Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media

Abdullaev, S. S.; Zaslavskiĭ, G. M.

doi:10.3367/ufnr.0161.199108a.0001

Cited by 44 publications

(28 citation statements)

References 11 publications

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“…The explanation of this behaviour makes use of the actionangle description of the motion of particles in the background flow (e.g. Abdullaev and Zaslavsky, 1991). Let…”

Section: Particle Trajectory Stabilitymentioning

confidence: 99%

Passive tracer patchiness and particle trajectory stability in incompressible two-dimensional flows

Beron-Vera

Olascoaga

Brown

2004

Nonlin. Processes Geophys.

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Abstract. Particle motion is considered in incompressible two-dimensional flows consisting of a steady background gyre on which an unsteady wave-like perturbation is superimposed. A dynamical systems point of view that exploits the action-angle formalism is adopted. It is argued and demonstrated numerically that for a large class of problems one expects to observe a mixed phase space, i.e. the occurrence of "regular islands" in an otherwise "chaotic sea." This leads to patchiness in the evolution of passive tracer distributions. Also, it is argued and demonstrated numerically that particle trajectory stability is largely controlled by the background flow: trajectory instability, quantified by various measures of the "degree of chaos," increases on average with increasing |dω/dI |, where ω(I ) is the angular frequency of the trajectory in the background flow and I is the action.

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“…The explanation of this behaviour makes use of the actionangle description of the motion of particles in the background flow (e.g. Abdullaev and Zaslavsky, 1991). Let…”

Section: Particle Trajectory Stabilitymentioning

confidence: 99%

Passive tracer patchiness and particle trajectory stability in incompressible two-dimensional flows

Beron-Vera

Olascoaga

Brown

2004

Nonlin. Processes Geophys.

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“…In particular, classical equations of motion can be integrable or non-integrable, depending on the geometrical shape of the billiard boundary. Earlier, billiards were the topic of extensive study in the context of nonlinear dynamics and quantum chaos theory [1][2][3][4][5]. It was found that, depending on the shape of the billiard walls, particle dynamics can be chaotic, regular or mixed.…”

Section: Introductionmentioning

confidence: 99%

Particle dynamics in corrugated rectangular billiard

Akhmadjanov¹,

Rakhimov²,

Otajanov³

2015

Nanosist.: fiz. him. mat.

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“…In describing ray trajectories we apply the Hamiltonian formalism taken in terms of the action-angle variables [5,6]. It is shown that each mode is formed by contributions from rays whose action variables up to a multiplicative constant are equal to the mode number.…”

Section: Introductionmentioning

confidence: 99%

Variations of mode amplitudes in a range-dependent waveguide

2004

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An analogue of the geometrical optics for description of the modal structure of a wave field in a range-dependent waveguide is considered. In the scope of this approach the mode amplitude is expressed through solutions of the ray equations. This analytical description accounts for mode coupling and remains valid in a nonadiabatic environment. It has been used to investigate the applicability condition of the adiabatic approximation. An applicability criterion is formulated as a restriction on variations of the action variable of the ray.

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Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media

Cited by 44 publications

References 11 publications

Passive tracer patchiness and particle trajectory stability in incompressible two-dimensional flows

Passive tracer patchiness and particle trajectory stability in incompressible two-dimensional flows

Particle dynamics in corrugated rectangular billiard

Variations of mode amplitudes in a range-dependent waveguide

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