@unpublished{Feudel1996, author = {Feudel, Ulrike}, title = {Komplexes Verhalten in multistabilen, schwach dissipativen Systemen}, url =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 Diese Systeme zeichnen sich durch eine extrem hohe Flexibilit{\"a}t ihres Verhaltens aus.}, language = {de} } @unpublished{MeklerBoeckmannSokolovskaia2000, author = {Mekler, A. A. and B{\"o}ckmann, Christine and Sokolovskaia, N.}, title = {Particle distribution from spectral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technique allows us to determine via inversion the particle distributions of different types.}, language = {en} } @unpublished{ZakharovMeister2000, author = {Zakharov, Venjamin E. and Meister, Claudia-Veronika}, title = {Acceleration and heating in the auroral magnetosphere by current driven electrostatic ion cyclotron turbulence}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14959}, year = {2000}, abstract = {A numerical MHD model is developed to investigate acceleration and heating of both thermal and auroral plasma. This is done for magnetospheric flux tubes in which intensive field aligned currents flow. To give each of these tubes, the empirical Tsyganenko model of the magnetospheric field is used. The parameters of the background plasma outside the flux tube as well as the strength of the electric field of magnetospheric convection are given. Performing the numerical calculations, the distributions of the plasma densities, velocities, temperatures, parallel electric field and current, and of the coefficients of thermal conductivity are obtained in a self-consistent way. It is found that EIC turbulence develops effectively in the thermal plasma. The parallel electric field develops under the action of the anomalous resistivity. This electric field accelerates both the thermal and the auroral plasma. The thermal turbulent plasma is also subjected to an intensive heating. The increase of the plasma of the Earth's ionosphere. Besides, studying the growth and dispersion properties of oblique ion cyclotron waves excited in a drifting magnetized plasma, it is shown that under non-stationary conditions such waves may reveal the properties of bursts of polarized transverse electromagnetic waves at frequencies near the patron gyrofrequency.}, language = {en} } @unpublished{VolosevichMeister2000, author = {Volosevich, Alexandra and Meister, Claudia-Veronika}, title = {Nonlinear electrostatic ion-acoustic waves in the solar atmosphere}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14968}, year = {2000}, abstract = {Basing on recent solar models, the excitation of ion-acoustic turbulence in the weaklycollisional, fully and partially-ionized regions of the solar atmosphere is investigated. Within the frame of hydrodynamics, conditions are found under which the heating of the plasma by ion-acoustic type waves is more effective than the Joule heating. Taking into account wave and Joule heating effects, a nonlinear differential equation is derived, which describes the evolution of nonlinear ion-acoustic waves in the collisional plasma.}, 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} } @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{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} } @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} } @unpublished{VolosevichMeister1998, author = {Volosevich, Alexandra V. and Meister, Claudia-Veronika}, title = {Nonlinear interaction of Farley-Buneman waves}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14851}, year = {1998}, abstract = {The nonlinear interaction of waves excited by the modified two-stream instability (Farley-Buneman instability) is considered. It is found that, during the linear stage of wave growth, the enhanced pressure of the high-frequency part of the waves locally generates a ponderomotive force. This force acts on the plasma particles and redistributes them. Thus an additional electrostatic polarization field occurs, which influences the low-frequency part of the waves. Then, the low-frequency waves also cause a redistribution of the high-frequency waves. In the paper, a self-consistent system of equations is obtained, which describes the nonlinear interaction of the waves. It is shown that the considered mechanism of wave interaction causes a nonlinear stabilization of the high-frequency waves' growth and a formation of local density structures of the charged particles. The density modifications of the charged particles during the non-linear stage of wave growth and the possible interval of aspect angles of the high-frequency waves are estimated.}, 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{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{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{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} } @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} } @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{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} } @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} } @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} } @misc{OPUS4-5024, title = {T{\"a}tigkeitsbericht 1994-2000}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-48483}, year = {2004}, abstract = {Das Interdisziplin{\"a}re Zentrum f{\"u}r Nichtlineare Dynamik an der Universit{\"a}t Potsdam verbindet theoretisch-methodische Untersuchungen in Mathematik und theoretischer Physik mit einer Vielzahl anderer Wissenschaften und zielt auf eine fruchtbare Wechselwirkung zwischen Theorie und Experiment. Unter Einbezug von Instituten und Großforschungseinrichtungen, die insbesondere im Potsdamer Raum angesiedelt sind, soll sich ein {\"u}berregional bedeutender Schwerpunkt entwickeln, wie er an keiner anderen deutschen Universit{\"a}t in gleicher Weise interdisziplin{\"a}r angelegt ist.}, language = {de} } @phdthesis{Yin2010, author = {Yin, Fan}, title = {Mathematic approaches for the calibration of the CHAMP satellite magnetic field measurements}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-41201}, school = {Universit{\"a}t Potsdam}, year = {2010}, abstract = {CHAMP (CHAllenging Minisatellite Payload) is a German small satellite mission to study the earth's gravity field, magnetic field and upper atmosphere. Thanks to the good condition of the satellite so far, the planned 5 years mission is extended to year 2009. The satellite provides continuously a large quantity of measurement data for the purpose of Earth study. The measurements of the magnetic field are undertaken by two Fluxgate Magnetometers (vector magnetometer) and one Overhauser Magnetometer (scalar magnetometer) flown on CHAMP. In order to ensure the quality of the data during the whole mission, the calibration of the magnetometers has to be performed routinely in orbit. The scalar magnetometer serves as the magnetic reference and its readings are compared with the readings of the vector magnetometer. The readings of the vector magnetometer are corrected by the parameters that are derived from this comparison, which is called the scalar calibration. In the routine processing, these calibration parameters are updated every 15 days by means of scalar calibration. There are also magnetic effects coming from the satellite which disturb the measurements. Most of them have been characterized during tests before launch. Among them are the remanent magnetization of the spacecraft and fields generated by currents. They are all considered to be constant over the mission life. The 8 years of operation experience allow us to investigate the long-term behaviors of the magnetometers and the satellite systems. According to the investigation, it was found that for example the scale factors of the FGM show obvious long-term changes which can be described by logarithmic functions. The other parameters (offsets and angles between the three components) can be considered constant. If these continuous parameters are applied for the FGM data processing, the disagreement between the OVM and the FGM readings is limited to \pm1nT over the whole mission. This demonstrates, the magnetometers on CHAMP exhibit a very good stability. However, the daily correction of the parameter Z component offset of the FGM improves the agreement between the magnetometers markedly. The Z component offset plays a very important role for the data quality. It exhibits a linear relationship with the standard deviation of the disagreement between the OVM and the FGM readings. After Z offset correction, the errors are limited to \pm0.5nT (equivalent to a standard deviation of 0.2nT). We improved the corrections of the spacecraft field which are not taken into account in the routine processing. Such disturbance field, e.g. from the power supply system of the satellite, show some systematic errors in the FGM data and are misinterpreted in 9-parameter calibration, which brings false local time related variation of the calibration parameters. These corrections are made by applying a mathematical model to the measured currents. This non-linear model is derived from an inversion technique. If the disturbance field of the satellite body are fully corrected, the standard deviation of scalar error \triangle B remains about 0.1nT. Additionally, in order to keep the OVM readings a reliable standard, the imperfect coefficients of the torquer current correction for the OVM are redetermined by solving a minimization problem. The temporal variation of the spacecraft remanent field is investigated. It was found that the average magnetic moment of the magneto-torquers reflects well the moment of the satellite. This allows for a continuous correction of the spacecraft field. The reasons for the possible unknown systemic error are discussed in this thesis. Particularly, both temperature uncertainties and time errors have influence on the FGM data. Based on the results of this thesis the data processing of future magnetic missions can be designed in an improved way. In particular, the upcoming ESA mission Swarm can take advantage of our findings and provide all the auxiliary measurements needed for a proper recovery of the ambient magnetic field.}, 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{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} } @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} } @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} } @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} } @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{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} } @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{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} } @unpublished{ZienickeSeehaferFeudel1997, author = {Zienicke, Egbert and Seehafer, Norbert and Feudel, Fred}, title = {Bifurcations in two-dimensional Rayleigh-B{\´e}nard convection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14534}, year = {1997}, abstract = {Two-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at top and bottom and periodic boundary conditions in the horizontal direction is investigated by means of numerical simulation and bifurcation-analysis techniques. As the bouyancy forces increase, the primary stationary and symmetric convection rolls undergo successive Hopf bifurcations, bifurcations to traveling waves, and phase lockings. We pay attention to symmetry breaking and its connection with the generation of large-scale horizontal flows. Calculations of Lyapunov exponents indicate that at a Rayleigh number of 2.3×105 no temporal chaos is reached yet, but the system moves nonchaotically on a 4-torus in phase space.}, 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{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} } @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{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{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{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{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{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{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{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{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{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} } @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} } @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} } @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} } @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{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} } @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} } @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} } @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} } @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} } @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} } @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} } @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} } @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} } @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} } @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} } @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} } @book{VossKurthsSchwarz1996, author = {Voss, Henning U. and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Reconstruction of grand minima of solar activity from radiocarbon data : linear and nonlinear signal analysis}, series = {Preprint NLD}, volume = {28}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {14 S.}, year = {1996}, 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{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} } @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} } @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} } @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} } @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} } @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{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} } @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{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{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} } @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} } @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} } @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} } @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} } @unpublished{VossKurthsSchwarz1996, author = {Voss, Henning and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14083}, year = {1996}, abstract = {Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record.}, 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} } @unpublished{WittNeimanKurths1997, author = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen}, title = {Characterizing the dynamics of stochastic bistable systems by measures of complexity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14556}, year = {1997}, abstract = {The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.}, 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{WesselKonvickaWeidermannetal.2004, author = {Wessel, Niels and Konvicka, Jan and Weidermann, Frank and Nestmann, S. and Neugebauer, R. and Schwarz, U. and Wessel, A. and Kurths, J{\"u}rgen}, title = {Predicting thermal displacements in modular tool systems}, issn = {1054-1500}, year = {2004}, abstract = {In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated firstly from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE-algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and get again promising results. The thermally inducedaccuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems. errors can be estimated with 1-2 micrometer}, language = {en} } @article{WesselAssmusWeidermannetal.2004, author = {Wessel, Niels and Aßmus, Joerg and Weidermann, Frank and Konvicka, Jan and Nestmann, S. and Neugebauer, R. and Schwarz, Udo and Kurths, J{\"u}rgen}, title = {Modeling thermal displacements in modular tool systems}, year = {2004}, abstract = {In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated firstly from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE-algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and get again promising results. The thermally induced errors can be estimated with 1-2\${mu m}\$ accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.}, 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{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} } @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} } @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} } @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{WuLiChenetal.2009, author = {Wu, Ye and Li, Ping and Chen, Maoyin and Xiao, Jinghua and Kurths, J{\"u}rgen}, title = {Response of scale-free networks with community structure to external stimuli}, issn = {0378-4371}, doi = {10.1016/j.physa.2009.03.037}, year = {2009}, abstract = {The response of scale-free networks with community structure to external stimuli is studied. By disturbing some nodes with different strategies, it is shown that the robustness of this kind of network can be enhanced due to the existence of communities in the networks. Some of the response patterns are found to coincide with topological communities. We show that such phenomena also occur in the cat brain network which is an example of a scale-free like network with community structure. Our results provide insights into the relationship between network topology and the functional organization in complex networks from another viewpoint.}, 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} } @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{ZolotovaPonyavinMarwanetal.2009, author = {Zolotova, Nadezhda V. and Ponyavin, Dmitri I. and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Long-term asymmetry in the wings of the butterfly diagram}, issn = {0004-6361}, doi = {10.1051/0004-6361/200811430}, year = {2009}, abstract = {Aims. Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles. Methods. We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots. Results. We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator.}, language = {en} } @article{ZamoraLopezZhouKurths2009, author = {Zamora-Lopez, Gorka and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Graph analysis of cortical networks reveals complex anatomical communication substrate}, issn = {1054-1500}, doi = {10.1063/1.3089559}, year = {2009}, abstract = {Sensory information entering the nervous system follows independent paths of processing such that specific features are individually detected. However, sensory perception, awareness, and cognition emerge from the combination of information. Here we have analyzed the corticocortical network of the cat, looking for the anatomical substrate which permits the simultaneous segregation and integration of information in the brain. We find that cortical communications are mainly governed by three topological factors of the underlying network: (i) a large density of connections, (ii) segregation of cortical areas into clusters, and (iii) the presence of highly connected hubs aiding the multisensory processing and integration. Statistical analysis of the shortest paths reveals that, while information is highly accessible to all cortical areas, the complexity of cortical information processing may arise from the rich and intricate alternative paths in which areas can influence each other.}, language = {en} } @unpublished{WittKurthsKrauseetal.1994, author = {Witt, Annette and Kurths, J{\"u}rgen and Krause, F. and Fischer, K.}, title = {On the validity of a model for the reversals of the Earth's magnetic field}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13460}, year = {1994}, abstract = {We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.}, 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{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{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} } @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} }