@unpublished{Schmidtmann1995,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}
}
@article{FeudelSeehaferSchmidtmann1995,
  author    = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf},
  title     = {Fluid helicity and dynamo bifurcations},
  year      = {1995},
  language  = {en}
}
@unpublished{FeudelSeehaferSchmidtmann1995,
  author    = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf},
  title     = {Bifurcation phenomena of the magnetofluid equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13585},
  year      = {1995},
  abstract  = {We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier reprsentations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (incereasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non-magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by furhter, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory.},
  language  = {en}
}
@unpublished{FeudelSeehaferSchmidtmann1995,
  author    = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf},
  title     = {Fluid helicity and dynamo bifurcations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13882},
  year      = {1995},
  abstract  = {The bifurcation behaviour of the 3D magnetohydrodynamic equations has been studied for external forcings of varying degree of helicity. With increasing strength of the forcing a primary non-magnetic steady state loses stability to a magnetic periodic state if the helicity exceeds a threshold value and to different non-magnetic states otherwise.},
  language  = {en}
}
@phdthesis{Schmidtmann1996,
  author    = {Schmidtmann, Olaf},
  title     = {Nichlineare Galerkin-Verfahren f{\"u}r die 3D magnetohydrodynamischen Gleichungen},
  pages     = {IV, 93 S.},
  year      = {1996},
  language  = {de}
}
@article{SeehaferFeudelSchmidtmann1996,
  author    = {Seehafer, Norbert and Feudel, Fred and Schmidtmann, Olaf},
  title     = {Nonlinear dynamo with ABC forcing},
  year      = {1996},
  language  = {en}
}
@article{FeudelSeehaferSchmidtmann1996,
  author    = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf},
  title     = {Bifurcation phenomena of the magnetofluid equations},
  year      = {1996},
  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 representations 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 (increasing 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 further, 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}
}
@article{SchmidtmannFeudelSeehafer1997,
  author    = {Schmidtmann, Olaf and Feudel, Fred and Seehafer, Norbert},
  title     = {Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations},
  year      = {1997},
  language  = {en}
}
@book{SchmidtmannFeudelSeehafer1997,
  author    = {Schmidtmann, Olaf and Feudel, Fred and Seehafer, Norbert},
  title     = {Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations},
  series = {Preprint NLD},
  volume    = {35},
  journal   = {Preprint NLD},
  publisher = {Univ. Potsdam},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {16 S. : graph. Darst.},
  year      = {1997},
  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}
}