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  • 1
    Electronic Resource
    Electronic Resource
    Changes in the adiabatic invariant and streamline chaos in confined incompressible Stokes flow (1996)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 6 (1996), S. 67-77 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The steady incompressible flow in a unit sphere introduced by Bajer and Moffatt [J. Fluid Mech. 212, 337 (1990)] is discussed. The velocity field of this flow differs by a small perturbation from an integrable field whose streamlines are almost all closed. The unperturbed flow has two stationary saddle points (poles of the sphere) and a two-dimensional separatrix passing through them. The entire interior of the unit sphere becomes the domain of streamline chaos for an arbitrarily small perturbation. This phenomenon is explained by the nonconservation of a certain adiabatic invariant that undergoes a jump when a streamline crosses a small neighborhood of the separatrix of the unperturbed flow. An asymptotic formula is obtained for the jump in the adiabatic invariant. The accumulation of such jumps in the course of repeated crossings of the separatrix results in the complete breaking of adiabatic invariance and streamline chaos. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166151
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  • 2
    Electronic Resource
    Electronic Resource
    Estimates of stability time for nearly integrable systems with a quasiconvex Hamiltonian (1992)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 2 (1992), S. 495-499 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A Hamiltonian system differing from an integrable system by a small perturbation (approximately-equal-to)ε is analyzed. According to the Nekhoroshev theorem, the changes in the perturbed motion of the "action'' variables of the unperturbed system are small over a time interval which increases exponentially in length as ε decreases linearly. If the unperturbed Hamiltonian is a quasiconvex function of these "actions,'' the changes in them remain small ((approximately-equal-to)ε1/2n) over a time interval on the order of exp(const/ε1/2n), where n is the number of degrees of freedom of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.165891
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  • 3
    Electronic Resource
    Electronic Resource
    Lagrangian turbulence in nonstationary 2-D flows (1991)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 1 (1991), S. 206-211 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Lagrangian particle transport in nonstationary 2-D flows is studied both analytically and numerically. Analytic expressions for the diffusion coefficients are obtained for the adiabatic regime. Numerical estimates of the diffusion coefficients are found to agree with the theoretical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.165830
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  • 4
    Electronic Resource
    Electronic Resource
    Stable periodic motions in the problem on passage through a separatrix (1997)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 7 (1997), S. 2-11 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A Hamiltonian system with one degree of freedom depending on a slowly periodically varying in time parameter is considered. For every fixed value of the parameter there are separatrices on the phase portrait of the system. When parameter is changing in time, these separatrices are pulsing slowly periodically, and phase points of the system cross them repeatedly. In numeric experiments region swept by pulsing separatrices looks like a region of chaotic motion. However, it is shown in the present paper that if the system possesses some additional symmetry (like a pendulum in a slowly varying gravitational field), then typically in the region in question there are many periodic solutions surrounded by stability islands; total measure of these islands does not vanish and does not tend to 0 as rate of changing of the parameter tends to 0.© 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166236
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  • 5
    Electronic Resource
    Electronic Resource
    Adiabatic chaos in a two-dimensional mapping (1996)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 6 (1996), S. 514-518 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A close to identity symplectic mapping describing the dynamics of a charged particle in the field of an infinitely wide packet of electrostatic waves is studied. A region of chaotic dynamics, whose width is large for an arbitrarily small deviation of the mapping from the identity, exists on the phase cylinder. This is explained by the quasirandom change occurring in an adiabatic invariant of the problem when the phase trajectory crosses a resonance curve. An asymptotic formula is derived for the jump in the adiabatic invariant. The width of the chaos region and the density of the set of invariant curves near the boundary of the chaos region are estimated. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166198
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  • 6
    Electronic Resource
    Electronic Resource
    Regular and chaotic transport of impurities in steady flows (1994)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 4 (1994), S. 673-680 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: This paper considers the properties of the transport of impurity particles in steady fluid flows and describes the principal modes of particle motion. An impurity consisting of particles with a lower density than that of the medium is localized at stationary points of the flow, whereas a heavy impurity can perform a spatially unbounded motion. The conditions for the transition from the bounded motion of a heavy impurity to the long-range transport mode, which occurs as a result of a loss of the stability of the heteroclinic trajectory, are obtained for a model two-dimensional flow having an eddy-cell structure. A mode is found in which a particle, after being transported over a long distance, is trapped forever within the confines of one cell. The transition from regular to chaotic particle transport is analyzed. The question of the effect of a small noise (for example, molecular diffusion) on the character of the motion of a heavy impurity is investigated. It is shown that this effect is important at high viscosity and leads to a transition from bounded motion of the impurity particle to diffusion-type chaotic motion. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166044
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  • 7
    Electronic Resource
    Electronic Resource
    Probability phenomena due to separatrix crossing (1991)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 1 (1991), S. 42-48 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effect of a small or slow perturbation on a Hamiltonian system with one degree of freedom is considered. It is assumed that the phase portrait ("phase plane'') of the unperturbed system is divided by separatrices into several regions and that under the action of the perturbations phase points can cross these separatrices. The probabilistic phenomena are described that arise due to these separatrix crossings, including the scattering of trajectories, random jumps in the values of adiabatic invariants, and adiabatic chaos. These phenomena occur both in idealized problems in classical mechanics and in real physical systems in planetary science and plasma physics contexts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.165816
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  • 8
    Electronic Resource
    Electronic Resource
    Propagation of beams through smoothly irregular waveguides and theory of perturbations in hamiltonian systems (1982)
    Springer
    Radiophysics and quantum electronics 25 (1982), S. 157-164 
    Details
    ISSN: 1573-9120
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01034266
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