Brownian motion with adhesion: harmonic oscillator with fluctuating mass.

In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.

Spatiotemporal vortex matter oscillations in Bi2Sr2CaCu2O8+delta crystals.

We observed an oscillatory behavior, both in space and time, of the induction in Bi2Sr2CaCu2O8+delta crystals exposed to a steady magnetic field. This new "flux waves" phenomenon appears near the order-disorder vortex phase transition, under specific conditions of temperature and induction gradient. A theoretical description of this effect is based on two coupled equations: the Landau-Khalatnikov dynamic equation for the order parameter of the vortex phase transition and the diffusion equation for the time evolution of the magnetic induction. A linear stability analysis of these equations predicts an oscillatory instability characterized by a period and wavelength in accordance with the experimental results.

Random walks and anomalous diffusion in two-component random media.

The diffusion process in a random media consisting of two different components is studied by a random walk model. The latter is described by three parameters, namely, the fraction p of components, the ratio h of the diffusion coefficients in two components, and the parameter x defining a walker's jumps at the boundary. Depending on the values of these parameters the diffusion can be confined, normal, or anomalous (subdiffusion). The subdiffusion occurs, in particular, for h=0 (trapping model) and for x=0 (excluded volume model).

Phase transitions in moving systems.

The general stability criteria of the supercritical Ginzburg-Landau equations in moving media are considered for different forms of the convective velocity which may change in space and time both periodically and randomly. The results are correlated with experiments on the propagation of vortices in superconducting films under the influence of a bias current. The role of the finite size of a sample is discussed.

Harmonic oscillator with fluctuating damping parameter.

The multiplicative noise in the equation of motion of an underdamped harmonic oscillator produced by a fluctuating damping parameter has a dramatic effect on the average coordinate of an oscillator. Noise of a sufficiently large strength leads to an instability. In the presence of an external periodic force, the output signal shows a nonmonotonic dependence on the strength and the rate of a color noise (stochastic resonance). Contrary to the case of a random frequency, this effect exists for white noise as well.

Harmonic oscillator with multiplicative noise: nonmonotonic dependence on the strength and the rate of dichotomous noise.

The output signal of a undamped linear oscillator with a random frequency subject to a periodic force shows nonmonotonic dependence on the strength and the rate of color noise (stochastic resonance). The effect is absent for white noise.

Thermal decay of a metastable state: exact solution.

Exact solutions are obtained for the thermal decay of a metastable state for two different forms of the potential and for uniform and localized boundary conditions by using the Laplace transform method. The exact inverse Laplace transforms are found for a symmetric case, and the results are compared with other calculations and with the Kramers rate.

Stabilization of metastable states.

An exact solution is obtained for a particle moving in a piecewise square nonsymmetric potential of fluctuating height. It turns out that the population of a metastable state increases in the presence of fluctuations similar to a previously found effect due to an external periodic field.

Effect of noise on a particle moving in a periodic potential.

It is shown that for systems with a periodic potential, the flux is very sensitive to the strength of additive or/and multiplicative noise. Multiplicative noise becomes important when its strength is of the order of the barrier height, and it provides a means of additional control of the flux (voltage-current characteristics for a Josephson junction). In addition to a numerical analysis, the cases of weak and strong additive noise have also been considered analytically.

Mean first passage time for anomalous diffusion

When the random force acting on a particle diffusing in an interval [0,L] and subjected to a constant external force is a Gaussian white noise, the "Brownian" mean-squared displacement is described by the seminal relation =2Dt(gamma) with gamma=1. However, for more complicated random forces the diffusion may be slower (gamma<1, "subdiffusion") or faster (gamma>1, "superdiffusion") than the "normal" diffusion. For both these cases we calculated the mean free passage time (MFPT)-the time needed to reach one of the traps at boundaries. The simple formulas for the different diffusive regimes are compared quantitatively for the simplest case of the absence of an external field and for an initial position in the middle of the interval. It turns out that the MFPT's for anomalous diffusion can be both larger or smaller than that for normal diffusion depending on the values of the length of the interval and the diffusion coefficient. Moreover, the MFPT can show nonmonotonic changes with the degree of departure from normal diffusion.

Stochastic resonance in one-dimensional diffusion with one reflecting and one absorbing end point

An analysis of the nonmonotonic dependence of the mean-free-passage time on the frequency of a periodic signal [stochastic resonance (SR)] for diffusion on a segment with one absorbing and one reflecting end point shows that SR exists only for some restricted values of parameters. SR always exists if the periodic telegraph signal is replaced by a random one. The latter case is considered in detail.

Symmetry breaking in one-dimensional diffusion

The mean free passage time for one-dimensional diffusion on a line segment under the influence of a deterministic telegraph signal proves to be a nonmonotonic function of the signal rate ("stochastic resonance") if symmetry breaking takes place. The symmetry breaking may be expressed either in nonsymmetric boundary conditions (one end absorbing and the other reflecting) or in a nonsymmetric telegraph signal. The latter case is considered in detail. It turns out that the larger the asymmetry of a telegraph signal, the wider the range of parameters for which a stochastic resonance occurs.

The critical period: some thoughts on Grimshaw et al (1998)

Grimshaw et al. (1998), based on their study of an adolescent first language acquirer, support the notion of a critical period. This article discusses the findings of Grimshaw et al. in the context of second language acquisition research. The study by Grimshaw et al. is argued to be of potentially significant value in gaining an understanding of age-related differences in language acquisition. Some issues for Grimshaw et al. to address are raised.

Stochastic resonance in linear systems subject to multiplicative and additive noise.

Exact expressions have been found for the first two moments and the correlation function for an overdamped linear system subject to an external periodic field as well as to multiplicative and additive noise. Stochastic resonance is absent for Gaussian white noise. However, when the multiplicative noise has the form of an asymmetric dichotomous noise, the signal-to-noise ratio (SNR) becomes a nonmonotonic function of the correlation time and the asymmetry of noise. Moreover, the SNR turns out to be a nonmonotonic function of the frequency of the external field as well as strongly depending on the strength of the cross correlation between multiplicative and additive noise.

Diffusion through piecewise washboard potential.

We consider the influence of small periodic oscillations of barriers on the stationary motion of a particle through a piecewise washboard potential. Up to the second order in the amplitude of oscillation the corrections to the flux can be both positive and negative and, for equal widths of the well and barrier, they do not depend on the frequency of the oscillations.