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 - INPR A1 - Feudel, Ulrike T1 - Komplexes Verhalten in multistabilen, schwach dissipativen Systemen N2 - Anhand eines paradigmatischen Modellbeispiels werden die Konsequenzen der Koexistenz vieler Attraktoren auf die globale Dynamik schwach dissipativer Systeme studiert. Es wird gezeigt, dass diese Systeme eine sehr reichhaltige Dynamik besitzen und extrem sensitiv gegenüber Störungen in den Anfangsbedingungen sind. Diese Systeme zeichnen sich durch eine extrem hohe Flexibilität ihres Verhaltens aus. T3 - NLD Preprints - 34 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14412 ER - TY - INPR A1 - Jansen, Wolfgang T1 - A note on the determination of the type of communication areas N2 - The paper presents a method that determines, by standard numerical means, the type of mutual relations of fold and flip bifurcations (configured as a so-called communication area) of a map. Equation systems are developed for the computation of points where a transition between areas of different types occurs. Furthermore, it is shown that saddle area<->spring area transitions can exist which have not yet been considered in the literature. Analytical conditions of that transition are derived. T3 - NLD Preprints - 33 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14339 ER - TY - INPR A1 - Braun, Robert A1 - Feudel, Fred T1 - Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation N2 - We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set. T3 - NLD Preprints - 29 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14099 ER - TY - INPR A1 - Maaß, Peter A1 - Rieder, Andreas T1 - Wavelet-accelerated Tikhonov-Phillips regularization with applications N2 - Contents: 1 Introduction 1.1 Tikhanov-Phillips Regularization of Ill-Posed Problems 1.2 A Compact Course to Wavelets 2 A Multilevel Iteration for Tikhonov-Phillips Regularization 2.1 Multilevel Splitting 2.2 The Multilevel Iteration 2.3 Multilevel Approach to Cone Beam Reconstuction 3 The use of approximating operators 3.1 Computing approximating families {Ah} T3 - NLD Preprints - 30 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14104 ER - TY - INPR A1 - Feudel, Fred A1 - Seehafer, Norbert A1 - Galanti, Barak A1 - Rüdiger, Sten T1 - Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing N2 - We have studied the bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcing of the Arnold-Beltrami-Childress (ABC) type. Bifurcation-analysis techniques have been applied to explore the qualitative behavior of solution branches. Due to the symmetry of the forcing, the equations are equivariant with respect to a group of transformations isomorphic to the octahedral group, and we have paid special attention to symmetry-breaking effects. As the Reynolds number is increased, the primary nonmagnetic steady state, the ABC flow, loses its stability to a periodic magnetic state, showing the appearance of a generic dynamo effect; the critical value of the Reynolds number for the instability of the ABC flow is decreased compared to the purely hydrodynamic case. The bifurcating magnetic branch in turn is subject to secondary, symmetry-breaking bifurcations. We have traced periodic and quasi- periodic branches until they end up in chaotic states. In particular detail we have analyzed the subgroup symmetries of the bifurcating periodic branches, which are closely related to the spatial structure of the magnetic field. T3 - NLD Preprints - 31 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14317 ER - TY - INPR A1 - Seehafer, Norbert A1 - Zienicke, Egbert A1 - Feudel, Fred T1 - Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch N2 - We have numerically studied the bifurcation properties of a sheet pinch with impenetrable stress-free boundaries. An incompressible, electrically conducting fluid with spatially and temporally uniform kinematic viscosity and magnetic diffusivity is confined between planes at x1=0 and 1. Periodic boundary conditions are assumed in the x2 and x3 directions and the magnetofluid is driven by an electric field in the x3 direction, prescribed on the boundary planes. There is a stationary basic state with the fluid at rest and a uniform current J=(0,0,J3). Surprisingly, this basic state proves to be stable and apparently to be the only time-asymptotic state, no matter how strong the applied electric field and irrespective of the other control parameters of the system, namely, the magnetic Prandtl number, the spatial periods L2 and L3 in the x2 and x3 directions, and the mean values B¯2 and B¯3 of the magnetic-field components in these directions. T3 - NLD Preprints - 32 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14328 ER - TY - INPR A1 - Voss, Henning A1 - Kurths, Jürgen A1 - Schwarz, Udo T1 - Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis N2 - Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record. T3 - NLD Preprints - 28 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14083 ER - TY - INPR A1 - Böckmann, Christine A1 - Biele, Jens A1 - Neuber, Roland A1 - Niebsch, Jenny T1 - Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data N2 - The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed. T3 - NLD Preprints - 38 KW - Multiwavelength LIDAR KW - aerosol size distribution KW - ill-posed problem KW - inversion KW - mollifier method KW - coated and absorbing aerosols Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14360 ER - TY - INPR A1 - Braun, Robert A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Bifurcations and chaos in an array of forced vortices N2 - We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective. T3 - NLD Preprints - 37 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14564 ER - TY - INPR A1 - Zienicke, Egbert A1 - Seehafer, Norbert A1 - Feudel, Fred T1 - Bifurcations in two-dimensional Rayleigh-Bénard convection N2 - Two-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at top and bottom and periodic boundary conditions in the horizontal direction is investigated by means of numerical simulation and bifurcation-analysis techniques. As the bouyancy forces increase, the primary stationary and symmetric convection rolls undergo successive Hopf bifurcations, bifurcations to traveling waves, and phase lockings. We pay attention to symmetry breaking and its connection with the generation of large-scale horizontal flows. Calculations of Lyapunov exponents indicate that at a Rayleigh number of 2.3×105 no temporal chaos is reached yet, but the system moves nonchaotically on a 4-torus in phase space. T3 - NLD Preprints - 42 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14534 ER - TY - INPR A1 - Scheel, Stefan A1 - Seehafer, Norbert T1 - Bifurcation to oscillations in three-dimensional Rayleigh-Bénard convection N2 - Three-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at the top and bottom and periodic boundary conditions in the horizontal directions is investigated by means of numerical simulation and bifurcation-analysis techniques. The aspect ratio is fixed to a value of 2√2 and the Prandtl number to a value of 6.8. Two-dimensional convection rolls are found to be stable up to a Rayleigh number of 17 950, where a Hopf bifurcation leads to traveling waves. These are stable up to a Rayleigh number of 30 000, where a secondary Hopf bifurcation generates modulated traveling waves. We pay particular attention to the symmetries of the solutions and symmetry breaking by the bifurcations. T3 - NLD Preprints - 39 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14370 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 - Seehafer, Norbert A1 - Schumacher, Jörg T1 - Squire‘s theorem for the magnetohydrodynamic sheet pinch N2 - The stability of the quiescent ground state of an incompressible viscous fluid sheet bounded by two parallel planes, with an electrical conductivity varying across the sheet, and driven by an external electric field tangential to the boundaries is considered. It is demonstrated that irrespective of the conductivity profile, as magnetic and kinetic Reynolds numbers (based on the Alfvén velocity) are raised from small values, two-dimensional perturbations become unstable first. T3 - NLD Preprints - 40 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14628 ER - TY - INPR A1 - Engbert, Ralf A1 - Scheffczyk, Christian A1 - Krampe, Ralf-Thomas A1 - Rosenblum, Mikhael A1 - Kurths, Jürgen A1 - Kliegl, Reinhold T1 - Tempo-induced transitions in polyrhythmic hand movements N2 - We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components. T3 - NLD Preprints - 41 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14380 ER - 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 - 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 - TY - INPR A1 - Braun, Robert A1 - Feudel, Fred A1 - Guzdar, Parvez T1 - The route to chaos for a two-dimensional externally driven flow N2 - We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario. T3 - NLD Preprints - 46 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14717 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 - Böckmann, Christine A1 - Niebsch, Jenny T1 - Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator N2 - The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored. T3 - NLD Preprints - 47 KW - multiwavelength lidar KW - aerosol size distribution KW - inverse ill-posed problem KW - multilayered coated and absorbing aerosol KW - new recursive algorithm Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14725 ER -