@unpublished{ZienickeSeehaferFeudel1997,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@unpublished{WittNeimanKurths1997,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@unpublished{VossKurthsSchwarz1996,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{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{SeehaferSchumacher1998,
  author    = {Seehafer, Norbert and Schumacher, J{\"o}rg},
  title     = {Resistivity profile and instability of the plane sheet pinch},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14686},
  year      = {1998},
  abstract  = {The stability of the quiescent ground state of an incompressible, viscous and electrically conducting fluid sheet, bounded by stress-free parallel planes and driven by an external electric field tangential to the boundaries, is studied numerically. The electrical conductivity varies as cosh-2(x1/a), where x1 is the cross-sheet coordinate and a is the half width of a current layer centered about the midplane of the sheet. For a <~ 0.4L, where L is the distance between the boundary planes, the ground state is unstable to disturbances whose wavelengths parallel to the sheet lie between lower and upper bounds depending on the value of a and on the Hartmann number. Asymmetry of the configuration with respect to the midplane of the sheet, modelled by the addition of an externally imposed constant magnetic field to a symmetric equilibrium field, acts as a stabilizing factor.},
  language  = {en}
}
@unpublished{SeehaferSchumacher1997,
  author    = {Seehafer, Norbert and Schumacher, J{\"o}rg},
  title     = {Squire's theorem for the magnetohydrodynamic sheet pinch},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14628},
  year      = {1997},
  abstract  = {The stability of the quiescent ground state of an incompressible viscous fluid sheet bounded by two parallel planes, with an electrical conductivity varying across the sheet, and driven by an external electric field tangential to the boundaries is considered. It is demonstrated that irrespective of the conductivity profile, as magnetic and kinetic Reynolds numbers (based on the Alfv{\´e}n velocity) are raised from small values, two-dimensional perturbations become unstable first.},
  language  = {en}
}
@unpublished{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{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}
}