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George M. Zaslavsky

Publications and source records attributed to George M. Zaslavsky.

8 recordsLinked to original sources
PubMed2001

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. The results show the existence of self-similar solutions as well as possible logarithmic deviations. (c) 2001 American Institute of Physics.

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PubMed1997

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. The method has a clear physical interpretation presenting the solution in a form of decomposition of the process of fractal Brownian motion and Levy-type process. Fractional generalization of the Kolmogorov-Feller equation is introduced and its solutions are analyzed. (c) 1997 American Institute of Physics.

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PubMed1995

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. This result offers a new view of the Hamiltonian chaos and its role in the foundation of statistical mechanics. (c) 1995 American Institute of Physics.

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PubMed1994

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.

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PubMed1992

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.

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PubMed1991

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.

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PubMed1991

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. It is shown that due to the finite observation time, the particle diffusion possesses strong nonhomogeneous properties. Existence of long-living bundles of orbits with coherent propagation property is checked. These bundles are named "chaotic jets." The same name is used for a part of the trajectory if this part corresponds to long-living trapping or flight. The existence of chaotic jets depends on the topological properties of the phase space and influences the asymptotic law of transport. The particle transport can be considered as a random walk in the multifractal space-time that is produced by flights and trappings of a test particle in some area of its phase space. Levy random walk theory and its generalization for the multifractal space-time situation is considered and asymptotic laws for displacements are derived. Different intermediate asymptotics are discussed.

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