26 research outputs found
Critical Phenomena and Diffusion in Complex Systems
Editorial of the International Conference on Critical Phenomena and Diffusion
in Complex Systems held on 5--7 December, 2006 in Nizhniy Novgorod State
University, Russia and was dedicated to the memory and 80th anniversary of
Professor Askold N. Malakhov.Comment: 4 pages, to appear in International Journal of Bifurcation and Chao
Noise Enhanced Stability
The noise can stabilize a fluctuating or a periodically driven metastable
state in such a way that the system remains in this state for a longer time
than in the absence of white noise. This is the noise enhanced stability
phenomenon, observed experimentally and numerically in different physical
systems. After shortly reviewing all the physical systems where the phenomenon
was observed, the theoretical approaches used to explain the effect are
presented. Specifically the conditions to observe the effect: (a) in systems
with periodical driving force, and (b) in random dichotomous driving force, are
discussed. In case (b) we review the analytical results concerning the mean
first passage time and the nonlinear relaxation time as a function of the white
noise intensity, the parameters of the potential barrier, and of the
dichotomous noise.Comment: 18 pages, 6 figures, in press Acta Physica Polonica (2004
L\'evy flights versus L\'evy walks in bounded domains
L\'evy flights and L\'evy walks serve as two paradigms of random walks
resembling common features but also bearing fundamental differences. One of the
main dissimilarities are discontinuity versus continuity of their trajectories
and infinite versus finite propagation velocity. In consequence, well developed
theory of L\'evy flights is associated with their pathological physical
properties, which in turn are resolved by the concept of L\'evy walks. Here, we
explore L\'evy flights and L\'evy walks models on bounded domains examining
their differences and analogies. We investigate analytically and numerically
whether and under which conditions both approaches yield similar results in
terms of selected statistical observables characterizing the motion: the
survival probability, mean first passage time and stationary PDFs. It is
demonstrated that similarity of models is affected by the type of boundary
conditions and value of the stability index defining asymptotics of the jump
length distribution.Comment: 15 pages, 13 figure
Noise Enhanced Stability in Fluctuating Metastable States
We derive general equations for the nonlinear relaxation time of Brownian
diffusion in randomly switching potential with a sink. For piece-wise linear
dichotomously fluctuating potential with metastable state, we obtain the exact
average lifetime as a function of the potential parameters and the noise
intensity. Our result is valid for arbitrary white noise intensity and for
arbitrary fluctuation rate of the potential. We find noise enhanced stability
phenomenon in the system investigated: the average lifetime of the metastable
state is greater than the time obtained in the absence of additive white noise.
We obtain the parameter region of the fluctuating potential where the effect
can be observed. The system investigated also exhibits a maximum of the
lifetime as a function of the fluctuation rate of the potential.Comment: 7 pages, 5 figures, to appear in Phys. Rev. E vol. 69 (6),200
Escape Times in Fluctuating Metastable Potential and Acceleration of Diffusion in Periodic Fluctuating Potentials
The problems of escape from metastable state in randomly flipping potential
and of diffusion in fast fluctuating periodic potentials are considered. For
the overdamped Brownian particle moving in a piecewise linear dichotomously
fluctuating metastable potential we obtain the mean first-passage time (MFPT)
as a function of the potential parameters, the noise intensity and the mean
rate of switchings of the dichotomous noise. We find noise enhanced stability
(NES) phenomenon in the system investigated and the parameter region of the
fluctuating potential where the effect can be observed. For the diffusion of
the overdamped Brownian particle in a fast fluctuating symmetric periodic
potential we obtain that the effective diffusion coefficient depends on the
mean first-passage time, as discovered for fixed periodic potential. The
effective diffusion coefficients for sawtooth, sinusoidal and piecewise
parabolic potentials are calculated in closed analytical form.Comment: 10 pages, 2 figures. In press in Physica A, 2004. In press in Physica
A, 200
The spike train statistics for consonant and dissonant musical accords
The simple system composed of three neural-like noisy elements is considered.
Two of them (sensory neurons or sensors) are stimulated by noise and periodic
signals with different ratio of frequencies, and the third one (interneuron)
receives the output of these two sensors and noise. We propose the analytical
approach to analysis of Interspike Intervals (ISI) statistics of the spike
train generated by the interneuron. The ISI distributions of the sensory
neurons are considered to be known. The frequencies of the input sinusoidal
signals are in ratios, which are usual for music. We show that in the case of
small integer ratios (musical consonance) the input pair of sinusoids results
in the ISI distribution appropriate for more regular output spike train than in
a case of large integer ratios (musical dissonance) of input frequencies. These
effects are explained from the viewpoint of the proposed theory.Comment: 22 pages, 6 figure
Acceleration of Diffusion in Randomly Switching Potential with Supersymmetry
We investigate the overdamped Brownian motion in a supersymmetric periodic potential switched by Markovian dichotomous noise between two configurations. The two configurations differ from each other by a shift of one-half period. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential. For the sawtooth potential, we obtain the exact expression for the effective diffusion coefficient, which is valid for the arbitrary mean rate of potential switchings and arbitrary intensity of white Gaussian noise. We find the acceleration of diffusion in comparison with the free diffusion case and a finite net diffusion in the absence of thermal noise. Such a potential could be used to enhance the diffusion over its free value by an appropriate choice of parameter
Diffusion Acceleration in Randomly Switching Sawtooth Potential
We investigate an overdamped Brownian motion in symmetric sawtooth periodic potential switched by Markovian dichotomous noise between two configurations. The two configurations differ each other by a translation of half of period. The calculation of the effective diffusion coefficient is reduced to the mean first-passage time problem, and we obtain the exact expression valid for arbitrary mean rate of switchings and arbitrary intensity of white Gaussian noise. We find the area at parameters plane where acceleration of diffusion in comparison with the free diffusion case takes plac