Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

1 Publication
Krein space related perturbation theory for MHD α²-dynamos and resonant unfolding of diabolical points
Kirillov, O.; Günther, U.;
The spectrum of the spherically symmetric α²-dynamo is studied in the case of idealized boundary conditions. Starting from the exact analytical solutions of models with constant α²-profiles a perturbation theory and a Galerkin technique are developed in a Krein-space approach. With the help of these tools a very pronounced α²-resonance pattern is found in the deformations of the spectral mesh as well as in the unfolding of the diabolical points located at the nodes of this mesh. Non-oscillatory as well as oscillatory dynamo regimes are obtained. A Fourier component based estimation technique is developed for obtaining the critical α²-profiles at which the eigenvalues enter the right spectral half-plane with nonvanishing imaginary components (at which overcritical oscillatory dynamo regimes form). Finally, Fréchet derivative (gradient) based methods are developed, suitable for further numerical investigations of Krein-space related setups like MHD α²-dynamos or models of PT-symmetric quantum mechanics.
Keywords: Krein space, MHD dynamo, diabolical point, exceptional point, spectral deformation, perturbation theory, resonance, Galerkin method
  • Lecture (Conference)
    International Congress of Mathematicians, 22.-30.08.2006, Madrid, Spain

Publ.-Id: 8346