We study transmission through locally periodic potentials in the framework of space-fractional quantum mechanics (SFQM). In particular, we calculate the transmission probabilities T(N) for a particle in a chain of N Dirac-δ barriers and, for the other case, a chain of N square barriers. We use...

There are roughly speaking the two extreme types of dynamical density functional theories: one is deterministic without noise and another is fully stochastic with noise. We attempt to interpolate these extreme limiting theories for general reduced description of time evolution by making use of a...

We offer a new method to characterized cointegration properties of higher orders. This method relies on a very simple device. We first examine the question in a deterministic framework, where cointegration porperties pertains to rate of growth. We relate these properties to the structure of the...

Suppose a two-dimensional dynamical system has a stable attractor that is surrounded by an unstable limit cycle. If the system is additively perturbed by white noise, the rate of escape through the limit cycle will fall off exponentially as the noise strength. The presence of this slowly...

We have analyzed the interplay between noise and periodic modulations in a mean field model of a neural excitable medium. To this purpose, we have considered two types of modulations; namely, variations of the resistance and oscillations of the threshold. In both cases, stochastic resonance is...

Thermal pulsations in a transition from a nucleate to a film regime of water boiling on a wire heater with a periodic Joule heat release have been studied experimentally. At frequencies of the periodic action smaller than 0.1 Hz the intermittency of the nucleate and film boiling regimes was...

We outline two interesting phenomena, stochastic resonance and ratchets, in which the fluctuating environment is utilized. Some new manifestations of these phenomena are illustrated by the example of overdamped driven pendulum with fluctuating internal and external parameters.

The biological systems described as soft matter on mesoscopic scales manifest, in contrast to hard (condensed) matter, a number of characteristics: complexity, flexibility, and fluctuations. Due to these, there arise a variety of conformational and nonequilibrium phase transitions at...

We study the overdamped motion of a Brownian particle in a driven double-well system to understand various physical phenomena observed experimentally. These phenomena include hysteresis, stochastic resonance, and net undirectional motion in a symmetric periodic system. We argue that the area of...

Here we present a study of stochastic resonance (SR) in an extended FitzHugh–Nagumo system with a field dependent activator diffusion. We show that the system response (here measured through the output signal-to-noise ratio (SNR)) is enhanced due to the particular form of the non-homogeneous...