TY - BOOK A1 - Blechman, Ilja I. A1 - Landa, Polina S. A1 - Rosenblum, Michael T1 - Synchronization and chaotization in interacting dynamical systems T3 - Preprint NLD Y1 - 1995 VL - 24 PB - Univ. CY - Potsdam ER - TY - INPR A1 - Dicken, Volker A1 - Maaß, Peter T1 - Wavelet-Galerkin methods for ill-posed problems N2 - Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelette decompositions enable the realization of especially fast algorithms for certain operators. T3 - NLD Preprints - 22 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13890 ER - TY - INPR A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Bifurcations and pattern formation in a 2D Navier-Stokes fluid N2 - We report on bifurcation studies for the incompressible Navier-Stokes equations in two space dimensions with periodic boundary conditions and an external forcing of the Kolmogorov type. Fourier representations of velocity and pressure have been used to approximate the original partial differential equations by a finite-dimensional system of ordinary differential equations, which then has been studied by means of bifurcation-analysis techniques. A special route into chaos observed for increasing Reynolds number or strength of the imposed forcing is described. It includes several steady states, traveling waves, modulated traveling waves, periodic and torus solutions, as well as a period-doubling cascade for a torus solution. Lyapunov exponents and Kaplan-Yorke dimensions have been calculated to characterize the chaotic branch. While studying the dynamics of the system in Fourier space, we also have transformed solutions to real space and examined the relation between the different bifurcations in Fourier space and toplogical changes of the streamline portrait. In particular, the time-dependent solutions, such as, e.g., traveling waves, torus, and chaotic solutions, have been characterized by the associated fluid-particle motion (Lagrangian dynamics). T3 - NLD Preprints - 23 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13907 ER - TY - INPR A1 - Feudel, Fred A1 - Seehafer, Norbert A1 - Schmidtmann, Olaf T1 - Bifurcation phenomena of the magnetofluid equations N2 - We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier reprsentations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (incereasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non-magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by furhter, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory. T3 - NLD Preprints - 9 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13585 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 - BOOK A1 - Feudel, Ulrike A1 - Kurths, Jürgen A1 - Neiman, Alexander T1 - The cumulant approach for investigating the noise influence on mode-locking bifurcations T3 - Preprint NLD Y1 - 1995 VL - 16 PB - Univ. CY - Potsdam ER - TY - INPR A1 - Jansen, Wolfgang T1 - CANDYS/QA : algorithms, programs, and user‘s manual N2 - Contents: I. Algorithms 1. Theoretical Backround 2. Numerical Procedures 3. Graph Representation of the Solutions 4. Applications and Example II. Users' Manual 5. About the Program 6. The Course of a Qualitative Analysis 7. The Model Module 8. Input description 9. Output Description 10. Example 11. Graphics T3 - NLD Preprints - 27 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13920 ER - TY - BOOK A1 - Jansen, Wolfgang T1 - CANDYS/QA : algorithms, programs and user's manual T3 - Preprint NLD Y1 - 1995 VL - 27 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Witt, Annette T1 - Non-linear data analysis in solar radio astronomy N2 - We have discussed some tools from nonlinear dynamics which may help to analyze transient phenomena, such as solar bursts. The structure function known from turbulence theory is an appropriate method to find out some scaling behavior of fluctuations in time. More generally, the wavelet analysis, which is some generalization of the power spectrum, exhibits information on the location as well as the size of hidden characteristic features. Applying both techniques to microwave bursts, we have found some scaling properties that refer to the existence of hierarchic time structures. This is in good accordance with the electric circuit model for describing the flare-particle energization process. Y1 - 1995 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/lnp.ps.gz ER - TY - BOOK A1 - Liperovskij, Viktor A. A1 - Meister, Claudia-Veronika T1 - Sporadic e-layers as current generator : two-dimensional model T3 - Preprint NLD Y1 - 1995 VL - 20 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Meister, Claudia-Veronika T1 - Stochastic forces in space plasmas with ion-acoustic and lower-hybrid-drift turbulence T3 - Preprint NLD Y1 - 1995 VL - 10 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Meister, Claudia-Veronika A1 - Kubyshkin, I. V. T1 - Recalculation of the diffusion tensor for plasmas with ion-acoustic turbulence T3 - Preprint NLD Y1 - 1995 VL - 26 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Meister, Claudia-Veronika A1 - Liperovsky, Viktor A. A1 - Schlegel, K. A1 - Haldoupis, Ch. T1 - Currents and turbulence in and near mid-latitude sporadic e-layers caused by strong acoustic impulses JF - Preprint NLD Y1 - 1995 VL - 11 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Morin, Paul T1 - Visualization in the geosciences : course notes T3 - Preprint NLD Y1 - 1995 VL - 19 PB - Univ. CY - Potsdam ER - TY - INPR A1 - Pikovskij, Arkadij A1 - Zaks, Michael A. A1 - Feudel, Ulrike A1 - Kurths, Jürgen T1 - Singular continuous spectra in dissipative dynamics N2 - We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique. T3 - NLD Preprints - 15 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13787 ER - TY - BOOK A1 - Rosenblum, Michael A1 - Kurths, Jürgen T1 - A model of neural control of heart rate T3 - Preprint NLD Y1 - 1995 VL - 12 PB - Univ. CY - Potsdam 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 - BOOK A1 - Spahn, Frank A1 - Hertzsch, Jan-Martin A1 - Brilliantov, Nikolai V. T1 - The role of particle collisions for the dynamics in planetary rings T3 - Preprint NLD Y1 - 1995 VL - 14 PB - Univ. CY - Potsdam 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 -