@article{ArenasBorgeHolthoeferGomezetal.2010, author = {Arenas, Alexandre and Borge-Holthoefer, Javier and Gomez, Sergio and Zamora-Lopez, Gorka}, title = {Optimal map of the modular structure of complex networks}, issn = {1367-2630}, doi = {10.1088/1367-2630/12/5/053009}, year = {2010}, abstract = {The modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and the function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have the contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as much data as the number of modules times the number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and then we use truncated singular value decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allows us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.}, language = {en} } @book{BlechmanLandaRosenblum1995, author = {Blechman, Ilja I. and Landa, Polina S. and Rosenblum, Michael}, title = {Synchronization and chaotization in interacting dynamical systems}, series = {Preprint NLD}, volume = {24}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {40 S.}, year = {1995}, language = {en} } @article{BraunDitlevsenKurthsetal.2010, author = {Braun, Holger and Ditlevsen, Peter D. and Kurths, J{\"u}rgen and Mudelsee, Manfred}, title = {Limitations of red noise in analysing Dansgaard-Oeschger events}, issn = {1814-9324}, doi = {10.5194/cp-6-85-2010}, year = {2010}, abstract = {During the last glacial period, climate records from the North Atlantic region exhibit a pronounced spectral component corresponding to a period of about 1470 years, which has attracted much attention. This spectral peak is closely related to the recurrence pattern of Dansgaard-Oeschger (DO) events. In previous studies a red noise random process, more precisely a first-order autoregressive (AR1) process, was used to evaluate the statistical significance of this peak, with a reported significance of more than 99\%. Here we use a simple mechanistic two-state model of DO events, which itself was derived from a much more sophisticated ocean-atmosphere model of intermediate complexity, to numerically evaluate the spectral properties of random (i.e., solely noise-driven) events. This way we find that the power spectral density of random DO events differs fundamentally from a simple red noise random process. These results question the applicability of linear spectral analysis for estimating the statistical significance of highly non-linear processes such as DO events. More precisely, to enhance our scientific understanding about the trigger of DO events, we must not consider simple "straw men" as, for example, the AR1 random process, but rather test against realistic alternative descriptions.}, language = {en} } @unpublished{BraunFeudel1996, author = {Braun, Robert and Feudel, Fred}, title = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14099}, year = {1996}, abstract = {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.}, language = {en} } @book{BraunFeudel1996, author = {Braun, Robert and Feudel, Fred}, title = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation}, series = {Preprint NLD}, volume = {29}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {8 S.}, year = {1996}, language = {en} } @unpublished{BraunFeudelGuzdar1998, author = {Braun, Robert and Feudel, Fred and Guzdar, Parvez}, title = {The route to chaos for a two-dimensional externally driven flow}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14717}, year = {1998}, abstract = {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.}, language = {en} } @unpublished{BraunFeudelSeehafer1997, author = {Braun, Robert and Feudel, Fred and Seehafer, Norbert}, title = {Bifurcations and chaos in an array of forced vortices}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14564}, year = {1997}, abstract = {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.}, language = {en} } @unpublished{BoeckmannBieleNeuberetal.1997, author = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny}, title = {Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14360}, year = {1997}, abstract = {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.}, language = {en} } @unpublished{BoeckmannNiebsch1998, author = {B{\"o}ckmann, Christine and Niebsch, Jenny}, title = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14725}, year = {1998}, abstract = {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.}, language = {en} } @book{BoeckmannNiebsch1998, author = {B{\"o}ckmann, Christine and Niebsch, Jenny}, title = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on operator}, series = {Preprint NLD}, volume = {47}, journal = {Preprint NLD}, publisher = {Univ. Potsdam}, address = {Potsdam}, issn = {1432-2935}, pages = {16 S. : Abb.}, year = {1998}, language = {en} } @unpublished{BoeckmannSarkoezi1999, author = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos}, title = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14847}, year = {1999}, abstract = {The ill-posed problem of aerosol distribution determination from a small number of backscatter and extinction lidar measurements was solved successfully via a hybrid method by a variable dimension of projection with B-Splines. Numerical simulation results with noisy data at different measurement situations show that it is possible to derive a reconstruction of the aerosol distribution only with 4 measurements.}, language = {en} } @book{BoeckmannSarkoezi1999, author = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos}, title = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection}, series = {Preprint NLD}, volume = {53}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {[7] S. : graph. Darst.}, year = {1999}, language = {en} } @article{CserDonnerSchwarzetal.2001, author = {Cser, Adrienn and Donner, Reik Volker and Schwarz, Udo and Feudel, Ulrike and Otto, Andreas H.}, title = {Statistical parameters of a control strategy of laser beam melt ablation}, year = {2001}, abstract = {Laser beam melt ablation - a contact-free machining process - offers several advantages compared to conventional processing mechanisms: there exists no tool wear and even extremely hard or brittle materials can be processed. During ablation the workpiece is molten by a CO2-laser beam, this melt is then driven out by the impulse of a process gas. The idea behind laser ablation is rather simple, but it has a major limitation in practical applications: with increasing ablation rates surface quality of the workpiece processed declines rapidly. At high ablation rates, depending on the process parameters different periodic-like structures can be observed on the ablated surface. These structures show a dependence on the line energy, which has been identified as a fundamental control parameter. In dependence on this parameter several regimes with different behaviours of the process have been separated. These regimes are distinguishable as well in the surfaces obtained as in the signals gained by the measurement of the process emissions. Further aim is to identify the different modes of the system and reach a deeper understanding of the dynamics of the molten material in order to understand the formation of these surface structures. With this it should be possible to influence the system in the direction of avoiding structure formation even at high ablation rates. Relying on the results on-line monitoring and control of the process should be studied.}, language = {en} } @unpublished{DemircanScheelSeehafer1999, author = {Demircan, Ayhan and Scheel, Stefan and Seehafer, Norbert}, title = {Heteroclinic behavior in rotating Rayleigh-B{\´e}nard convection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14914}, year = {1999}, abstract = {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.}, language = {en} } @unpublished{DemircanSeehafer2000, author = {Demircan, Ayhan and Seehafer, Norbert}, title = {Nonlinear square patterns in Rayleigh-B{\´e}nard convection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14986}, year = {2000}, abstract = {We numerically investigate nonlinear asymmetric square patterns in a horizontal convection layer with up-down reflection symmetry. As a novel feature we find the patterns to appear via the skewed varicose instability of rolls. The time-independent nonlinear state is generated by two unstable checkerboard (symmetric square) patterns and their nonlinear interaction. As the bouyancy forces increase, the interacting modes give rise to bifurcations leading to a periodic alternation between a nonequilateral hexagonal pattern and the square pattern or to different kinds of standing oscillations.}, language = {en} } @unpublished{Dicken1998, author = {Dicken, Volker}, title = {Simultaneous activity and attenuation reconstruction in emission tomography}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14747}, year = {1998}, abstract = {In single photon emission computed tomography (SPECT) one is interested in reconstructing the activity distribution f of some radiopharmaceutical. The data gathered suffer from attenuation due to the tissue density µ. Each imaged slice incorporates noisy sample values of the nonlinear attenuated Radon transform (formular at this place in the original abstract) Traditional theory for SPECT reconstruction treats µ as a known parameter. In practical applications, however, µ is not known, but either crudely estimated, determined in costly additional measurements or plainly neglected. We demonstrate that an approximation of both f and µ from SPECT data alone is feasible, leading to quantitatively more accurate SPECT images. The result is based on nonlinear Tikhonov regularization techniques for parameter estimation problems in differential equations combined with Gauss-Newton-CG minimization.}, language = {en} } @book{Dicken1998, author = {Dicken, Volker}, title = {Simultaneous activity and attenuation reconstruction in emission tomography}, series = {Preprint NLD}, volume = {50}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {27 S. : graph. Darst.}, year = {1998}, language = {en} } @unpublished{DickenMaass1995, author = {Dicken, Volker and Maaß, Peter}, title = {Wavelet-Galerkin methods for ill-posed problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13890}, year = {1995}, abstract = {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.}, language = {en} } @article{EbelingMolgedeyKurthsetal.2002, author = {Ebeling, Werner and Molgedey, Lutz and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Entropy, complexity, predictability, and data analysis of time series and letter sequences}, isbn = {3-540-41324-3}, year = {2002}, abstract = {The structure of time series and letter sequences is investigated using the concepts of entropy and complexity. First conditional entropy and transinformation are introduced and several generalizations are discussed. Further several measures of complexity are introduced and discussed. The capability of these concepts to describe the structure of time series and letter sequences generated by nonlinear maps, data series from meteorology, astrophysics, cardiology, cognitive psychology and finance is investigated. The relation between the complexity and the predictability of informational strings is discussed. The relation between local order and the predictability of time series is investigated.}, language = {en} } @unpublished{EngbertScheffczykKrampeetal.1997, author = {Engbert, Ralf and Scheffczyk, Christian and Krampe, Ralf-Thomas and Rosenblum, Mikhael and Kurths, J{\"u}rgen and Kliegl, Reinhold}, title = {Tempo-induced transitions in polyrhythmic hand movements}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14380}, year = {1997}, abstract = {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.}, language = {en} } @article{FatkullinFoersterSchwarz1999, author = {Fatkullin, Mars N. and F{\"o}rster, Matthias and Schwarz, Udo}, title = {Irregularities of electron density and temperature in the day sector of the plasmasphere base during the summer season at high solar activity by observations of the aktivnyi satellite}, year = {1999}, abstract = {Based on the data of the Magion2 subsatellite of the Intercosmos24 satellite, an example of small-scale irregularities of the electron concentration with linear dimensions l ~ 100-300 m in the polar ion- osphere of the morning sector under field-aligned currents at altitudes of 1800-2030 km during the main phase of the magnetic storm of June 13, 1990 is presented. The dependence of the spectral index of the above small-scale irregularities on latitude is determined for the first time. Certain mechanisms of the generation of these small-scale irregularities are also qualitatively discussed.}, language = {en} } @unpublished{FeudelSeehafer1995, author = {Feudel, Fred and Seehafer, Norbert}, title = {Bifurcations and pattern formation in a 2D Navier-Stokes fluid}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13907}, year = {1995}, abstract = {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).}, language = {en} } @unpublished{FeudelSeehafer1994, author = {Feudel, Fred and Seehafer, Norbert}, title = {On the bifurcation phenomena in truncations of the 2D Navier-Stokes equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13390}, year = {1994}, abstract = {We have studied bifurcation phenomena for the incompressable Navier-Stokes equations in two space dimensions with periodic boundary conditions. Fourier representations of velocity and pressure have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. Invariant sets, notably steady states, have been traced for varying Reynolds number or strength of the imposed forcing, respectively. A complete bifurcation sequence leading to chaos is described in detail, including the calculation of the Lyapunov exponents that characterize the resulting chaotic branch in the bifurcation diagram.}, language = {en} } @unpublished{FeudelSeehaferGalantietal.1996, author = {Feudel, Fred and Seehafer, Norbert and Galanti, Barak and R{\"u}diger, Sten}, title = {Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14317}, year = {1996}, abstract = {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.}, language = {en} } @article{FeudelSeehaferRuediger1996, author = {Feudel, Fred and Seehafer, Norbert and R{\"u}diger, Sten}, title = {Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing}, series = {Preprint NLD}, volume = {31}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {10 S.}, year = {1996}, language = {en} } @unpublished{FeudelSeehaferSchmidtmann1995, author = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf}, title = {Bifurcation phenomena of the magnetofluid equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13585}, year = {1995}, abstract = {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.}, language = {en} } @unpublished{FeudelSeehaferSchmidtmann1995, author = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf}, title = {Fluid helicity and dynamo bifurcations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13882}, year = {1995}, abstract = {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.}, language = {en} } @unpublished{Feudel1996, author = {Feudel, Ulrike}, title = {Komplexes Verhalten in multistabilen, schwach dissipativen Systemen}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14412}, year = {1996}, abstract = {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 gegen{\"u}ber St{\"o}rungen in den Anfangsbedingungen sind. Diese Systeme zeichnen sich durch eine extrem hohe Flexibilit{\"a}t ihres Verhaltens aus.}, language = {de} } @book{Feudel1996, author = {Feudel, Ulrike}, title = {Komplexes Verhalten in multistabilen, schwach dissipativen Systemen}, series = {Preprint NLD}, volume = {34}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {11 S.}, year = {1996}, language = {de} } @book{FeudelKurthsNeiman1995, author = {Feudel, Ulrike and Kurths, J{\"u}rgen and Neiman, Alexander}, title = {The cumulant approach for investigating the noise influence on mode-locking bifurcations}, series = {Preprint NLD}, volume = {16}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {20 S.}, year = {1995}, language = {en} } @article{FlorenceDahlemAlmeidaetal.2009, author = {Florence, Gerson and Dahlem, Markus A. and Almeida, Ant{\^o}nio-Carlos G. and Bassani, Jos{\´e} W. M. and Kurths, J{\"u}rgen}, title = {The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression : a computational study}, issn = {0022-5193}, doi = {10.1016/j.jtbi.2009.01.032}, year = {2009}, abstract = {Experimental evidences point Out the participation of nonsynaptic mechanisms (e.g., fluctuations in extracellular tons) in epileptiform bursting and spreading depression (SD). During these abnormal oscillatory patterns, it is observed an increase of extracellular potassium concentration [K+](o) and a decrease of extracellular calcium concentration [Ca2+](o) which raises the neuronal excitability. However, whether the high [K+](o) triggers and propagates these abnormal neuronal activities or plays a secondary role into this process is unclear. To better understand the influence of extracellular potassium dynamics in these oscillatory patterns, the experimental conditions of high [K+](o) and zero [Ca2+](o) were replicated in an extended Golomb model where we added important regulatory mechanisms of ion concentration as Na+-K+ pump, ion diffusion and glial buffering. Within these Conditions, simulations of the cell model exhibit seizure-like discharges (ictal bursting). The SD was elicited by the interruption of the Na+- K+ pump activity, mimicking the effect of cellular hypoxia (an experimental protocol to elicit SD, the hypoxia-induced SD). We used the bifurcation theory and the fast-slow method to analyze the interference of K+ dynamics in the cellular excitability. This analysis indicates that the system loses its stability at a high [K+](o), transiting to an elevated state of neuronal excitability. Effects of high [K+](o), are observed in different stages of ictal bursting and SD. In the initial stage, the increase of [K+](o) creates favorable conditions to trigger both oscillatory patterns. During the neuronal activity, a continuous growth of [K+](o) by outward K+ flow depresses K+ Currents in a positive feedback way. At the last stage, due to the depression of K+ currents, the Na+-K+ pump is the main mechanism in the end of neuronal activity. Thus, this work suggests that [K+](o) dynamics may play a fundamental role in these abnormal oscillatory patterns.}, language = {en} } @article{FujiwaraKurths2009, author = {Fujiwara, Naoya and Kurths, J{\"u}rgen}, title = {Spectral universality of phase synchronization in non-identical oscillator networks}, issn = {1434-6028}, doi = {10.1140/epjb/e2009-00078-6}, year = {2009}, abstract = {We employ a spectral decomposition method to analyze synchronization of a non-identical oscillator network. We study the case that a small parameter mismatch of oscillators is characterized by one parameter and phase synchronization is observed. We derive a linearized equation for each eigenmode of the coupling matrix. The parameter mismatch is reflected on inhomogeneous term in the linearized equation. We find that the oscillation of each mode is essentially characterized only by the eigenvalue of the coupling matrix with a suitable normalization. We refer to this property as spectral universality, because it is observed irrespective of network topology. Numerical results in various network topologies show good agreement with those based on linearized equation. This universality is also observed in a system driven by additive independent Gaussian noise.}, language = {en} } @article{GomezGardenesZamoraLopezMorenoetal.2010, author = {Gomez-Garde{\~n}es, Jes{\´u}s and Zamora-Lopez, Gorka and Moreno, Yamir and Arenas, Alexandre}, title = {From modular to centralized organization of synchronization in functional areas of the cat cerebral cortex}, issn = {1932-6203}, doi = {10.1371/journal.pone.0012313}, year = {2010}, abstract = {Recent studies have pointed out the importance of transient synchronization between widely distributed neural assemblies to understand conscious perception. These neural assemblies form intricate networks of neurons and synapses whose detailed map for mammals is still unknown and far from our experimental capabilities. Only in a few cases, for example the C. elegans, we know the complete mapping of the neuronal tissue or its mesoscopic level of description provided by cortical areas. Here we study the process of transient and global synchronization using a simple model of phase-coupled oscillators assigned to cortical areas in the cerebral cat cortex. Our results highlight the impact of the topological connectivity in the developing of synchronization, revealing a transition in the synchronization organization that goes from a modular decentralized coherence to a centralized synchronized regime controlled by a few cortical areas forming a Rich-Club connectivity pattern.}, language = {en} } @unpublished{GuastiEngbertKrampeetal.2000, author = {Guasti, Giovanna and Engbert, Ralf and Krampe, Ralf T. and Kurths, J{\"u}rgen}, title = {Phase transitions, complexity, and stationarity in the production of polyrhythms}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14933}, year = {2000}, abstract = {Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook}, language = {en} } @article{HellandGapelyukSuhrbieretal.2010, author = {Helland, Vanessa Carolina Figuera and Gapelyuk, Andrej and Suhrbier, Alexander and Riedl, Maik and Penzel, Thomas and Kurths, J{\"u}rgen and Wessel, Niels}, title = {Investigation of an automatic sleep stage classification by means of multiscorer hypnogram}, issn = {0026-1270}, doi = {10.3414/Me09-02-0052}, year = {2010}, abstract = {Objectives: Scoring sleep visually based on polysomnography is an important but time-consuming element of sleep medicine. Where-as computer software assists human experts in the assignment of sleep stages to polysomnogram epochs, their performance is usually insufficient. This study evaluates the possibility to fully automatize sleep staging considering the reliability of the sleep stages available from human expert sleep scorers. Methods: We obtain features from EEG, ECG and respiratory signals of polysomnograms from ten healthy subjects. Using the sleep stages provided by three human experts, we evaluate the performance of linear discriminant analysis on the entire polysomnogram and:only on epochs where the three experts agree in their-sleep stage scoring. Results: We show that in polysomnogram intervals, to which all three scorers assign the same sleep stage, our algorithm achieves 90\% accuracy. This high rate of agreement with the human experts is accomplished with only a small set of three frequency features from the EEG. We increase-the performance to 93\% by including ECG and respiration features. In contrast, on intervals of ambiguous sleep stage, the sleep stage classification obtained from our algorithm, agrees with the human consensus scorer in approximately 61\%. Conclusions: These findings suggest that machine classification is highly consistent with human sleep staging and that error in the algorithm's assignments is rather a problem of lack of well-defined criteria for human experts to judge certain polysomnogram epochs than an insufficiency of computational procedures}, language = {en} } @article{ItohKurths2010, author = {Itoh, Naoki and Kurths, J{\"u}rgen}, title = {Change-point detection of climate time series by nonparametric method}, issn = {2078-0958}, year = {2010}, abstract = {In one of the data mining techniques, change-point detection is of importance in evaluating time series measured in real world. For decades this technique has been developed as a nonlinear dynamics. We apply the method for detecting the change points, Singular Spectrum Transformation (SST), to the climate time series. To know where the structures of climate data sets change can reveal a climate background. In this paper we discuss the structures of precipitation data in Kenya and Wrangel Island (Arctic land) by using the SST.}, language = {en} } @unpublished{Jansen1996, author = {Jansen, Wolfgang}, title = {A note on the determination of the type of communication areas}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14339}, year = {1996}, abstract = {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.}, language = {en} } @unpublished{Jansen1995, author = {Jansen, Wolfgang}, title = {CANDYS/QA : algorithms, programs, and user's manual}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13920}, year = {1995}, abstract = {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}, language = {en} } @book{Jansen1995, author = {Jansen, Wolfgang}, title = {CANDYS/QA : algorithms, programs and user's manual}, series = {Preprint NLD}, volume = {27}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {140 S.}, year = {1995}, language = {en} } @book{Jansen1996, author = {Jansen, Wolfgang}, title = {A note on the determination of the type of communication areas}, series = {Preprint NLD}, volume = {33}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {32 S.}, year = {1996}, language = {en} } @unpublished{KurthsPikovskijScheffczyk1994, author = {Kurths, J{\"u}rgen and Pikovskij, Arkadij and Scheffczyk, Christian}, title = {Roughening interfaces in deterministic dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13447}, year = {1994}, abstract = {Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface.}, language = {en} } @article{KurthsSchwarz1993, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Application of techniques of nonlinear dynamics to SS Cyg}, isbn = {0-7503-0282-8}, year = {1993}, abstract = {We look for structural properties in the light curve of the dwarf nova SS Cyg by means of techniques from nonlinear dynamics. Applying the popular Grassberger-Procaccia procedure, Cannizzo and Goddings (1988) showed that there is no evidence for a low-dimensional attractor underlying this record. Because there are some hints for order in the light curve, we search for other signatures of deterministic systems. Therefore, we use other methods recently developed in this theory, such as local linear prediction and recurrence maps. Our main findings are: i] the prediction error grows exponentially during outburst phases, but via a power law in the quiescent states, ii] there are some rather regular patterns in this light curve which sometimes recur, but the recurrence is not regular. This leads to the following conclusions: i] The outburst dynamics shows a higher degree of order than the quiescent one. There are some hints for deterministic chaos in the outburst behavior. ii] The light curve is a complex mixture of deterministic and stochastic structures. The analysis presented in this paper shows that methods of nonlinear dynamics can be an efficient tool for the study of complex processes, even if there is no evidence for a low-dimensional attractor.}, language = {en} } @article{KurthsSchwarz1994, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Chaos theory and radio emission}, year = {1994}, abstract = {The application of chaos theory has become popular to understand the nature of various features of solar activity because most of them are far from regular. The usual approach, however, that is basing on finding low- dimensional structures of the underlying processes seems to be successful only in a few exceptional cases, such as in rather coherent phenomena as coronal pulsations. It is important to note that most phenomena in solar radio emission are more complex. We present two kinds of techniques from nonlinear dynamics which can be useful to analyse such phenomena: i] Fragmentation processes observed in solar spike events are studied by means of symbolic dynamics methods. Different measures of complexity calculated from such observations reveal that there is some order in this fragmentation. ii] Bursts are a typical transient phenomenon. To study energization processes causing impulsive microwave bursts, the wavelet analysis is applied. It exhibits structural differences of the pre- and post-impulsive phase in cases where the power spectra of both are not distinct.}, language = {en} } @article{KurthsSchwarz2001, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Nichtlineare Wissenschaften - neue Paradigmen und Konzepte}, issn = {0177- 3674}, year = {2001}, abstract = {In den letzten 2 Jahrzehnten des 20. Jahrhunderts hat sich mit der rasanten Entwicklung der Nichtlinearen Wissenschaften ein weiterer Umbruch vollzogen, der eine ausgepraegte Nachhaltigkeit in Wissenschaft und Technik ebenso wie in der Gesellschaft erwarten laesst. Die Nichtlinearen Wissenschaften werden auch als Nichtlineare Dynamik, Wissenschaft Komplexer Systeme oder etwas eingegrenzt Chaostheorie bezeichnet.}, language = {de} } @article{KurthsSchwarzParlitzetal.1994, author = {Kurths, J{\"u}rgen and Schwarz, Udo and Parlitz, Ulrich and Sonett, Charles P.}, title = {Testing for nonlinearity in radiocarbon data}, issn = {1023-5809}, year = {1994}, abstract = {The radiocarbon record that has been extended from 7199 BC to 1891 AD is of fundamental importance to understand century-scale variations of solar activity. We have, therefore, studied how to extract information from dynamic reconstructions of this observational record. Using some rather unusual methods of nonlinear dynamics, we have found that the data are significantly different from linear colored noise and that there is some evidence of nonlinear behavior. The method of recurrence plots exhibits that the grand minima of solar activity are quite different in their recurrence. Most remarkably, it suggests that the recent epoch seems to be similar to the Medieval maximum.}, language = {en} } @article{KurthsSchwarzWitt1995, author = {Kurths, J{\"u}rgen and Schwarz, Udo and Witt, Annette}, title = {Non-linear data analysis in solar radio astronomy}, year = {1995}, abstract = {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.}, language = {en} } @unpublished{KurthsVossWittetal.1994, author = {Kurths, J{\"u}rgen and Voss, A. and Witt, Annette and Saparin, P. and Kleiner, H. J. and Wessel, Niels}, title = {Quantitative analysis of heart rate variability}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13470}, year = {1994}, abstract = {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.}, language = {en} } @unpublished{LiperovskayaMeisterParrotetal.2006, author = {Liperovskaya, E. V. and Meister, Claudia-Veronika and Parrot, M. and Bogdanov, V. V. and Vasil'eva, N. E.}, title = {On Es-spread effects in the ionosphere connected to earthquakes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15003}, year = {2006}, abstract = {In the present work, phenomena in the ionosphere are studied, which are connected with earthquakes (16 events) having a depth of less than 50 km and a magnitude M larger than 4. Analysed are night-time Es-spread effects using data of the vertical sounding station Petropavlovsk- Kanchatsky (φ=53.0°, λ=158.7°) from May 2004 until August 2004 registered every 15 minutes. It is found that the maximum distance of the earthquake from the sounding station, where pre-seismic phenomena are yet observable, depends on the magnitude of the earthquake. Further it is shown that 1-2 days before the earthquakes, in the premidnight hours, the appearance of Es-spread increases. The reliability of this increase amounts to 0.95.}, language = {en} } @unpublished{LiperovskayaParrotBogdanovetal.2006, author = {Liperovskaya, E. V. and Parrot, M. and Bogdanov, V. V. and Meister, Claudia-Veronika and Rodkin, M. V. and Liperovsky, V. A.}, title = {On long-term variations of foF2 in the mid-latitude ionosphere before strong earthquakes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15017}, year = {2006}, abstract = {The statistical analysis of the variations of the dayly-mean frequency of the maximum ionospheric electron density foF2 is performed in connection with the occurrence of (more than 60) earthquakes with magnitudes M > 6.0, depths h < 80 km and distances from the vertical sounding station R < 1000 km. For the study, data of the Tokyo sounding station are used, which were registered every hour in the years 1957-1990. It is shown that, on the average, foF2 decreases before the earthquakes. One day before the shock the decrease amounts to about 5 \%. The statistical reliability of this phenomenon is obtained to be better than 0.95. Further, the variations of the occurrence probability of the turbulization of the F-layer (F spread) are investigated for (more than 260) earthquakes with M > 5.5, h < 80 km, R < 1000 km. For the analysis, data of the Japanese station Akita from 1969-1990 are used, which were obtained every hour. It is found that before the earthquakes the occurrence probability of F spread decreases. In the week before the event, the decrease has values of more than 10 \%. The statistical reliability of this phenomenon is also larger than 0.95. Examining the seismo-ionospheric effects, here periods of time with weak heliogeomagnetic disturbances are considered, the Wolf number is less than 100 and the index ∑ Kp is smaller than 30.}, language = {en} } @book{LiperovskijMeister1995, author = {Liperovskij, Viktor A. and Meister, Claudia-Veronika}, title = {Sporadic e-layers as current generator : two-dimensional model}, series = {Preprint NLD}, volume = {20}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {23 S.}, year = {1995}, language = {en} } @unpublished{LiperovskyMeisterDodaetal.2005, author = {Liperovsky, V. A. and Meister, Claudia-Veronika and Doda, L. N. and Liperovskaya, E. V. and Davidov, V. F. and Bogdanov, V. V.}, title = {On the possible influence of radon and aerosol injection on the atmosphere and ionosphere before earthquakes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14995}, year = {2005}, abstract = {A model of the generation of pulses of local electric fields with characteristic time scales of 1-10 minutes is considered for atmospheric conditions above fracture regions of earthquakes. In the model, it is proposed that aerosols, increased ionization velocity and upstreaming air flows occur at night-time conditions. The pulses of local electric fields cause respective pulses of infrared emissions. But infrared emissions with time scales of 1-10 minutes were not observed up to now experimentally. The authors think, that the considered non-stationary field and radiation effects might be a new-type of applicable earthquake indicators and ask to perform special earth-based and satellite observations of the night-time atmosphere in seismoactive fracture regions.}, language = {en} } @unpublished{LiperovskyPochotelovLiperovskayaetal.1998, author = {Liperovsky, V.A. and Pochotelov, O.A. and Liperovskaya, E.V. and Parrot, M. and Meister, C.-V. and Alimov, O. A.}, title = {Modifications of sporadic E-layers caused by seismic activity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14799}, year = {1998}, abstract = {Contents: 1 Introduction 2 Formation and destruction of sporadic E-layers 3 Temporal variations of parameters of sporadic E-layers during earthquake preparation 3.1 Temporal variations of fbEs with time-scales of a few hours 3.2 Study of fbEs variations with characteristic time-scales of 0.5-3 hours 3.3 Variations of the parameters of sporadic E-layers with characteristic time-scales of 15-45 minutes 3.4 Sporadic E-layer variations with characteristic time-scales of 2-15 minutes 4 On the spatial scales of sporadic E-layer disturbances related to seismic activity 5 Complex experimental researches of the ionosphere, electromagnetic noise and the geomagnetic field 5.1 Ionospheric and electromagnetic phenomena of the Kayraccum earthquake in 1985 5.2 Comparison of anomalies with characteristic time-scales of 2-3 hours for ionospheric E- and F-layers, and temporal behaviour of electromagnetic noise emission intensity 5.3 Night airglow emissions in the E-region before earthquakes and sporadic E-layer variations 6 Physical models of lithosphere-ionosphere links 6.1 Lithosphere-ionosphere links due to AGW 6.2 Electromagnetic models for the lithosphere-ionosphere coupling 6.3 Sporadic E-layers as current generators 7 Discussion and conclusion}, language = {en} } @article{LiperovskyPochotelovLiperovskayaetal.1998, author = {Liperovsky, Viktor A. and Pochotelov, O. A. and Liperovskaya, E. V. and Parrot, M. and Meister, Claudia-Veronika and Alimov, O. A.}, title = {Modifications of sporadic E-layers caused by seismic activity}, series = {Preprint NLD}, volume = {49}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {46 S. : graph. Darst.}, year = {1998}, language = {en} } @unpublished{Lukaschewitsch1998, author = {Lukaschewitsch, Michael}, title = {Geoelectrical conductivity problems on unbounded domains}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14704}, year = {1998}, abstract = {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. Poincar{\´e} 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.}, language = {en} } @unpublished{MaassPereverzevRamlauetal.1998, author = {Maaß, Peter and Pereverzev, Sergei V. and Ramlau, Ronny and Solodky, Sergei G.}, title = {An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14739}, year = {1998}, abstract = {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.}, language = {en} } @article{MaassPereverzevRamlauetal.1998, author = {Maaß, Peter and Pereverzev, Sergei V. and Ramlau, Ronny and Solodky, Sergei G.}, title = {An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection}, series = {Preprint NLD}, volume = {48}, journal = {Preprint NLD}, publisher = {Univ. Potsdam}, address = {Potsdam}, issn = {1432-2935}, pages = {19 S.}, year = {1998}, language = {en} } @unpublished{MaassRieder1996, author = {Maaß, Peter and Rieder, Andreas}, title = {Wavelet-accelerated Tikhonov-Phillips regularization with applications}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14104}, year = {1996}, abstract = {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}}, language = {en} } @book{MaassRieder1996, author = {Maaß, Peter and Rieder, Andreas}, title = {Wavelet-accelerated Tikhonov-Phillips regularization with applications}, series = {Preprint NLD}, volume = {30}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {25 S.}, year = {1996}, language = {en} } @article{MarwanKurths2009, author = {Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Comment on "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" by Rohde et al. : [Physica D 237 (2008) 619-629]}, issn = {0167-2789}, doi = {10.1016/j.physd.2009.04.018}, year = {2009}, abstract = {In the recent article "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process.}, language = {en} } @book{Meister1994, author = {Meister, Claudia-Veronika}, title = {Stochastic forces on electrons in the solar flare plasma}, series = {Preprint NLD}, volume = {7}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {12 S.}, year = {1994}, language = {en} } @book{Meister1995, author = {Meister, Claudia-Veronika}, title = {Stochastic forces in space plasmas with ion-acoustic and lower-hybrid-drift turbulence}, series = {Preprint NLD}, volume = {10}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {23 S.}, year = {1995}, language = {en} } @unpublished{MeisterDziourkevich2000, author = {Meister, Claudia-Veronika and Dziourkevich, Natalia S.}, title = {Temperature-anisotropy driven mirror waves in space plasma}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14977}, year = {2000}, abstract = {In this paper an analysis of the excitation conditions of mirror waves is done, which propagate parallel to an external magnetic field. There are found analytical expressions for the dispersion relations of the waves in case of different plasma conditions. These relations may be used in future to develop the nonlinear theory of mirror waves. In comparison with former analytical works, in the study the inuence of the magnetic field and nite temperatures of the ions parallel to the magnetic field are taken into account. Application is done for the earth's magnetosheath.}, language = {en} } @book{MeisterKubyshkin1995, author = {Meister, Claudia-Veronika and Kubyshkin, I. V.}, title = {Recalculation of the diffusion tensor for plasmas with ion-acoustic turbulence}, series = {Preprint NLD}, volume = {26}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {16 S.}, year = {1995}, language = {en} } @article{MeisterLiperovskySchlegeletal.1995, author = {Meister, Claudia-Veronika and Liperovsky, Viktor A. and Schlegel, K. and Haldoupis, Ch.}, title = {Currents and turbulence in and near mid-latitude sporadic e-layers caused by strong acoustic impulses}, series = {Preprint NLD}, volume = {11}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {15 S.}, year = {1995}, language = {en} } @unpublished{MeklerBoeckmannSokolovskaia2000, author = {Mekler, A. A. and B{\"o}ckmann, Christine and Sokolovskaia, N.}, title = {Particle distribution from spectral Mie-scattering: kernel representation and singular-value spectrum}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14948}, year = {2000}, abstract = {This paper deals with the Mie scattering kernels for multi-spectral data. The kernels may be represented in form of power series. Furthermore, the singular-value spectrum and the degree of ill-posedness in dependence on the refractive index of the particles are numerically approximated. A special hybrid regularization technique allows us to determine via inversion the particle distributions of different types.}, language = {en} } @book{Montada1996, author = {Montada, Leo}, title = {Gerechtigkeitsanspr{\"u}che und Ungerechtigkeitserleben in den neuen Bundesl{\"a}ndern}, series = {Bericht / Zentrum f{\"u}r Gerechtigkeitsforschung, Potsdam}, volume = {4}, journal = {Bericht / Zentrum f{\"u}r Gerechtigkeitsforschung, Potsdam}, publisher = {Univ.}, address = {Potsdam}, pages = {55 S.}, year = {1996}, language = {de} } @book{Morin1995, author = {Morin, Paul}, title = {Visualization in the geosciences : course notes}, series = {Preprint NLD}, volume = {19}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {123 S.}, year = {1995}, language = {en} } @article{PalusKurthsSchwarzetal.2001, author = {Palus, Milan and Kurths, J{\"u}rgen and Schwarz, Udo and Novotn{\´a}, Dagmar and Charv{\´a}tov{\´a}, Ivanka}, title = {Is the solar activity cycle synchronized with the solar inertial motion?}, year = {2001}, abstract = {The 300 year record of the yearly sunspot numbers and numerically generated trajectory of the solar inertial motion (SIM) were subjects of a synchronization analysis. Phase synchronization of the sunspot cycle and a fast component of the SIM have been found and confirmed with statistical significance in three epochs (1727-1757, 1802-1832 and 1863-1922) of the entire 1700-1997 record. This result can be considered as a quantitative support for the hypothesis that there is a weak interaction of gravity and solar activity.}, language = {en} } @article{PavlovAnisimovSemyachkinaGlushkovskayaetal.2009, author = {Pavlov, Alexey N. and Anisimov, A. A. and Semyachkina-Glushkovskaya, Oxana V. and Matasova, E. G. and Kurths, J{\"u}rgen}, title = {Analysis of blood pressure dynamics in male and female rats using the continuous wavelet transform}, issn = {0967-3334}, doi = {10.1088/0967-3334/30/7/013}, year = {2009}, abstract = {We study gender-related particularities in cardiovascular responses to stress and nitric oxide (NO) deficiency in rats using HR, mean arterial pressure (MAP) and a proposed wavelet-based approach. Blood pressure dynamics is analyzed: (1) under control conditions, (2) during immobilization stress and recovery and (3) during nitric oxide blockade by N-G-nitro-L-arginine-methyl ester (L-NAME). We show that cardiovascular sensitivity to stress and NO deficiency depends upon gender. Actually, in females the chronotropic effect of stress is more pronounced, while the pressor effect is weakened compared with males. We conclude that females demonstrate more favorable patterns of cardiovascular responses to stress and more effective NO control of cardiovascular activity than males.}, language = {en} } @unpublished{PikovskijFeudel1994, author = {Pikovskij, Arkadij and Feudel, Ulrike}, title = {Characterizing strange nonchaotic attractors}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13405}, year = {1994}, abstract = {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.}, language = {en} } @unpublished{PikovskijZaksFeudeletal.1995, author = {Pikovskij, Arkadij and Zaks, Michael A. and Feudel, Ulrike and Kurths, J{\"u}rgen}, title = {Singular continuous spectra in dissipative dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13787}, year = {1995}, abstract = {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 Poincar{\´e} map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincar{\´e} 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.}, language = {en} } @article{PortaDiRienzoWesseletal.2009, author = {Porta, Alberto and Di Rienzo, Marco and Wessel, Niels and Kurths, J{\"u}rgen}, title = {Addressing the complexity of cardiovascular regulation}, issn = {1364-503X}, doi = {10.1098/rsta.2008.0292}, year = {2009}, language = {en} } @article{RetzlaffBauernschmittMalbergetal.2009, author = {Retzlaff, Beatrice and Bauernschmitt, Robert and Malberg, Hagen and Brockmann, Gernot and Uhl, Christian and Lange, Ruediger and Kurths, J{\"u}rgen and Bretthauer, Georg and Wessel, Niels}, title = {Depression of cardiovascular autonomic function is more pronounced after mitral valve surgery : evidence for direct trauma}, issn = {1364-503X}, doi = {10.1098/rsta.2008.0272}, year = {2009}, abstract = {The analysis of baroreflex sensitivity (BRS) and heart rate variability (HRV) leads to additional insights into patients' prognosis after cardiovascular events. The following study was performed to assess the differences in the post-operative recovery of autonomic regulation after mitral valve (MV) and aortic valve (AV) surgery with a heart lung machine. Among the 43 consecutive male patients enrolled in a prospective study, 26 underwent isolated AV surgery and 17 isolated MV surgery. Blood pressure as well as ECG signals were recorded the day before, 24 hours after and one week after surgery. BRS was calculated according to the dual sequence method, and HRV was calculated using standard linear as well as nonlinear parameters. There were no major differences between the two groups in the pre-operative values. At 24 hours a comparable depression of HRV and BRS in both groups was observed, while at 7 days there was partial recovery in AV patients, which was absent in MV patients: p(AV versus MV) < 0.001. While the response of the autonomic system to surgery is similar in AV and MV patients, there is obviously a decreased ability to recover in MV patients, probably attributed to traumatic lesions of the autonomic nervous system by opening the atria. Ongoing research is required for further clarification of the pathophysiology of this phenomenon and to establish strategies to restore autonomic function.}, language = {en} } @article{RiedlvanLeeuwenSuhrbieretal.2009, author = {Riedl, Maik and van Leeuwen, Peter Jan and Suhrbier, Alexander and Malberg, Hagen and Groenemeyer, Dietrich and Kurths, J{\"u}rgen and Wessel, Niels}, title = {Testing foetal-maternal heart rate synchronization via model-based analyses}, issn = {1364-503X}, doi = {10.1098/rsta.2008.0277}, year = {2009}, abstract = {The investigation of foetal reaction to internal and external conditions and stimuli is an important tool in the characterization of the developing neural integration of the foetus. An interesting example of this is the study of the interrelationship between the foetal and the maternal heart rate. Recent studies have shown a certain likelihood of occasional heart rate synchronization between mother and foetus. In the case of respiratory-induced heart rate changes, the comparison with maternal surrogates suggests that the evidence for detected synchronization is largely statistical and does not result from physiological interaction. Rather, they simply reflect a stochastic, temporary stability of two independent oscillators with time-variant frequencies. We reanalysed three datasets from that study for a more local consideration. Epochs of assumed synchronization associated with short-term regulation of the foetal heart rate were selected and compared with synchronization resulting from white noise instead of the foetal signal. Using data-driven modelling analysis, it was possible to identify the consistent influence of the heartbeat duration of maternal beats preceding the foetal beats during epochs of synchronization. These maternal beats occurred approximately one maternal respiratory cycle prior to the affected foetal beat. A similar effect could not be found in the epochs without synchronization. Simulations based on the fitted models led to a higher likelihood of synchronization in the data segments with assumed foetal-maternal interaction than in the segment without such assumed interaction. We conclude that the data-driven model-based analysis can be a useful tool for the identification of synchronization.}, language = {en} } @article{RomanoThielSchwarzetal.2001, author = {Romano, Maria Carmen and Thiel, Marco and Schwarz, Udo and Kurths, J{\"u}rgen and Lange, Holger and Hauhs, M.}, title = {Conceptual model of runoff from a forested catchment}, year = {2001}, abstract = {We investigate the relationship between precipitation and runoff data from a small forested catchment in the Harz mountains (Germany). For this purpose, we develop a conceptual model including memory effects to predict the runoff signal using the precipitation data as input. An enhanced variant of the model also includes air temperature as input variable. We show in terms of correlation functions that this model describes main dynamical properties of the runoff, especially the delay between rain event and runoff response as the annual persistence in the runoff data.}, language = {en} } @book{RosenblumKurths1995, author = {Rosenblum, Michael and Kurths, J{\"u}rgen}, title = {A model of neural control of heart rate}, series = {Preprint NLD}, volume = {12}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {22 S.}, year = {1995}, language = {en} } @unpublished{RunovPudovkinMeister1999, author = {Runov, A. V. and Pudovkin, M. I. and Meister, Claudia-Veronika}, title = {The dynamics of tail-like current sheets under the influence of small-scale plasma turbulence}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14906}, year = {1999}, abstract = {A 2D-magnetohydrodynamic model of current-sheet dynamics caused by anomalous electrical resistivity as result of small-scale plasma turbulence is proposed. The anomalous resistivity is assumed to be proportional to the square of the gradient of the magnetic pressure as may be valid for instance in the case of lower-hybrid-drift turbulence. The initial resistivity pulse is given. Then the temporal and spatial evolution of the magnetic and electric fields, plasma density, pressure, convection and resistivity are considered. The motion of the induced electric field is discussed as indicator of the plasma disturbances. The obtained results found using much improved numerical methods show a magnetic field evolution with x-line formation and plasma acceleration. Besides, in the current sheet, three types of magnetohydrodynamic waves occur, fast magnetoacoustic waves of compression and rarefaction as well as slow magnetoacoustic waves.}, language = {en} } @unpublished{RuedigerFeudelSeehafer1998, author = {R{\"u}diger, Sten and Feudel, Fred and Seehafer, Norbert}, title = {Dynamo bifurcations in an array of driven convection-like rolls}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14678}, year = {1998}, abstract = {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.}, language = {en} } @unpublished{ScheelSeehafer1997, author = {Scheel, Stefan and Seehafer, Norbert}, title = {Bifurcation to oscillations in three-dimensional Rayleigh-B{\´e}nard convection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14370}, year = {1997}, abstract = {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.}, language = {en} } @article{SchinkelMarwanDimigenetal.2009, author = {Schinkel, Stefan and Marwan, Norbert and Dimigen, Olaf and Kurths, J{\"u}rgen}, title = {Confidence bounds of recurrence-based complexity measures}, issn = {0375-9601}, doi = {10.1016/j.physleta.2009.04.045}, year = {2009}, abstract = {In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real- life data.}, language = {en} } @article{SchinkelMarwanKurths2009, author = {Schinkel, Stefan and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Brain signal analysis based on recurrences}, issn = {0928-4257}, doi = {10.1016/j.jphysparis.2009.05.007}, year = {2009}, abstract = {The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to Such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis.}, language = {en} } @unpublished{Schmidtmann1995, author = {Schmidtmann, Olaf}, title = {Modelling of the interaction of lower and higher modes in two-dimensional MHD-equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13790}, year = {1995}, abstract = {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}, language = {en} } @unpublished{SchmidtmannFeudelSeehafer1997, author = {Schmidtmann, Olaf and Feudel, Fred and Seehafer, Norbert}, title = {Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14431}, year = {1997}, abstract = {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.}, language = {en} } @unpublished{SchumacherSeehafer1999, author = {Schumacher, J{\"o}rg and Seehafer, Norbert}, title = {Bifurcation analysis of the plane sheet pinch}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14926}, year = {1999}, abstract = {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.}, language = {en} } @unpublished{Schwarz1994, author = {Schwarz, Udo}, title = {Einf{\"u}hrung in die nichtlineare Dynamik}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13525}, year = {1994}, abstract = {Aus dem Inhalt: 1. Einf{\"u}hrung 2. Motivation f{\"u}r die nichtlineare Dynamik 3. Logistische Abbildung (Parabel-Abbildung) 4. Lorenz-Gleichungen 5. Fraktale Selbst{\"a}hnlichkeit 6. Die Brownsche Bewegung 7. St{\"o}ße \& Billards 8. K{\"o}rper mit gravitativer Wechselwirkung 9. Glossar 10. Turbo-Pascal-Texte 11. IDL-Texte 12. Reduce-Texte}, language = {de} } @article{Schwarz1994, author = {Schwarz, Udo}, title = {Das Maunder-Minimum : alles sonnenklar, oder?}, year = {1994}, abstract = {Im vorletzten Absatz des o.g. Kurzberichtes befindet sich eine falsche Aussage zur C14-Produktion waehrend des Maunder-Minimums. Wie aus der in meiner Abbildung gezeigten Delta C14-Haeufigkeit fuer den Zeitraum des Maunder-Minimums hervorgeht, war die C14-Produktion zu dieser Zeit erhoeht statt, wie von Herrn Buehrke und anderen Autoren in der Literatur behauptet, erniedrigt. Die allgemein akzeptierte Begruendung fuer die erhoehte C14-Produktion lautet: Der geringere Sonnenwind schirmt die Erde weniger stark von der kosmischen Strahlung ab.}, language = {de} } @article{SchwarzBenzKurthsetal.1993, author = {Schwarz, udo and Benz, Arnold O. and Kurths, J{\"u}rgen and Witt, Annette}, title = {Analysis of solar spike events by means of symbolic dynamics methods}, issn = {004-6361}, year = {1993}, abstract = {Using quantities of symbolic dynamics, such as mutual information, Shannon information and algorithmic complexity, we have searched for interrelations of spikes emitted simultaneously at different frequencies during the impulsive phase of a flare event. As the spikes are related to the flare energy release and are interpreted as emissions originating at different sites having different magnetic field strengths, any relation in frequency is interpretated as a relation in space. This approach is appropriate to characterize such spatio-temporal patterns, whereas the popular estimate of fractal dimensions can be applied to low-dimensional systems only. Depending on the energy release and emission processes, two types of fragmentation are possible: a scenario of global organization (spikes are emitted in a succession of similar events by the same system) or a scenario of local organization (many systems triggered by an initial event). Mutual information which is a generalization of correlation indicates a relation in frequency beyond the bandwidth of individual spikes. The scans in the spectrograms with large mutual information also show a low level of Shannon information and algorithmic complexity, indicating that the simultaneous appearance of spikes at other frequencies is not a completely stochastic phenomenon (white noise). It may be caused by a nonlinear deterministic system or by a Markov process. By means of mutual information we find a memory over frequency intervals up to 60 MHz. Shannon information and algorithmic complexity concern the mbox{whole} frequency region, i.e. the global source region. A global organization is also apparent in quasi-periodic changes of the Shannon information and algorithmic complexity in the range of 2 - 8 seconds. The finding is compatible with a scenario of local organization in which the information of one event spreads spatially and triggers further events at different places. The region is not an ensemble of independently flashing sources, each representing a system that cascades in energy after an initial trigger. On the contrary, there is a causal connection between the sources at any time. The analysis of the four spike events suggests that the structure in frequency is not stochastic but a process in which spikes at nearby locations are simultaneously triggered by a common exciter.}, language = {en} } @unpublished{Seehafer1995, author = {Seehafer, Norbert}, title = {Nature of the α effect in magnetohydrodynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13919}, year = {1995}, abstract = {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.}, language = {en} } @unpublished{SeehaferSchumacher1998, author = {Seehafer, Norbert and Schumacher, J{\"o}rg}, title = {Resistivity profile and instability of the plane sheet pinch}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14686}, year = {1998}, abstract = {The stability of the quiescent ground state of an incompressible, viscous and electrically conducting fluid sheet, bounded by stress-free parallel planes and driven by an external electric field tangential to the boundaries, is studied numerically. The electrical conductivity varies as cosh-2(x1/a), where x1 is the cross-sheet coordinate and a is the half width of a current layer centered about the midplane of the sheet. For a <~ 0.4L, where L is the distance between the boundary planes, the ground state is unstable to disturbances whose wavelengths parallel to the sheet lie between lower and upper bounds depending on the value of a and on the Hartmann number. Asymmetry of the configuration with respect to the midplane of the sheet, modelled by the addition of an externally imposed constant magnetic field to a symmetric equilibrium field, acts as a stabilizing factor.}, language = {en} } @unpublished{SeehaferSchumacher1997, author = {Seehafer, Norbert and Schumacher, J{\"o}rg}, title = {Squire's theorem for the magnetohydrodynamic sheet pinch}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14628}, year = {1997}, abstract = {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 Alfv{\´e}n velocity) are raised from small values, two-dimensional perturbations become unstable first.}, language = {en} } @unpublished{SeehaferZienickeFeudel1996, author = {Seehafer, Norbert and Zienicke, Egbert and Feudel, Fred}, title = {Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14328}, year = {1996}, abstract = {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.}, language = {en} } @book{SeehaferZienickeFeudel1996, author = {Seehafer, Norbert and Zienicke, Egbert and Feudel, Fred}, title = {Absence of magnetohydrodynamic activity in the voltage-driven sheet}, series = {Preprint NLD}, volume = {32}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {8 S.}, year = {1996}, language = {en} } @article{SitzSchwarzKurths2004, author = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen}, title = {The unscented Kalman filter : a powerful tool for data analysis}, year = {2004}, language = {en} } @article{SitzSchwarzKurthsetal.2001, author = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen and Maus, Doris and Wiese, Michael and Warnecke, G{\"u}nter}, title = {Signatures of acoustic emission signals generated during high speed cutting}, year = {2001}, abstract = {Acoustic emission signals generated during high speed cutting of steel are investigated. The data are represen ted in time-folded form. Several methods from linear and nonlinear data analysis based on time- and frequency- domain are applied to the data and reveal signatures of the observed acoustic emission signal. These investiga tions are necessary for modeling the cutting process by means of differential equations.}, language = {en} } @book{SpahnHertzschBrilliantov1995, author = {Spahn, Frank and Hertzsch, Jan-Martin and Brilliantov, Nikolai V.}, title = {The role of particle collisions for the dynamics in planetary rings}, series = {Preprint NLD}, volume = {14}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {23 S.}, year = {1995}, language = {en} } @article{SpahnKrivovSremcevicetal.2003, author = {Spahn, Frank and Krivov, Alexander V. and Sremcevic, Miodrag and Schwarz, U. and Kurths, J{\"u}rgen}, title = {Stochastic forces in circumplanetary dust dynamics}, year = {2003}, abstract = {Charged dust grains in circumplanetary environments experience, beyond various deterministic forces, also stochastic perturbations caused, by fluctuations of the magnetic field, the charge of the grains, by chaotic rotation of aspherical grains, etc. Here we investigate the dynamics of a dust population in a circular orbit around a planet which is perturbed by a stochastic planetary magnetic field B', modeled by an isotropically Gaussian white noise. The resulting perturbation equations give rise to a modified diffusion of the inclinations i and eccentricities e. The diffusion coefficient is found to be D proportional to w^2 O /n^2 , where the gyrofrequency, the Kepler frequency, and the synodic frequency are denoted by w , O, and n, respectively. This behavior has been checked against numerical simulations. We have chosen dust grains (1 m in radius) ejected from Jupiter's satellite Europa in circular equatorial orbits around Jupiter and integrated numerically their trajectories over their typical lifetimes (100 years). The particles were exposed to a Gaussian fluctuating magnetic field B' with the same statistical properties as in the analytical treatment. These simulations have confirmed the analytical results. The theoretical studies showed the statistical properties of B' to be of decisive importance. To estimate them, we analyzed the magnetic field data obtained by the Galileo spacecraft magnetometer at Jupiter and found almost Gaussian fluctuations of about 5\% of the mean field and exponentially decaying correlations. This results in a diffusion of orbital inclinations and eccentricities of the dust grains of about ten percent over the lifetime of the particles. For smaller dusty motes or for close-in particles (e.g., in Jovian gossamer rings) stochastics might well dominate the dynamics.}, language = {en} } @article{ThielRomanoSchwarzetal.2001, author = {Thiel, Marco and Romano, Maria Carmen and Schwarz, Udo and Kurths, J{\"u}rgen and Hasinger, G{\"u}nther and Belloni, Tomaso}, title = {Nonlinear Time series analysis of the X-ray flux of compact objects}, issn = {0004-640x}, year = {2001}, abstract = {We analyse the X-ray light curves of compact objects using linear and nonlinear time series analysis methods. A Power Density Spectrum (PDS) describes the overall second order properties of the observed data well. To look beyond we propose the nonlinear Q-statistic to detect an asymmetry of the time series. This allows us to find relevant time scales. This method even grants a subclassification of the known states of X-ray sources.}, language = {en} } @unpublished{ThiessenhusenEspositoKurthsetal.1995, author = {Thiessenhusen, Kai-Uwe and Esposito, Larry W. and Kurths, J{\"u}rgen and Spahn, Frank}, title = {Detection of hidden resonances in Saturn's B-ring}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13618}, year = {1995}, abstract = {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.}, language = {en} } @article{TimmerSchwarzVossetal.2000, author = {Timmer, Jens and Schwarz, Udo and Voss, Henning U. and Wardinski, Ingo and Belloni, Tomaso and Hasinger, G{\"u}nther and VanDerKlis, Michael and Kurths, J{\"u}rgen}, title = {Linear and Nonlinear Time Series Analysis of the Black Hole Candidate Cygnus X-1}, year = {2000}, abstract = {We analyze the variability in the x-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the overall second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear and nonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data.}, language = {en} } @book{VolosevichMeister1998, author = {Volosevich, A. V. and Meister, Claudia-Veronika}, title = {Nonlinear interaction of Farley-Buneman waves}, series = {Preprint NLD}, volume = {52}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {13 S.}, year = {1998}, language = {en} }