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  • 1
    Digitale Medien
    Digitale Medien
    Blowout bifurcations and the onset of magnetic dynamo action : The 42nd annual meeting of the division of plasma physics of the American Physical Society and the 10th international congress on plasma physics (2001)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 8 (2001), S. 1944-1952 
    Details
    ISSN: 1089-7674
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: This paper numerically investigates the magnetohydrodynamic equations in three dimensions with periodic boundary conditions in a parameter range where a forced fluid flow is chaotic. It is found that the transition to dynamo action, whereby the magnetic field is sustained by interaction with the forced flow, is a blowout bifurcation. The blowout bifurcation is typified by bursting behavior, or "on-off intermittency." In particular, near the transition there are short, intermittently occurring bursts of strong magnetic field activity where the total magnetic energy is comparable to the total flow kinetic energy. Between these bursts the magnetic energy is very small. As one approaches the transition from the dynamo-active side, the time between bursts becomes longer and longer, approaching infinity at the transition. Numerical verification is given for the presence of signature scaling laws in numerical computations utilizing a pseudospectral model with triply periodic boundary conditions. This work implies specific testable predictions for experimental dynamos. © 2001 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.1342228
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  • 2
    Digitale Medien
    Digitale Medien
    Targeting in Hamiltonian systems that have mixed regular/chaotic phase spaces (1997)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 7 (1997), S. 512-519 
    Details
    ISSN: 1089-7682
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: The problem of directing a trajectory of a chaotic dynamical system to a target has been previously considered, and it has been shown that chaos allows targeting using only small controls. In this paper we consider targeting in a Hamiltonian system, whose phase space contains a mixture of regular quasi-periodic and chaotic regions. A multistep forward–backward method targeting strategic intermediate points is found to be efficient and robust. It takes full advantage of the phase space structure and is believed to yield optimal transport times. It is robust under the influence of small noise and small modeling errors and recovers from temporary loss of control. Two illustrative examples, the standard map and the restricted circular three body problem, are presented. (The latter corresponds to motion of a space probe in the presence of the earth and the moon.) Comparisons are made of our method to other targeting strategies. © 1997 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.166277
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  • 3
    Digitale Medien
    Digitale Medien
    Chaotic flows and kinematic magnetic dynamos: A tutorial review : The 39th annual meeting of division of plasma physics of APS (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 1636-1646 
    Details
    ISSN: 1089-7674
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: This paper reviews results on fast kinematic dynamo theory, emphasizing the recent realization that Lagrangian chaos of the underlying flow is the key element for understanding of the problem. Simple models for singular behavior of the magnetic field in the large magnetic Reynolds number limit are described and used to illustrate the tendency for fractal magnetic field distributions with extreme cancellation properties. The relation of ergodic properties of the chaotic flow to properties of the dynamo (e.g., growth rate, fractal dimension) are also discussed. © 1998 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.872832
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  • 4
    Digitale Medien
    Digitale Medien
    Scaling properties of magnetic dynamo wavenumber power spectra generated by Lagrangian chaotic flows (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 151-155 
    Details
    ISSN: 1089-7674
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: Wavenumber power spectra of the magnetic field in kinematic dynamos of Lagrangian chaotic flows are investigated. Numerical integration of the kinematic dynamo equations with magnetic Reynolds number Rm up to 105 shows that the wavenumber power spectrum of the magnetic field generated by smooth, Lagrangian chaotic flows obeys a power-law. This property is theoretically predicted by a wavepacket model, whereby magnetic field wavepackets are evolved according to ordinary differential equations. © 1998 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.872713
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  • 5
    Digitale Medien
    Digitale Medien
    Conditions for the abrupt bifurcation to chaotic scattering (1993)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 3 (1993), S. 495-503 
    Details
    ISSN: 1089-7682
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: One of the generic ways in which chaotic scattering can come about as a system parameter is varied is the so-called "abrupt bifurcation'' in which the scattering is nonchaotic on one side of the bifurcation and is chaotic and hyperbolic on the other side. Previous work demonstrating the abrupt bifurcation [S. Bleher et al., Phys. Rev. Lett. 63, 919 (1989); Physica D 46, 87 (1990)] was primarily for the case where the scattering potential had maxima ("hilltops'') which had locally circular isopotential contours. Here we extend these considerations to the more general case of locally elliptically shaped isopotential contours at the hilltops. It turns out that the conditions for the abrupt bifurcation change drastically as soon as even a small amount of noncircularity is included (i.e., the circular case is singular). The illustrative case of scattering from three isolated potential hills is dealt with in detail. One interesting result is a simple geometrical sufficient condition for an abrupt bifurcation in the case of large enough ellipticity of the hill with lowest potential at its hilltop.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.165955
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  • 6
    Digitale Medien
    Digitale Medien
    Quasi-two-dimensional fast kinematic dynamo instabilities of chaotic fluid flows (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 2564-2578 
    Details
    ISSN: 1089-7674
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: This paper tests previous heuristically derived general theoretical results for the fast kinematic dynamo instability of a smooth, chaotic flow by comparison of the theoretical results with numerical computations on a particular class of model flows. The class of chaotic flows studied allows very efficient high resolution computation. It is shown that an initial spatially uniform magnetic field undergoes two phases of growth, one before and one after the diffusion scale has been reached. Fast dynamo action is obtained for large magnetic Reynolds number Rm. The initial exponential growth rate of moments of the magnetic field, the long time dynamo growth rate, and multifractal dimension spectra of the magnetic fields are calculated from theory using the numerically determined finite time Lyapunov exponent probability distribution of the flow and the cancellation exponent. All these results are numerically tested by generating a quasi-two-dimensional dynamo at magnetic Reynolds number Rm of order up to 105. © 1996 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.871964
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  • 7
    Digitale Medien
    Digitale Medien
    Chaotic scattering: An introduction (1993)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 3 (1993), S. 417-426 
    Details
    ISSN: 1089-7682
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: In recent years chaotic behavior in scattering problems has been found to be important in a host of physical situations. Concurrently, a fundamental understanding of the dynamics in these situations has been developed, and such issues as symbolic dynamics, fractal dimension, entropy, and bifurcations have been studied. The quantum manifestations of classical chaotic scattering is also an extremely active field, with new analytical techniques being developed and with experiments being carried out. This issue of Chaos provides an up-to-date survey of the range of work in this important field of study.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.165949
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  • 8
    Digitale Medien
    Digitale Medien
    Stalactite basin structure of dynamical systems with transient chaos in an invariant manifold (2000)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 10 (2000), S. 291-298 
    Details
    ISSN: 1089-7682
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: Dynamical systems with invariant manifolds occur in a variety of situations (e.g., identical coupled oscillators, and systems with a symmetry). We consider the case where there is both a nonchaotic attractor (e.g., a periodic orbit) and a nonattracting chaotic set (or chaotic repeller) in the invariant manifold. We consider the character of the basins for the attracting nonchaotic set in the invariant manifold and another attractor not in the invariant manifold. It is found that the boundary separating these basins has an interesting structure: The basin of the attractor not in the invariant manifold is characterized by thin cusp shaped regions ("stalactites") extending down to touch the nonattracting chaotic set in the invariant manifold. We also develop theoretical scalings applicable to these systems, and compare with numerical experiments. © 2000 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.166495
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  • 9
    Digitale Medien
    Digitale Medien
    Finite Larmor radius diocotron instability (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 941-948 
    Details
    ISSN: 1089-7666
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: The diocotron instability of an electron layer in which the electron Larmor radius is of the order of the layer thickness is studied. Remarkably, exact analytical solutions are obtainable in a nontrivial special case. These results allow an examination of the effects of finite Larmor radius for arbitrary ratios of Larmor radius to wavelength and of Larmor radius to layer thickness. In addition, an energy principle which yields a necessary and sufficient condition for instability for general distribution functions is derived.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.865065
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  • 10
    Digitale Medien
    Digitale Medien
    The role of chaotic orbits in the determination of power spectra of passive scalars (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 3094-3104 
    Details
    ISSN: 1089-7666
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: This paper relates properties of the power spectrum of a passive scalar convected by a chaotic fluid flow to the distribution of finite time Lyapunov exponents. The properties considered include the early time evolution of the power spectrum, the late time exponential decay of the scalar variance, and the wave number dependence of the power spectrum in the presence of a source of scalar variance. Theoretical predictions are tested by comparing full numerical solutions of the relevant partial differential equation to solutions of a model system which includes diffusion and involves integrations along the fluid orbits only. The model system is shown to give results in close agreement with the numerical solutions of the full problem. This suggests the possible general utility of the model equations for a broad range of problems involving passive scalar convection. © 1996 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.869083
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