Diffusion Time-Scale Invariance, Markovization 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 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 estimated numerically statistical memory effects of diffusion in detail.Comment: 10 pages, 3 figure

Time-scale invariance of relaxation processes of density fluctuation in slow neutron scattering in liquid cesium

The realization of idea of time-scale invariance for relaxation processes in liquids has been performed by the memory functions formalism. The best agreement with experimental data for the dynamic structure factor $S(k,\omega)$ of liquid cesium near melting point in the range of wave vectors (0.4 \ang^{-1} \leq k \leq 2.55 \ang^{-1}) is found with the assumption of concurrence of relaxation scales for memory functions of third and fourth orders. Spatial dispersion of the four first points in spectrum of statistical parameter of non-Markovity $\epsilon_{i}(k,\omega)$ at $i=1,2,3,4$ has allowed to reveal the non-Markov nature of collective excitations in liquid cesium, connected with long-range memory effect.Comment: REVTEX +3 ps figure

Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis

The basic purpose of the paper is to draw the attention of researchers to new possibilities of differentiation of similar signals having different nature. One of examples of such kind of signals is presented by seismograms containing recordings of earthquakes (EQ's) and technogenic explosions (TE's). We propose here a discrete stochastic model for possible solution of a problem of strong EQ's forecasting and differentiation of TE's from the weak EQ's. Theoretical analysis is performed by two independent methods: with the use of statistical theory of discrete non-Markov stochastic processes (Phys. Rev. E62,6178 (2000)) and the local Hurst exponent. Time recordings of seismic signals of the first four dynamic orthogonal collective variables, six various plane of phase portrait of four dimensional phase space of orthogonal variables and the local Hurst exponent have been calculated for the dynamic analysis of the earth states. The approaches, permitting to obtain an algorithm of strong EQ's forecasting and to differentiate TE's from weak EQ's, have been developed.Comment: REVTEX +12 ps and jpg figures. Accepted for publication in Phys. Rev. E, December 200

Analysis of the Dynamics of Liquid Aluminium: Recurrent Relation Approach

By use of the recurrent relation approach (RRA) we study the microscopic dynamics of liquid aluminium at T=973 K and develop a theoretical model which satisfies all the corresponding sum rules. The investigation covers the inelastic features as well as the crossover of our theory into the hydrodynamical and the free-particle regimes. A comparison between our theoretical results with those following from a generalized hydrodynamical approach is also presented. In addition to this we report the results of our molecular dynamics simulations for liquid aluminium, which are also discussed and compared to experimental data. The received results reveal that (i) the microscopical dynamics of density fluctuations is defined mainly by the first four even frequency moments of the dynamic structure factor, and (ii) the inherent relation of the high-frequency collective excitations observed in experimental spectra of dynamic structure factor $S(k,\omega)$ with the two-, three- and four-particle correlations.Comment: 11 pages, 4 figure

Frequency and Phase Synchronization in Neuromagnetic Cortical Responses to Flickering-Color Stimuli

In our earlier study dealing with the analysis of neuromagnetic responses (magnetoencephalograms - MEG) to flickering-color stimuli for a group of control human subjects (9 volunteers) and a patient with photosensitive epilepsy (a 12-year old girl), it was shown that Flicker-Noise Spectroscopy (FNS) was able to identify specific differences in the responses of each organism. The high specificity of individual MEG responses manifested itself in the values of FNS parameters for both chaotic and resonant components of the original signal. The present study applies the FNS cross-correlation function to the analysis of correlations between the MEG responses simultaneously measured at spatially separated points of the human cortex processing the red-blue flickering color stimulus. It is shown that the cross-correlations for control (healthy) subjects are characterized by frequency and phase synchronization at different points of the cortex, with the dynamics of neuromagnetic responses being determined by the low-frequency processes that correspond to normal physiological rhythms. But for the patient, the frequency and phase synchronization breaks down, which is associated with the suppression of cortical regulatory functions when the flickering-color stimulus is applied, and higher frequencies start playing the dominating role. This suggests that the disruption of correlations in the MEG responses is the indicator of pathological changes leading to photosensitive epilepsy, which can be used for developing a method of diagnosing the disease based on the analysis with the FNS cross-correlation function.Comment: 21 pages, 14 figures; submitted to "Laser Physics", 2010, 2

A simple measure of memory for dynamical processes described by the 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