Fractional dynamics of coupled oscillators with long-range interaction.

We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1//n-m/alpha+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order alpha, when 0 View Article and Find Full Text PDF

Anomalous transport in Charney-Hasegawa-Mima flows.

The transport properties of particles evolving in a system governed by the Charney-Hasegawa-Mima equation are investigated. Transport is found to be anomalous with a nonlinear evolution of the second moments with time. The origin of this anomaly is traced back to the presence of chaotic jets within the flow.

Ray dynamics in a long-range acoustic propagation experiment.

A ray-based wave-field description is employed in the interpretation of broadband basin-scale acoustic propagation measurements obtained during the Acoustic Thermometry of Ocean Climate program's 1994 Acoustic Engineering Test. Acoustic observables of interest are wavefront time spread, probability density function (PDF) of intensity, vertical extension of acoustic energy in the reception finale, and the transition region between temporally resolved and unresolved wavefronts. Ray-based numerical simulation results that include both mesoscale and internal-wave-induced sound-speed perturbations are shown to be consistent with measurements of all the aforementioned observables, even though the underlying ray trajectories are predominantly chaotic, that is, exponentially sensitive to initial and environmental conditions.

Fractional kinetic equations: solutions and applications.

Fractional generalization of the diffusion equation includes fractional derivatives with respect to time and coordinate. It had been introduced to describe anomalous kinetics of simple dynamical systems with chaotic motion. We consider a symmetrized fractional diffusion equation with a source and find different asymptotic solutions applying a method which is similar to the method of separation of variables.

Directional fractional kinetics.

Kinetic equations used to describe systems with dynamical chaos may contain fractional derivatives of an order alpha in space and beta in time in order to represent processes of stickiness, intermittency, and so on. We demonstrate for a simple example that the kinetics is anisotropic not only in the angular dependence of the diffusion constant, but also in the angular dependence of the exponents alpha and beta. A theory of such kinetic processes has been developed on the basis of integral representation and asymptotic solutions for different cases have been obtained.

Ray dynamics in long-range deep ocean sound propagation.

Recent results relating to ray dynamics in ocean acoustics are reviewed. Attention is focused on long-range propagation in deep ocean environments. For this class of problems, the ray equations may be simplified by making use of a one-way formulation in which the range variable appears as the independent (timelike) variable.

Jets, stickiness, and anomalous transport.

Dynamical and statistical properties of the vortex and passive particle advection in chaotic flows generated by 4- and 16-point vortices are investigated. General transport properties of these flows are found to be anomalous and exhibit a superdiffusive behavior with typical second moment exponent mu approximately 1.75.

From Hamiltonian chaos to Maxwell's Demon.

The problem of the existence of Maxwell's Demon (MD) is formulated for systems with dynamical chaos. Property of stickiness of individual trajectories, anomalous distribution of the Poincare recurrence time, and anomalous (non-Gaussian) transport for a typical system with Hamiltonian chaos results in a possibility to design a situation equivalent to the MD operation. A numerical example demonstrates a possibility to set without expenditure of work a thermodynamically non-equilibrium state between two contacted domains of the phase space lasting for an arbitrarily long time.

The width of the exponentially narrow stochastic layers.

Exponentially small splitting of the separatrix has been calculated for a high frequency large amplitude perturbation and the correspondent correction to the width of the stochastic layer is obtained. The result can be applied to the large amplitude perturbation.

Billiard in a barrel.

Orbits in the three-dimensional billiard of the form of a truncated ellipsoid ("barrel") are studied both analytically and numerically. A special form of mapping is proposed to get the expression for Kolmogorov-Sinai entropy, and the transition from strong chaos to weak chaos is obtained.

Chaotic jets with multifractal space-time random walk.

The problem of normal and anomalous diffusion is examined for the four-dimensional (4-D) map that arises from the problem of particle motion in a constant magnetic field and electrostatic wave packet. This 4-D map consists of two coupled 2-D maps: a standard map and a web map. The case of a weak chaos is considered.

Stochastic webs and their applications.

The conditions for the appearance of a stochastic web in degenerate dynamic systems and typical physical problems that lead to such a web are analyzed. Examples of webs are considered, as well as their symmetry, width, and structural changes. A description is given of a change in the diffusion dynamics along the web channels as a function of the number of the degrees of freedom and the phenomenon of stochastic percolation is discussed.