Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos

We consider a chain of nonlinear oscillators with long-range interaction of the type 1/l^{1+alpha}, where l is a distance between oscillators and 0< alpha <2. In the continues limit the system's dynamics is described by the Ginzburg-Landau equation with complex coefficients. Such a system has a new parameter alpha that is responsible for the complexity of the medium and that strongly influences possible regimes of the dynamics. We study different spatial-temporal patterns of the dynamics depending on alpha and show transitions from synchronization of the motion to broad-spectrum oscillations and to chaos.Comment: 22 pages, 10 figure

A theory of non-local linear drift wave transport

Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated through a Fokker-Planck equation with fractional velocity derivatives. A dispersion relation for density gradient driven linear drift modes is derived including the effects of the fractional velocity derivative in the Fokker-Planck equation. It is found that a small deviation (a few percent) from the Maxwellian distribution function alters the dispersion relation such that the growth rates are substantially increased and thereby may cause enhanced levels of transport.Comment: 22 pages, 2 figures. Manuscript submitted to Physics of Plasma

Divergence of the Chaotic Layer Width and Strong Acceleration of the Spatial Chaotic Transport in Periodic Systems Driven by an Adiabatic ac Force

We show for the first time that a {\it weak} perturbation in a Hamiltonian system may lead to an arbitrarily {\it wide} chaotic layer and {\it fast} chaotic transport. This {\it generic} effect occurs in any spatially periodic Hamiltonian system subject to a sufficiently slow ac force. We explain it and develop an explicit theory for the layer width, verified in simulations. Chaotic spatial transport as well as applications to the diffusion of particles on surfaces, threshold devices and others are discussed.Comment: 4 pages including 3 EPS figures, this is an improved version of the paper (accepted to PRL, 2005

Quantum Breaking Time Scaling in the Superdiffusive Dynamics

We show that the breaking time of quantum-classical correspondence depends on the type of kinetics and the dominant origin of stickiness. For sticky dynamics of quantum kicked rotor, when the hierarchical set of islands corresponds to the accelerator mode, we demonstrate by simulation that the breaking time scales as $\tau_{\hbar} \sim (1/\hbar)^{1/\mu}$ with the transport exponent $\mu > 1$ that corresponds to superdiffusive dynamics. We discuss also other possibilities for the breaking time scaling and transition to the logarithmic one $\tau_{\hbar} \sim \ln(1/\hbar)$ with respect to $\hbar$

Estimation of Site Effects in the Israel Seacoast Area by Ambient Noise Records for Microzonation

Owing to the proximity to seismically active faults as well as the population density in the band of Israel Seacoast between the towns of Ashqelon and Haifa, this region may be considered a high seismic risk zone. For quantitative assessment of seismic response in terms of horizontal-to-vertical (H/V) spectral ratios the ambient noise survey was carried out at 190 sites. Results derived from H/V analysis indicate site amplifications ranging from 1 to 8 within the frequency band 1.0-6.0 Hz. The soil profiles at the investigated sites were very different. Some sites have simple profiles in the uppermost surface layer and clear seismic impedance between the soft soil layer and the bedrock. Other sites had complicated surface soil layers and a less distinct contrast between the surface soil and underlying bedrock. In many cases our attempts to estimate depth to the hardrock reflector from borehole data failed. Only when the distribution maps of the predominant frequency and the distribution of maximum amplification were constructed was the strong correlation between geological features and measurement results revealed. The observed resonance frequencies and their amplifications were correlated with analytical functions that correspond to the 1-D subsurface model. Collection of available geological, geotechnical and geophysical data relevant to local geology and combination of the theoretical and experimental response functions provided reliable estimations of analytical site effects

A Fractional Fokker-Planck Model for Anomalous Diffusion

In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the transition from a Gaussian distribution to a L\'evy distribution. The statistical properties of the distribution functions are assessed by a generalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.Comment: 22 pages, 14 figure

Correlations between distribution coefficients of various biomolecules in different polymer/polymer aqueous two-phase systems

Distribution coefficients for a variety of proteins and certain other biomolecules (peptides, amino acids, and carbohydrates) (overall 27 different solutes) were measured in aqueous two-phase systems (ATPSs) dextran (Dex)–polyethylene glycol (PEG) and Dex–Ucon 50-HB-5100 (Ucon—a random copolymer of ethylene glycol and propylene glycol) both containing 0.15MNaCl in 0.01Mphosphate buffer, pH 7.4, at 23 ◦C. Distribution coefficients of some selected solutes were also measured in the above two-phase systems at three different polymer concentrations for each system. It was established that the distribution coefficients for all the proteins examined in the ATPSs are correlated according to the so-called Collander linear equation.Fundação para a Ciência e a Tecnologia (FCT)FEDE

Bottlenecks to vibrational energy flow in OCS: Structures and mechanisms

Finding the causes for the nonstatistical vibrational energy relaxation in the planar carbonyl sulfide (OCS) molecule is a longstanding problem in chemical physics: Not only is the relaxation incomplete long past the predicted statistical relaxation time, but it also consists of a sequence of abrupt transitions between long-lived regions of localized energy modes. We report on the phase space bottlenecks responsible for this slow and uneven vibrational energy flow in this Hamiltonian system with three degrees of freedom. They belong to a particular class of two-dimensional invariant tori which are organized around elliptic periodic orbits. We relate the trapping and transition mechanisms with the linear stability of these structures.Comment: 13 pages, 13 figure

Out of Equilibrium Solutions in the XYXY-Hamiltonian Mean Field model

Out of equilibrium magnetised solutions of the $XY$-Hamiltonian Mean Field ($XY$-HMF) model are build using an ensemble of integrable uncoupled pendula. Using these solutions we display an out-of equilibrium phase transition using a specific reduced set of the magnetised solutions

“On the collander equation”: protein partitioning in polymer/polymer aqueous two-phase systems

Distribution coefficients of randomly selected proteins were measured in aqueous two-phase systems (ATPSs) formed by different combinations of Dextran-75 (Dex), Ficoll-70, polyethylene glycol-8000 (PEG), hydroxypropyl starch-100 (PES), and Ucon50HB5100 (Ucon, a random copolymer of ethylene glycol and propylene glycol) at particular polymer concentrations, all containing 0.15 M NaCl in 0.01 M phosphate buffer, pH 7.4. Most of the proteins in the PEG-Ucon system precipitated at the interface. In the other ATPSs, namely, PES-PEG, PES-Ucon, Ficoll-PEG, Ficoll-Ucon, and in Dex-PEG and Dex-Ucon described earlier the distribution coefficients for the proteins were correlated according to the solvent regression equation: ln Ki = aio ln Ko + bio, where Ki and Ko are the distribution coefficients for any protein in the ith and oth two-phase systems. Coefficients aio and bio are constants, the values of which depend upon the particular compositions of the two-phase systems under comparison.Fundo Europeu de Desenvolvimento Regional (FEDER)Fundação para a Ciência e a Tecnologia (FCT