@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}
}
@article{Seehafer1995,
  author    = {Seehafer, Norbert},
  title     = {The turbulent electromotive force in the high-conductivity limit},
  year      = {1995},
  language  = {en}
}
@article{FeudelSeehaferSchmidtmann1995,
  author    = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf},
  title     = {Fluid helicity and dynamo bifurcations},
  year      = {1995},
  language  = {en}
}
@article{SeehaferFeudelSchmidtmann1996,
  author    = {Seehafer, Norbert and Feudel, Fred and Schmidtmann, Olaf},
  title     = {Nonlinear dynamo with ABC forcing},
  year      = {1996},
  language  = {en}
}
@article{Seehafer1996,
  author    = {Seehafer, Norbert},
  title     = {Nature of the alpha effect in magnetohydrodynamics},
  year      = {1996},
  language  = {en}
}
@article{MirandaRempelChianetal.2013,
  author    = {Miranda, Rodrigo A. and Rempel, Erico L. and Chian, Abraham C.-L. and Seehafer, Norbert and Toledo, Benjamin A.},
  title     = {Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations},
  year      = {2013},
  language  = {en}
}
@article{HassaninKliemSeehafer2016,
  author    = {Hassanin, Alshaimaa and Kliem, Bernhard and Seehafer, Norbert},
  title     = {Helical kink instability in the confined solar eruption on 2002 May 27},
  series = {Astronomische Nachrichten = Astronomical notes},
  volume    = {337},
  journal   = {Astronomische Nachrichten = Astronomical notes},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {0004-6337},
  doi       = {10.1002/asna.201612446},
  pages     = {1082 -- 1089},
  year      = {2016},
  language  = {en}
}
@article{KuzanyanPipinSeehafer2006,
  author    = {Kuzanyan, Kirill M. and Pipin, Valerij V. and Seehafer, Norbert},
  title     = {The alpha effect and the observed twist and current helicity of solar magnetic fields},
  issn      = {0038-0938},
  doi       = {10.1007/s11207-006-1636-6},
  year      = {2006},
  abstract  = {We present a straightforward comparison of model calculations for the alpha-effect, helicities, and magnetic field line twist in the solar convection zone with magnetic field observations at atmospheric levels. The model calculations are carried out in a mixing-length approximation for the turbulence with a profile of the solar internal rotation rate obtained from helioseismic inversions. The magnetic field data consist of photospheric vector magnetograms of 422 active regions for which spatially-averaged values of the force-free twist parameter and of the current helicity density are calculated, which are then used to determine latitudinal profiles of these quantities. The comparison of the model calculations with the observations suggests that the observed twist and helicity are generated in the bulk of the convection zone, rather than in a layer close to the bottom. This supports two-layer dynamo models where the large-scale toroidal field is generated by differential rotation in a thin layer at the bottom while the alpha-effect is operating in the bulk of the convection zone. Our previous observational finding was that the moduli of the twist factor and of the current helicity density increase rather steeply from zero at the equator towards higher latitudes and attain a certain saturation at about 12 - 15 degrees. In our dynamo model with algebraic nonlinearity, the increase continues, however, to higher latitudes and is more gradual. This could be due to the neglect of the coupling between small-scale and large-scale current and magnetic helicities and of the latitudinal drift of the activity belts in the model},
  language  = {en}
}
@article{DonnerSeehaferSanjuanetal.2006,
  author    = {Donner, Reik Volker and Seehafer, Norbert and Sanjuan, Miguel Angel Fernandez and Feudel, Fred},
  title     = {Low-dimensional dynamo modelling and symmetry-breaking bifurcations},
  series = {Physica. D, Nonlinear phenomena},
  volume    = {223},
  journal   = {Physica. D, Nonlinear phenomena},
  number    = {2},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2006.08.022},
  pages     = {151 -- 162},
  year      = {2006},
  abstract  = {Motivated by the successful Karlsruhe dynamo experiment, a relatively low-dimensional dynamo model is proposed. It is based on a strong truncation of the magnetohydrodynamic (MHD) equations with an external forcing of the Roberts type and the requirement that the model system satisfies the symmetries of the full MHD system, so that the first symmetry-breaking bifurcations can be captured. The backbone of the Roberts dynamo is formed by the Roberts flow, a helical mean magnetic field and another part of the magnetic field coupled to these two by triadic mode interactions. A minimum truncation model (MTM) containing only these energetically dominating primary mode triads is fully equivalent to the widely used first-order smoothing approximation. However, it is shown that this approach works only in the limit of small wave numbers of the excited magnetic field or small magnetic Reynolds numbers (\$Rm ll 1\$). To obtain dynamo action under more general conditions, secondary mode},
  language  = {en}
}
@article{PalusKurthsSchwarzetal.2007,
  author    = {Palus, Milan and Kurths, J{\"u}rgen and Schwarz, Udo and Seehafer, Norbert and Novotna, Dagmar and Charvatova, Ivanka},
  title     = {The solar activity cycle is weakly synchronized with the solar inertial motion},
  doi       = {10.1016/j.physleta.2007.01.039},
  year      = {2007},
  abstract  = {We study possible interrelations between the 300-year record of the yearly sunspot numbers and the solar inertial motion (SIM) using the recently developed technique of synchronization analysis. Phase synchronization of the sunspot cycle and the SIM is found and statistically confirmed in three epochs (1734-1790, 1855-1875 and 1907-1960) of the whole period 1700-2000. These results give quantitative support to the hypothesis that there is a weak interaction between the solar activity and the SIM.},
  language  = {en}
}
@article{FeudelTuckermanGellertetal.2015,
  author    = {Feudel, Fred and Tuckerman, L. S. and Gellert, Marcus and Seehafer, Norbert},
  title     = {Bifurcations of rotating waves in rotating spherical shell convection},
  series = {Physical Review E},
  volume    = {92},
  journal   = {Physical Review E},
  number    = {5},
  publisher = {American Physical Society},
  address   = {Woodbury},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.92.053015},
  year      = {2015},
  abstract  = {The dynamics and bifurcations of convective waves in rotating and buoyancy-driven spherical Rayleigh-Benard convection are investigated numerically. The solution branches that arise as rotating waves (RWs) are traced by means of path-following methods, by varying the Rayleigh number as a control parameter for different rotation rates. The dependence of the azimuthal drift frequency of the RWs on the Ekman and Rayleigh numbers is determined and discussed. The influence of the rotation rate on the generation and stability of secondary branches is demonstrated. Multistability is typical in the parameter range considered.},
  language  = {en}
}
@article{KuzanyanPipinSeehafer2005,
  author    = {Kuzanyan, Kirill M. and Pipin, V. V. and Seehafer, Norbert},
  title     = {On the alpha effect and current helicity of solar magnetic fields},
  isbn      = {92-9092-911-1},
  year      = {2005},
  language  = {en}
}
@article{ZienickeSeehaferLietal.2003,
  author    = {Zienicke, Egbert and Seehafer, Norbert and Li, B.-W. and Schumacher, J{\"o}rg and Politano, H. and Thess, H.},
  title     = {Voltage-driven instability of electrically conducting fluids},
  year      = {2003},
  language  = {en}
}
@article{SeehaferFuhrmannValorietal.2007,
  author    = {Seehafer, Norbert and Fuhrmann, M. and Valori, Gherardo and Kliem, Bernhard},
  title     = {Force-free magnetic fields in the solar atmosphere},
  year      = {2007},
  language  = {en}
}
@article{FeudelGellertRuedigeretal.2003,
  author    = {Feudel, Fred and Gellert, Marcus and R{\"u}diger, Sten and Witt, Annette and Seehafer, Norbert},
  title     = {Dynamo effect in a driven helical flow},
  year      = {2003},
  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}
}
@article{KliemSeehafer2022,
  author    = {Kliem, Bernhard and Seehafer, Norbert},
  title     = {Helicity shedding by flux rope ejection},
  series = {Astronomy and astrophysics : an international weekly journal},
  volume    = {659},
  journal   = {Astronomy and astrophysics : an international weekly journal},
  publisher = {EDP Sciences},
  address   = {Les Ulis},
  issn      = {0004-6361},
  doi       = {10.1051/0004-6361/202142422},
  pages     = {9},
  year      = {2022},
  abstract  = {We quantitatively address the conjecture that magnetic helicity must be shed from the Sun by eruptions launching coronal mass ejections in order to limit its accumulation in each hemisphere. By varying the ratio of guide and strapping field and the flux rope twist in a parametric simulation study of flux rope ejection from approximately marginally stable force-free equilibria, different ratios of self- and mutual helicity are set and the onset of the torus or helical kink instability is obtained. The helicity shed is found to vary over a broad range from a minor to a major part of the initial helicity, with self helicity being largely or completely shed and mutual helicity, which makes up the larger part of the initial helicity, being shed only partly. Torus-unstable configurations with subcritical twist and without a guide field shed up to about two-thirds of the initial helicity, while a highly twisted, kink-unstable configuration sheds only about one-quarter. The parametric study also yields stable force-free flux rope equilibria up to a total flux-normalized helicity of 0.25, with a ratio of self- to total helicity of 0.32 and a ratio of flux rope to external poloidal flux of 0.94. These results numerically demonstrate the conjecture of helicity shedding by coronal mass ejections and provide a first account of its parametric dependence. Both self- and mutual helicity are shed significantly; this reduces the total initial helicity by a fraction of ∼0.4--0.65 for typical source region parameters.},
  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}
}
@article{SeehaferSchumacher2000,
  author    = {Seehafer, Norbert and Schumacher, J{\"o}rg},
  title     = {Patterns in an electrically driven conducting fluid layer},
  year      = {2000},
  abstract  = {The equilibrium states of electrically conducting fluids or plasmas have been a subject of intense study for a long time, motivated in particular by the interest in controlled thermonuclear fusion, as well as that in space and astrophysical phenomena such as plasma loops in the solar corona. If high temperatures prohibit solid walls, a conducting fluid can be held together by the action of an electric current passing through it with the pressure gradients being balanced by the Lorentz force. The resultant configuration is known as a pinch. In this paper we report on studies of the pinch in the geometry of a plane sheet.},
  language  = {en}
}
@article{SeehaferSchumacher2000,
  author    = {Seehafer, Norbert and Schumacher, J{\"o}rg},
  title     = {Bifurcation analysis of an electrically driven fluid layer},
  year      = {2000},
  abstract  = {The equilibrium states of electrically conducting fluids or plasmas have been a subject of intense study for a long time, motivated in particular by the interest in controlled thermonuclear fusion, as well as that in space and astrophysical phenomena such as plasma loops in the solar corona. If high temperatures prohibit solid walls, a conducting fluid can be held together by the action of an electric current passing through it with the pressure gradients being balanced by the Lorentz force. The resultant configuration is known as a pinch. In this paper we report on studies of the pinch in the geometry of a plane sheet.},
  language  = {en}
}
@article{DemircanSeehafer2000,
  author    = {Demircan, Ayhan and Seehafer, Norbert},
  title     = {Heteroclinic behavior in rotating Rayleigh-B{\´e}nard convection},
  year      = {2000},
  abstract  = {We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven, rotating fluid layer. Periodic boundary conditions in the horizontal directions and stress-free boundary conditions at the top and bottom are assumed.},
  language  = {en}
}
@article{KurthsSeehaferSpahn1999,
  author    = {Kurths, J{\"u}rgen and Seehafer, Norbert and Spahn, Frank},
  title     = {Nichtlineare Dynamik in der Physik : Forschungsbeispiele und Forschungstrends},
  isbn      = {3-540-65329- 5},
  year      = {1999},
  language  = {de}
}
@article{BrownCanfieldFieldetal.1999,
  author    = {Brown, M. R. and Canfield, R. C. and Field, G. and Kulsrud, R. and Pevtsov, A. A. and Rosner, R. and Seehafer, Norbert},
  title     = {Magnetic helicity in space and laboratory plasmas: Editorial summary},
  year      = {1999},
  language  = {en}
}
@article{DemircanSeehafer1999,
  author    = {Demircan, Ayhan and Seehafer, Norbert},
  title     = {Bifurcation to oscillations and chaos in rotating convection},
  year      = {1999},
  language  = {en}
}
@article{SchumacherKliemSeehafer2000,
  author    = {Schumacher, J{\"o}rg and Kliem, Bernhard and Seehafer, Norbert},
  title     = {Three-dimensional spontaneous magnetic reconnection in neutral current sheets},
  year      = {2000},
  language  = {en}
}
@book{SchumacherKliemSeehafer1999,
  author    = {Schumacher, J{\"o}rg and Kliem, Bernhard and Seehafer, Norbert},
  title     = {Three-dimensional spontaneous magnetic reconnection in neutral current sheets},
  series = {Preprint series / Astrophysikalisches Institut Potsdam},
  volume    = {99,42},
  journal   = {Preprint series / Astrophysikalisches Institut Potsdam},
  publisher = {AIP},
  address   = {Potsdam},
  pages     = {26 S. : graph. Darst.},
  year      = {1999},
  language  = {en}
}
@article{RuedigerFeudelSeehafer1998,
  author    = {R{\"u}diger, Sten and Feudel, Fred and Seehafer, Norbert},
  title     = {Dynamo bifurcations in an array of driven convectionlike rolls},
  year      = {1998},
  language  = {en}
}
@article{SeehaferFeudelGalanti1998,
  author    = {Seehafer, Norbert and Feudel, Fred and Galanti, B.},
  title     = {Bifurcations in a magnetofluid with helical forcing},
  isbn      = {1-563-47284-8},
  year      = {1998},
  language  = {en}
}
@article{Seehafer1998,
  author    = {Seehafer, Norbert},
  title     = {Filaments and the solar dynamo},
  isbn      = {1-88673-370-8},
  year      = {1998},
  language  = {en}
}
@article{SchmidtmannFeudelSeehafer1998,
  author    = {Schmidtmann, Olaf and Feudel, Fred and Seehafer, Norbert},
  title     = {Nonlinear Galerkin methods based on the concept of determining modes for the magnetohydrodynamic equations},
  year      = {1998},
  language  = {en}
}
@article{ZienickeSeehaferFeudel1998,
  author    = {Zienicke, Egbert and Seehafer, Norbert and Feudel, Fred},
  title     = {Bifurcations in two-dimensional Rayleigh-B{\´e}nard convection},
  year      = {1998},
  language  = {en}
}
@article{ScheelSeehafer1997,
  author    = {Scheel, S. and Seehafer, Norbert},
  title     = {Bifurcation to oscillations in three-dimensional Rayleigh-B{\´e}nard convection},
  year      = {1997},
  language  = {en}
}
@article{BraunFeudelSeehafer1997,
  author    = {Braun, Robert and Feudel, Fred and Seehafer, Norbert},
  title     = {Bifurcations and chaos in an array of forced vortices},
  year      = {1997},
  language  = {en}
}
@book{RuedigerFeudelSeehafer1998,
  author    = {R{\"u}diger, Sten and Feudel, Fred and Seehafer, Norbert},
  title     = {Dynamo bifurcations in an array of driven convectionlike rolls},
  series = {Preprint NLD},
  volume    = {43},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {6 S. : Ill.},
  year      = {1998},
  language  = {en}
}
@article{SeehaferSchumacher1998,
  author    = {Seehafer, Norbert and Schumacher, J{\"o}rg},
  title     = {Resistivity profile and instability of the plane sheet pinch},
  year      = {1998},
  language  = {en}
}