Olga A. Chichigina

Stochastic acceleration in generalized squared Bessel processes

We analyze the time behavior of generalized squared Bessel processes, which are useful for modeling the relevant scales of stochastic acceleration problems. These nonstationary stochastic processes obey a Langevin equation with a non-Gaussian multiplicative noise. We obtain the long-time asymptotic behavior of the probability density function for non-Gaussian white and colored noise sources. We find that the functional form of the probability density functions is independent of the statistics of the noise source considered. Theoretical results are in good agreement with those obtained by numerical simulations of the Langevin equation with pulse noise sources.

THERMODYNAMICS OF DISPERSING BILLIARDS WITH TIME-DEPENDENT BOUNDARIES

By means of a thermodynamic approach we analyze billiards in the form of the Lorentz gas with the open horizon. For periodic and stochastic oscillations of the scatterers, the average velocity of the particle ensemble as a function of time is analytically obtained. It is shown that the consequence of such oscillations is Fermi acceleration which is larger for periodic oscillations. The described results do not depend on the size of scatterers and their position. Only the property of the horizon openness is necessary. It is found that the developed thermodynamic approach is in a very good agreement with the results of the direct numerical simulations at which the corresponding billiard map is used.

Stochastic dynamics of enzymes - "molecular scissors

The problems studied here are relevant for an understanding of the functioning of hydrolytic enzyme molecules. These enzymes work like molecular machines breaking off the valence peptid bonds of substrates. In particular the role of Fermi resonance which is evident from a spectral lines of valence oscillations is studied. The influence of this resonance on valence splitting is discussed. It is shown that the breaking of these bonds has a higher probability, if the stochastic oscillations of atoms in catalytic groups at the active site have a large quality coefficient. We show that the corresponding low damping is essential for the Fermi resonance modes of these oscillations.

Relaxation dynamics in the presence of pulse multiplicative noise sources with different correlation properties.

The relaxation dynamics of a system described by a Langevin equation with pulse multiplicative noise sources with different correlation properties is considered. The solution of the corresponding Fokker-Planck equation is derived for Gaussian white noise. Moreover, two pulse processes with regulated periodicity are considered as a noise source: the dead-time-distorted Poisson process and the process with fixed time intervals, which is characterized by an infinite correlation time. We find that the steady state of the system is dependent on the correlation properties of the pulse noise. An increase of the noise correlation causes the decrease of the mean value of the solution at the steady state. The analytical results are in good agreement with the numerical ones.

A MODEL OF OSCILLATIONS OF MACROMOLECULE WITH ANOMALOUS QUALITY FACTOR

The effect of anomalously enhanced quality factor (small damping decrement) is demonstrated and explained by phase dependence of interaction with particles of medium. The dependence of quality factor on the temperature of the medium is described. The most suitable noise intensity is determined. Molecular dynamics simulations qualitatively confirm the results. The size and mass of real bio-molecules, the frequency, amplitude of their oscillations and the temperature of living body are suitable conditions for this effect.

The distribution of velocities in an ensemble of accelerated particles on a surface

An ensemble of particles diffusing with acceleration on a surface is considered as a 2D billiard system. The process of the finite-time diffusion of particles is studied using the balance equation. The probability distribution functions of the velocity and lifetime of particles are obtained analytically and by means of numerical simulations. A thermodynamic interpretation of the process is discussed. The effective temperature and entropy obey the relationship for an ideal gas.

Predator population depending on lemming cycles

In this paper, a Langevin equation for predator population with multiplicative correlated noise is analyzed. The noise source, which is a nonnegative random pulse noise with regulated periodicity, corresponds to the prey population cycling. The increase of periodicity of noise affects the average predator density at the stationary state.

Slow diffusion on the surface with equal potential wells

The diffusion process on the surface with equivalent potential wells is investigated. These wells are considered deep enough to keep the particle for longer than the correlation time. The quasi-equilibrium Boltzmann distribution is applied inside the well to calculate the escape time. This time characterizes jumps from a well to another one. The coefficient of such a diffusion is calculated as a function of temperature, shape, depth and localization of potential wells and the mass of the particles.

Stochastic model for the epitaxial growth of two-dimensional islands in the submonolayer regime

The diusion-based growth of islands composed of clusters of metal atoms on a substrate is considered in the aggregation regime. A stochastic approach is proposed to describe the dynamics of island growth based on a Langevin equation with multiplicative noise. The distribution of island sizes, obtained as a solution of the corresponding Fokker–Planck equation, is derived. The time-dependence of island growth on its fractal dimension is analysed. The eect of mobility of the small islands on the growth of large islands is considered. Numerical simulations are in a good agreement with theoretical results.

Superdiffusion in 2D open-horizon billiards with stochastically oscillating boundaries

It is shown that Fermi acceleration, which is inherent to time-dependent open-horizon two-dimensional billiards, leads to anomalous transport properties. The stochastic oscillations of the scatterers result in superdiffusion of particles with the mean squared displacement growing asymptotically quadratically in time: q2~t2.