrated that the excitable character of the system, and consequently the
firing activity, is suppressed for ratios above a given threshold value. In
addition, we show that the vibrational resonance phenomenon turns up for
sufficiently large noise strength values.Comment: 4 pages, 4 figures (to appear in Physical Review E
Gain in Stochastic Resonance: Precise Numerics versus Linear Response Theory beyond the Two-Mode Approximation
In the context of the phenomenon of Stochastic Resonance (SR) we study the
correlation function, the signal-to-noise ratio (SNR) and the ratio of output
over input SNR, i.e. the gain, which is associated to the nonlinear response of
a bistable system driven by time-periodic forces and white Gaussian noise.
These quantifiers for SR are evaluated using the techniques of Linear Response
Theory (LRT) beyond the usually employed two-mode approximation scheme. We
analytically demonstrate within such an extended LRT description that the gain
can indeed not exceed unity. We implement an efficient algorithm, based on work
by Greenside and Helfand (detailed in the Appendix), to integrate the driven
Langevin equation over a wide range of parameter values. The predictions of LRT
are carefully tested against the results obtained from numerical solutions of
the corresponding Langevin equation over a wide range of parameter values. We
further present an accurate procedure to evaluate the distinct contributions of
the coherent and incoherent parts of the correlation function to the SNR and
the gain. As a main result we show for subthreshold driving that both, the
correlation function and the SNR can deviate substantially from the predictions
of LRT and yet, the gain can be either larger or smaller than unity. In
particular, we find that the gain can exceed unity in the strongly nonlinear
regime which is characterized by weak noise and very slow multifrequency
subthreshold input signals with a small duty cycle. This latter result is in
agreement with recent analogue simulation results by Gingl et al. in Refs. [18,
19].Comment: 22 pages, 5 eps figures, submitted to PR
Double Entropic Stochastic Resonance
We demonstrate the appearance of a purely entropic stochastic resonance (ESR)
occurring in a geometrically confined system, where the irregular boundaries
cause entropic barriers. The interplay between a periodic input signal, a
constant bias and intrinsic thermal noise leads to a resonant ESR-phenomenon in
which feeble signals become amplified. This new phenomenon is characterized by
the presence of two peaks in the spectral amplification at corresponding
optimal values of the noise strength. The main peak is associated with the
manifest stochastic resonance synchronization mechanism involving the
inter-well noise-activated dynamics while a second peak relates to a regime of
optimal sensitivity for intra-well dynamics. The nature of ESR, occurring when
the origin of the barrier is entropic rather than energetic, offers new
perspectives for novel investigations and potential applications. ESR by itself
presents yet another case where one constructively can harvest noise in driven
nonequilibrium systems.Comment: 6 pages, 7 figures ; Europhys. Lett., in press (2009
Forced synchronization of a quantum dissipative dynamics
We generalize the phenomenon of forced stochastic synchronization into the quantum
domain within the framework of a paradigmatic spin-boson model (tunneling charge, or flipping
spin 1/2 coupled to an environment) which is driven by an external periodic rectangular field. The
overdamped regime of dissipative quantum tunneling is studied. Thermal noise assisted synchronization of a very high quality is shown to occur in a broad range of temperatures, driving strengths and frequencies, if the external driving frequency exceeds the zero-temperature limit of dissipative tunneling rate, the dissipation strength exceeds a critical value, and the driving is sufficiently strong. A simple criterion for such stochastic synchronization is established. Both the similarities and the profound differences with the akin phenomenon of quantum stochastic resonance are outlined.Ministerio de Educación y Ciencia (MEC). España FIS2005-0288
Thermal equilibrium and statistical thermometers in special relativity
There is an intense debate in the recent literature about the correct
generalization of Maxwell's velocity distribution in special relativity. The
most frequently discussed candidate distributions include the Juettner function
as well as modifications thereof. Here, we report results from fully
relativistic one-dimensional (1D) molecular dynamics (MD) simulations that
resolve the ambiguity. The numerical evidence unequivocally favors the Juettner
distribution. Moreover, our simulations illustrate that the concept of 'thermal
equilibrium' extends naturally to special relativity only if a many-particle
system is spatially confined. They make evident that 'temperature' can be
statistically defined and measured in an observer frame independent way.Comment: version accepted for publication (5 pages), part of the introduction
modified, new figures, additional reference
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