TY - JOUR A1 - Wessel, Niels A1 - Schwarz, Udo A1 - Saparin, Peter A1 - Kurths, Jürgen T1 - Symbolic dynamics for medical data analysis N2 - Observational data of natural systems, as measured in medical measurements are typically quite different from those obtained in laboratories. Due to the peculiarities of these data, wellknown characteristics, such as power spectra or fractal dimension, often do not provide a suitable description. To study such data, we present here some measures of complexity, which are basing on symbolic dynamics. Firstly, a motivation for using symbolic dynamics and measures of complexity in data analysis based on the logistic map is given and next, two applications to medical data are shown. We demonstrate that symbolic dynamics is a useful tool for the risk assessment of patients after myocardial infarction as well as for the evaluation of th e architecture of human cancellous bone. Y1 - 2002 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/EUROATTRACTOR2000.ps SN - 3-936142-09-2 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 - 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 - 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 - Maaß, Peter A1 - Pereverzev, Sergei V. A1 - Ramlau, Ronny A1 - Solodky, Sergei G. T1 - An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection N2 - The aim of this paper is to describe an efficient strategy for descritizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips-regularization χ^δ α = (a * a + α I)^-1 A * y ^δ with a finite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods. T3 - NLD Preprints - 48 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14739 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 - THES A1 - Yin, Fan T1 - Mathematic approaches for the calibration of the CHAMP satellite magnetic field measurements T1 - Mathematische Ansätze für die Kalibrierung des Satelliten CHAMP Magnetfeldmessungen N2 - CHAMP (CHAllenging Minisatellite Payload) is a German small satellite mission to study the earth's gravity field, magnetic field and upper atmosphere. Thanks to the good condition of the satellite so far, the planned 5 years mission is extended to year 2009. The satellite provides continuously a large quantity of measurement data for the purpose of Earth study. The measurements of the magnetic field are undertaken by two Fluxgate Magnetometers (vector magnetometer) and one Overhauser Magnetometer (scalar magnetometer) flown on CHAMP. In order to ensure the quality of the data during the whole mission, the calibration of the magnetometers has to be performed routinely in orbit. The scalar magnetometer serves as the magnetic reference and its readings are compared with the readings of the vector magnetometer. The readings of the vector magnetometer are corrected by the parameters that are derived from this comparison, which is called the scalar calibration. In the routine processing, these calibration parameters are updated every 15 days by means of scalar calibration. There are also magnetic effects coming from the satellite which disturb the measurements. Most of them have been characterized during tests before launch. Among them are the remanent magnetization of the spacecraft and fields generated by currents. They are all considered to be constant over the mission life. The 8 years of operation experience allow us to investigate the long-term behaviors of the magnetometers and the satellite systems. According to the investigation, it was found that for example the scale factors of the FGM show obvious long-term changes which can be described by logarithmic functions. The other parameters (offsets and angles between the three components) can be considered constant. If these continuous parameters are applied for the FGM data processing, the disagreement between the OVM and the FGM readings is limited to \pm1nT over the whole mission. This demonstrates, the magnetometers on CHAMP exhibit a very good stability. However, the daily correction of the parameter Z component offset of the FGM improves the agreement between the magnetometers markedly. The Z component offset plays a very important role for the data quality. It exhibits a linear relationship with the standard deviation of the disagreement between the OVM and the FGM readings. After Z offset correction, the errors are limited to \pm0.5nT (equivalent to a standard deviation of 0.2nT). We improved the corrections of the spacecraft field which are not taken into account in the routine processing. Such disturbance field, e.g. from the power supply system of the satellite, show some systematic errors in the FGM data and are misinterpreted in 9-parameter calibration, which brings false local time related variation of the calibration parameters. These corrections are made by applying a mathematical model to the measured currents. This non-linear model is derived from an inversion technique. If the disturbance field of the satellite body are fully corrected, the standard deviation of scalar error \triangle B remains about 0.1nT. Additionally, in order to keep the OVM readings a reliable standard, the imperfect coefficients of the torquer current correction for the OVM are redetermined by solving a minimization problem. The temporal variation of the spacecraft remanent field is investigated. It was found that the average magnetic moment of the magneto-torquers reflects well the moment of the satellite. This allows for a continuous correction of the spacecraft field. The reasons for the possible unknown systemic error are discussed in this thesis. Particularly, both temperature uncertainties and time errors have influence on the FGM data. Based on the results of this thesis the data processing of future magnetic missions can be designed in an improved way. In particular, the upcoming ESA mission Swarm can take advantage of our findings and provide all the auxiliary measurements needed for a proper recovery of the ambient magnetic field. N2 - CHAMP (CHAllenging Minisatellite Payload) ist eine deutsche Kleinsatellitenmission für die Forschung und Anwendung in Bereich der Geowissenschaften und Atmosphärenphysik. Das Projekt wird vom GFZ geleitet. Mit seinen hochgenauen, multifunktionalen, sich ergänzenden Nutzlastelementen (Magnetometer, Akzelerometer, Sternsensor, GPS-Empfänger, Laser-Retroreflektor, Ionendriftmeter) liefert CHAMP erstmalig gleichzeitig hochgenaue Schwere- und Magnetfeldmessungen (seit Mitte 2000). Dank des bisherigen guten Zustandes des Satelliten ist die auf 5 Jahre ausgelegte Mission bis 2009 verlängert geworden. An Board befinden sich ein skalares Overhauser-Magnetometer(OVM) für Kalibrierungszwecke sowie zwei Fluxgate-Magnetometer(FGM) zur Messung des magnetischen Feldvektors. Die Messungen vom FGM werden immer verglichen mit denen vom OVM und korregiert im Fall von Widersprüche, das ist die sog. Skalar-Kalibrierung. Um eine zuverlässige Datenqualität während der 8 jährigen Mission zu garantieren, ist die Nachkalibrierung implementiert. Im Rahmen der standard mäßigen Datenverarbeitung werden die Instrumentenparameter des FGM alle 15 Tage neu bestimmt. Das Ziel der vorliegenden Arbeit ist es, eine Verbesserung der Vektormagnetfelddaten zu erzielen durch eine neue Methode der Kalibrierung, die die Eigenschaften der Sensoren und Störung vom Raumfahrzeug mit berücksichtigt. Die Erfahrung aus den zurückliegenden Jahren hat gezeigt, dass sich die Skalenfaktoren des FGM stark mit der Zeit ändern. Dieser Verlauf lässt sich gut durch eine Logarithmuskurve anpassen. Andere Parameter wie die Winkel und die Offsets scheinen stabil zu sein. Eine Ausnahme macht der Offset der Z-Komponent. Dieser bedarf einer regelmäßigen Korrektur. Während die Standardverarbeitung eine undifferenzierte Bestimmung aller 9 FGM Parameter durch nicht-lineare Inversion der skalar Daten vornimmt, beziehen wir jetzt die langzeitlichen Eigenschaften der Parameter in die Bestimmung mit ein. Eine weitere Verbesserung der CHAMP-Magnetfelddaten konnte erreicht werden durch geeignete Berücksichtigung von Störung vom Raumfahrzeug. Die verbleibenden Unsicherheiten konnten durch diese Maßnahmen auf eine Standardabweichung von 0.1nT reduziert werden. KW - Magnetische Feldmessungen KW - Magnetometer-Kalibrierung KW - Magnetfeld-Satellit KW - Magnetic field measurements KW - magnetometer calibration KW - magnetic field satellites Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-41201 ER - TY - INPR A1 - Witt, Annette A1 - Kurths, Jürgen A1 - Krause, F. A1 - Fischer, K. T1 - On the validity of a model for the reversals of the Earth‘s magnetic field N2 - We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information. T3 - NLD Preprints - 4 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13460 ER - TY - INPR A1 - Kurths, Jürgen A1 - Voss, A. A1 - Witt, Annette A1 - Saparin, P. A1 - Kleiner, H. J. A1 - Wessel, Niels T1 - Quantitative analysis of heart rate variability N2 - In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients. T3 - NLD Preprints - 5 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13470 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 - 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 - 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 - 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 - 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 - 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, 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 - 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 -