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- Alexander I. Saichev, George Zaslavsky
- Chaos
- 1997

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 whichâ€¦ (More)

A system of three point vortices in an unbounded plane has a special family of self-similarly contracting or expanding solutions: during the motion, vortex triangle remains similar to the original one, while its area decreases (grows) at a constant rate. A contracting con guration brings three vortices to a single point in a nite time; this phenomenon isâ€¦ (More)

- George Zaslavsky
- Chaos
- 1994

We present a general scheme to describe particle kinetics in the case of incomplete Hamiltonian chaos when a set of islands of stability forms a complicated fractal space-time dynamics and when there is orbit stickiness to the islands' boundary. This kinetics is alternative to the "normal" Fokker-Planck-Kolmogorov equation. A new kinetic equation describesâ€¦ (More)

- Vasily E. Tarasov, George Zaslavsky
- Chaos
- 2006

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,â€¦ (More)

Discrete nonlinear SchrÃ¶dinger equation (DNLS) describes a chain of oscillators with nearest neighbor interactions and a specific nonlinear term. We consider its modification with long-range interaction through a potential proportional to 1/l1+Î± with fractional Î± < 2 and l as a distance between oscillators. This model is called Î±DNLS. It exhibitsâ€¦ (More)

The one-dimensional chain of coupled oscillators with long-range power-law interaction is considered. The equation of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order Î±, when 0 < Î± < 2. The evolution of soliton-like and breather-like structures are obtained numerically and compared for bothâ€¦ (More)

- Michael G. Brown, John A. Colosi, Steven Tomsovic, A. L. Virovlyansky, Michael A. Wolfson, George Zaslavsky
- The Journal of the Acoustical Society of America
- 2003

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. Topics discussed includeâ€¦ (More)

- Valentin S. Afraimovich, George Zaslavsky
- Chaos
- 2003

New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with "flights," trappings, weak mixing, etc. The important part of the new notions is the first appearance of epsilon-separation of initiallyâ€¦ (More)

- George Zaslavsky
- Chaos
- 1995

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 MDâ€¦ (More)

- S. V. Prants, Mark Edelman, George Zaslavsky
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2002

We study dynamics of the atom-photon interaction in cavity quantum electrodynamics, considering a cold two-level atom in a single-mode high-finesse standing-wave cavity as a nonlinear Hamiltonian system with three coupled degrees of freedom: translational, internal atomic, and the field. The system proves to have different types of motion including LÃ©vyâ€¦ (More)