TY - INPR A1 - Witt, Annette A1 - Neiman, Alexander A1 - Kurths, Jürgen T1 - Characterizing the dynamics of stochastic bistable systems by measures of complexity N2 - The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum. T3 - NLD Preprints - 36 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14556 ER - TY - INPR A1 - Thiessenhusen, Kai-Uwe A1 - Esposito, Larry W. A1 - Kurths, Jürgen A1 - Spahn, Frank T1 - Detection of hidden resonances in Saturn's B-ring N2 - The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances. T3 - NLD Preprints - 13 KW - Planetary Rings Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13618 ER - TY - INPR A1 - Rüdiger, Sten A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Dynamo bifurcations in an array of driven convection-like rolls N2 - The bifurcations in a three-dimensional incompressible, electrically conducting fluid with an external forcing of the Roberts type have been studied numerically. The corresponding flow can serve as a model for the convection in the outer core of the Earth and is realized in an ongoing laboratory experiment aimed at demonstrating a dynamo effect. The symmetry group of the problem has been determined and special attention has been paid to symmetry breaking by the bifurcations. The nonmagnetic, steady Roberts flow loses stability to a steady magnetic state, which in turn is subject to secondary bifurcations. The secondary solution branches have been traced until they end up in chaotic states. T3 - NLD Preprints - 43 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14678 ER - TY - INPR A1 - Feudel, Fred A1 - Seehafer, Norbert A1 - Schmidtmann, Olaf T1 - Fluid helicity and dynamo bifurcations N2 - The bifurcation behaviour of the 3D magnetohydrodynamic equations has been studied for external forcings of varying degree of helicity. With increasing strength of the forcing a primary non-magnetic steady state loses stability to a magnetic periodic state if the helicity exceeds a threshold value and to different non-magnetic states otherwise. T3 - NLD Preprints - 18 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13882 ER - TY - INPR A1 - Lukaschewitsch, Michael T1 - Geoelectrical conductivity problems on unbounded domains N2 - This paper deals with the electrical conductivity problem in geophysics. It is formulated as an elliptic boundary value problem of second order for a large class of bounded and unbounded domains. A special boundary condition, the so called "Complete Electrode Model", is used. Poincaré inequalities are formulated and proved in the context of weighted Sobolev spaces, leading to existence and uniqueness statements for the boundary value problem. In addition, a parameter-to-solution operator arising from the inverse conductivity problem in medicine (EIT) and geophysics is investigated mathematically and is shown to be smooth and analytic. T3 - NLD Preprints - 45 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14704 ER - TY - INPR A1 - Demircan, Ayhan A1 - Scheel, Stefan A1 - Seehafer, Norbert T1 - Heteroclinic behavior in rotating Rayleigh-Bénard convection N2 - We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven fluid layer with stress-free top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewed-varicose instability leads from stationary rolls to a stationary mixed-mode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewed-varicose or mixed-mode type and in some parameter regions skewed-varicose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case, the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle. T3 - NLD Preprints - 55 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14914 ER - TY - INPR A1 - Schmidtmann, Olaf T1 - Modelling of the interaction of lower and higher modes in two-dimensional MHD-equations N2 - The present paper is related to the problem of approximating the exact solution to the magnetohydrodynamic equations (MHD). The behaviour of a viscous, incompressible and resistive fluid is exemined for a long period of time. Contents: 1 The magnetohydrodynamic equations 2 Notations and precise functional setting of the problem 3 Existence, uniqueness and regularity results 4 Statement and Proof of the main theorem 5 The approximate inertial manifold 6 Summary T3 - NLD Preprints - 17 KW - MHD-equations KW - approximate inertial manifolds Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13790 ER - TY - INPR A1 - Seehafer, Norbert T1 - Nature of the α effect in magnetohydrodynamics N2 - It is shown that the ff effect of mean-field magnetohydrodynamics, which consists in the generation of a mean electromotive force along the mean magnetic field by turbulently fluctuating parts of velocity and magnetic field, is equivalent to the simultaneous generation of both turbulent and mean-field magnetic helicities, the generation rates being equal in magnitude and opposite in sign. In the particular case of statistically stationary and homogeneous fluctuations this implies that the ff effect can increase the energy in the mean magnetic field only under the condition that also magnetic helicity is accumulated there. T3 - NLD Preprints - 25 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13919 ER - TY - INPR A1 - Schmidtmann, Olaf A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations N2 - The usage of nonlinear Galerkin methods for the numerical solution of partial differential equations is demonstrated by treating an example. We desribe the implementation of a nonlinear Galerkin method based on an approximate inertial manifold for the 3D magnetohydrodynamic equations and compare its efficiency with the linear Galerkin approximation. Special bifurcation points, time-averaged values of energy and enstrophy as well as Kaplan-Yorke dimensions are calculated for both schemes in order to estimate the number of modes necessary to correctly describe the behavior of the exact solutions. T3 - NLD Preprints - 35 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14431 ER - TY - INPR A1 - Volosevich, Alexandra V. A1 - Meister, Claudia-Veronika T1 - Nonlinear interaction of Farley-Buneman waves N2 - The nonlinear interaction of waves excited by the modified two-stream instability (Farley-Buneman instability) is considered. It is found that, during the linear stage of wave growth, the enhanced pressure of the high-frequency part of the waves locally generates a ponderomotive force. This force acts on the plasma particles and redistributes them. Thus an additional electrostatic polarization field occurs, which influences the low-frequency part of the waves. Then, the low-frequency waves also cause a redistribution of the high-frequency waves. In the paper, a self-consistent system of equations is obtained, which describes the nonlinear interaction of the waves. It is shown that the considered mechanism of wave interaction causes a nonlinear stabilization of the high-frequency waves’ growth and a formation of local density structures of the charged particles. The density modifications of the charged particles during the non-linear stage of wave growth and the possible interval of aspect angles of the high-frequency waves are estimated. T3 - NLD Preprints - 52 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14851 ER -