Simple measure of memory for dynamical processes described by a generalized Langevin equation.

Memory effects are a key feature in the description of the dynamical systems governed by the generalized Langevin equation, which presents an exact reformulation of the equation of motion. A simple measure for the estimation of memory effects is introduced within the framework of this description. Numerical calculations of the suggested measure and the analysis of memory effects are also applied for various model physical systems as well as for the phenomena of "long time tails" and anomalous diffusion.

Relaxation time scales in collective dynamics of liquid alkali metals.

In this paper the investigation of the dynamical processes of liquid alkali metals is executed by analyzing the time scales of relaxation processes in liquids. The obtained theoretical dynamic structure factor S(k,omega) for the case of liquid lithium is found to be in excellent agreement with the recently received inelastic x-ray scattering data. The comparison and interrelation with other theories are given here.

Diffusion time-scale invariance, randomization processes, and memory effects in Lennard-Jones liquids.

We report the results of calculation of diffusion coefficients for Lennard-Jones liquids, based on the idea of time-scale invariance of relaxation processes in liquids. The results were compared with the molecular dynamics data for the Lennard-Jones system and a good agreement of our theory with these data over a wide range of densities and temperatures was obtained. By calculations of the non-Markovity parameter we have numerically estimated statistical memory effects of diffusion in detail.

Quantification of heart rate variability by discrete nonstationary non-Markov stochastic processes.

We develop the statistical theory of discrete nonstationary non-Markov random processes in complex systems. The objective of this paper is to find the chain of finite-difference non-Markov kinetic equations for time correlation functions (TCF) in terms of nonstationary effects. The developed theory starts from careful analysis of time correlation through nonstationary dynamics of vectors of initial and final states and nonstationary normalized TCF.