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 - 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 - 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 - 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 - Schumacher, Jörg A1 - Seehafer, Norbert T1 - Bifurcation analysis of the plane sheet pinch N2 - A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three-dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three-dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state. T3 - NLD Preprints - 56 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14926 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 - 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 - INPR A1 - Pikovskij, Arkadij A1 - Feudel, Ulrike T1 - Characterizing strange nonchaotic attractors N2 - Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Secondly, we propose th characterize their strangeness by calculating a phase sensitivity exponent, that measures the sensitivity with respect to changes of the phase of the external force. It is shown, that phase sensitivity appears if there is a non-zero probability for positive local Lyapunov exponents to occur. T3 - NLD Preprints - 2 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13405 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 -