751 research outputs found
Quasi symplectic integrators for stochastic differential equations
Two specialized algorithms for the numerical integration of the equations of
motion of a Brownian walker obeying detailed balance are introduced. The
algorithms become symplectic in the appropriate limits, and reproduce the
equilibrium distributions to some higher order in the integration time step.
Comparisons with other existing integration schemes are carried out both for
static and dynamical quantities.Comment: 7 pages, revtex, 6 eps figure
Comment on "Influence of Noise on Force Measurements"
In a recent Letter [arXiv:1004.0874], Volpe et al. describe experiments on a
colloidal particle near a wall in the presence of a gravitational field for
which they study the influence of noise on the measurement of force. Their
central result is a striking discrepancy between the forces derived from
experimental drift measurements via their Eq. (1), and from the equilibrium
distribution. From this discrepancy they infer the stochastic calculus realised
in the system.
We comment, however: (a) that Eq. (1) does not hold for space-dependent
diffusion, and corrections should be introduced; and (b) that the "force"
derived from the drift need not coincide with the "force" obtained from the
equilibrium distribution.Comment: Comment submitted to a PRL letter; 1 page, 1 figur
Separatrix chaos: new approach to the theoretical treatment
We develop a new approach to the theoretical treatment of the separatrix
chaos, using a special analysis of the separatrix map. The approach allows us
to describe boundaries of the separatrix chaotic layer in the Poincar\'{e}
section and transport within the layer. We show that the maximum which the
width of the layer in energy takes as the perturbation frequency varies is much
larger than the perturbation amplitude, in contrast to predictions by earlier
theories suggesting that the maximum width is of the order of the amplitude.
The approach has also allowed us to develop the self-consistent theory of the
earlier discovered (PRL 90, 174101 (2003)) drastic facilitation of the onset of
global chaos between adjacent separatrices. Simulations agree with the theory.Comment: 10 pages, 4 figures, proceedings of the conference "Chaos, Complexity
and Transport" (Marseille, 5-9 June 2007), in pres
New approach to the treatment of separatrix chaos and its application to the global chaos onset between adjacent separatrices
We have developed the {\it general method} for the description of {\it
separatrix chaos}, basing on the analysis of the separatrix map dynamics.
Matching it with the resonant Hamiltonian analysis, we show that, for a given
amplitude of perturbation, the maximum width of the chaotic layer in energy may
be much larger than it was assumed before. We apply the above theory to explain
the drastic facilitation of global chaos onset in time-periodically perturbed
Hamiltonian systems possessing two or more separatrices, previously discovered
(PRL 90, 174101 (2003)). The theory well agrees with simulations. We also
discuss generalizations and applications. Examples of applications of the
facilitation include: the increase of the DC conductivity in spatially periodic
structures, the reduction of activation barriers for noise-induced transitions
and the related acceleration of spatial diffusion, the facilitation of the
stochastic web formation in a wave-driven or kicked oscillator.Comment: 29 pages, 16 figures (figs. are of reduced quality, original files
are available on request from authors), paper has been significantly revised
and resubmitted to PR
On the determination of the optimal parameters in the CAM model
In the field of complex systems, it is often possible to arrive at some simple stochastic or chaotic Low Order Models (LOMs) exploiting the time scale separation between leading modes of interest and fast fluctuations. These LOMs, although approximate, might provide interesting qualitative insights regarding some important aspects like the average time between two extreme events. Recently, the simplest example of a LOM with multiplicative noise, namely, a linear system with a linearly state dependent noise [also called correlated additive and multiplicative (CAM) model], has been considered as archetypal for numerous phenomena that present markedly non-Gaussian statistics. We show in this paper that the determination of the parameters of a CAM model from the (few) available data is far from trivial and that the actual most likely parameters might differ substantially from the ones determined directly from a (necessarily limited) short sequence of observations. We illustrate how this problem can be tackled, at least to the extent possible, using an approach that is based on Bayes' theorem. We shall focus on a CAM modeling the El Ninõ Southern Oscillation but the methodology can be extended to any phenomenon that can be described by a simplified LOM similar to the one examined here and where the available sequence of data is relatively short. We conclude that indeed a Bayesian approach can fix the problem
Fast Monte Carlo simulations and singularities in the probability distributions of non-equilibrium systems
A numerical technique is introduced that reduces exponentially the time
required for Monte Carlo simulations of non-equilibrium systems. Results for
the quasi-stationary probability distribution in two model systems are compared
with the asymptotically exact theory in the limit of extremely small noise
intensity. Singularities of the non-equilibrium distributions are revealed by
the simulations.Comment: 4 pages, 4 figure
Stochastic resonance in electrical circuits—II: Nonconventional stochastic resonance.
Stochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treate
Enlargement of a low-dimensional stochastic web
We consider an archetypal example of a low-dimensional stochastic web, arising in a 1D oscillator driven by a plane wave of a frequency equal or close to a multiple of the oscillator’s natural frequency. We show that the web can be greatly enlarged by the introduction of a slow, very weak, modulation of the wave angle. Generalizations are discussed. An application to electron transport in a nanometre-scale semiconductor superlattice in electric and magnetic fields is suggested
Stochastic resonance in electrical circuits—I: Conventional stochastic resonance.
Stochastic resonance (SR), a phenomenon in which a periodic signal in a nonlinear system can be amplified by added noise, is introduced and discussed. Techniques for investigating SR using electronic circuits are described in practical terms. The physical nature of SR, and the explanation of weak-noise SR as a linear response phenomenon, are considered. Conventional SR, for systems characterized by static bistable potentials, is described together with examples of the data obtainable from the circuit models used to test the theory
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