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- Vasily E Tarasov, George M 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,… (More)

- B A Carreras, V E Lynch, L Garcia, M Edelman, G M Zaslavsky
- Chaos
- 2003

In dynamical systems with a zero Lyapunov exponent, weak mixing can be governed by a specific topological structure of some surfaces that are invariant with respect to particle dynamics. In particular, when the genus of the invariant surfaces is more than one, they may have weak mixing and the corresponding fractional kinetics. This possibility is… (More)

- B A Carreras, V E Lynch, D E Newman, G M Zaslavsky
- Physical review. E, Statistical physics, plasmas…
- 1999

To explore the character of underlying transport in a sandpile, we have followed the motion of tracer particles. Moments of the distribution function of the particle positions, </x(t)-x(0)/(n)>=D(0)t(nnu(n)), are determined as a function of the elapsed time. The numerical results show that the transport mechanism for distances less than the sandpile length… (More)

- Michael G Brown, John A Colosi, Steven Tomsovic, Anatoly L Virovlyansky, Michael A Wolfson, George M 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 include… (More)

- Francisco J Beron-Vera, Michael G Brown, +4 authors George M Zaslavsky
- The Journal of the Acoustical Society of America
- 2003

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… (More)

- I P Smirnov, A L Virovlyansky, G M Zaslavsky
- Physical review. E, Statistical, nonlinear, and…
- 2001

Chaotic ray dynamics in deep sea propagation models is considered using the approaches developed in the theory of dynamical chaos. It has been demonstrated that the mechanism of emergence of ray chaos due to overlapping of nonlinear ray-medium resonances should play an important role in long range sound propagation. Analytical estimations, supported by… (More)

The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and field theory. For the fractional linear oscillator the physical meaning of the derivative of order ao2 is dissipation.… (More)

We derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg–Landau equation for fractal media are considered and different forms of… (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 α, when 0 < α < 2. The evolution of soliton-like and breather-like structures are obtained numerically and compared for both… (More)