| Item Type: |
Article
|
| Erschienen: |
2009 |
| Creators: |
Kirillov, O. N. and Günther, U. and Stefani, F. |
| Title: |
Determining role of Krein signature for three-dimensional Arnold tongues of oscillatory dynamos |
| Language: |
English |
| Journal or Publication Title: |
Physical Review E 79 |
| Divisions: |
16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Dynamics and Vibrations |
| Date Deposited: |
19 Sep 2012 14:21 |
| Official URL: |
http://link.aps.org/doi/10.1103/PhysRevE.79.016205 |
| Identification Number: |
doi:10.1103/PhysRevE.79.016205 |
| Alternative Abstract: |
| Alternative abstract | Language |
|---|
| Using a homotopic family of boundary eigenvalue problems for the mean-field α2 dynamo with helical turbulence parameter α(r)=α0+γΔα(r) and homotopy parameter β∊[0,1], we show that the underlying network of diabolical points for Dirichlet (idealized, β=0) boundary conditions substantially determines the choreography of eigenvalues and thus the character of the dynamo instability for Robin (physically realistic, β=1) boundary conditions. In the (α0,β,γ) space the Arnold tongues of oscillatory solutions at β=1 end up at the diabolical points for β=0. In the vicinity of the diabolical points the space orientation of the three-dimensional tongues, which are cones in first-order approximation, is determined by the Krein signature of the modes involved in the diabolical crossings at the apexes of the cones. The Krein space-induced geometry of the resonance zones explains the subtleties in finding α profiles leading to spectral exceptional points, which are important ingredients in recent theories of polarity reversals of the geomagnetic field. | English |
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