@unpublished{MaassRieder1996,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}
}
@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}
}
@unpublished{BraunFeudelGuzdar1998,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{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{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{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{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{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{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{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{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{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{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{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{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{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{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{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{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}
}