Inertial manifolds and completeness of eigenmodes for unsteady magnetic dynamos

Physica D: Nonlinear Phenomena

Volumn 194, Issue 3-4, 2004, Pages 297-319

  Liu, Weijiu ^a   Haller, George ^a  

^a Massachusetts Institute of Technology   (United States)

Author keywords

Eigenmodes; Inertial manifold; Magnetic dynamos

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; MAGNETIC DEVICES; MAGNETIC FIELDS; MATHEMATICAL TECHNIQUES; THEOREM PROVING;

EIGENMODES; INERTIAL MANIFOLD; MAGNETIC DYNAMOS; MAGNETIC ENERGY;

DC GENERATORS;

EID: 2942592397     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2003.03.002     Document Type: Article

References (25)

1. R. Adams, Sobolev Spaces, Academic Press, New York, 1975.
2. S. Childress, A. Gilbert, Stretch, Twist, and Fold: The Fast Dynamo, Springer-Verlag, Berlin, 1995.
3. Chow S., Lu K., Mallet-Paret J., Floquet theory for parabolic differential equations. J. Diff. Eq. 109:1994;147-200.
4. I.D. Chueshov, Introduction to the Theory of Infinite-dimensional Dissipative Systems, Acta Scientific Publishing House, Kharkiv, 2002.
5. Dudley N.L., James R.W., Time-dependent kinematic dynamos with stationary flows. Proc. R. Soc. London, Ser. A. 425:1989;407-429.
6. Gailitis A., Lielausis O., Dement'ev S., Platacis E., Cifersons A., Gerbeth G., Gundrum T., Stefani F., Christen M., Hänel H., Will G., Detection of a flow induced magnetic field eigenmode. Phys. Rev. Lett. 84:2000;4365-4368.
7. Gilbert A., Advected fields in maps, I, Magnetic flux growth in the stretch-fold-shear map. Physica D. 166:2002;167-196.
8. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, New York, 1981.
9. Kaiser R., Towards a poloidal magnetic field theorem. Geophys. Astrophys. Fluid Dynam. 80:1995;129-144.
10. N. Koksch, S. Siegmund, Inertial manifolds for abstract nonautonomous dynamical systems and for nonautonomous evolution equations, Proceedings of the EQUADIFF 2001, 2001, pp. 221-266.
11. Koksch N., Siegmund S., Pullback attracting inertial manifolds for nonautonomous dynamical systems. J. Dynam. Diff. Eqs. 14:2002;889-941.
12. N. Koksch, S. Siegmund, Cone Invariance and Squeezing Properties for Inertial Manifolds of Nonautonomous Evolution Equations, vol. 60, Banach Center Publications, pp. 27-48.
13. P. Kuchment, Floquet Theory for Partial Differential Equations, Birkhauser, Basel, 1993.
14. Liu W., Haller G., Strange eigenmodes and decay of variance in the mixing of diffusive tracers. Physica D. 188:2004;1-39.
15. Moffatt H.K., Proctor M.R.E., Topological constraints associated with fast dynamo action. J. Fluid Mech. 154:1985;493-507.
16. Normand C., Ponomarenko dynamo with time-periodic flow. Phys. Fluids. 15:2003;1606-1611.
17. Otani N.F., A fast kinematic dynamo in two-dimensional time-dependent flows. J. Fluid Mech. 253:1993;327-340.
18. Peffley N.L., Cawthorne A.B., Lathrop D.P., Toward a self-generating magnetic dynamo: the role of turbulence. Phys. Rev. E. 61:2000;5287-5294.
19. Pierrehumbert R.T., Tracer microstructure in the large-eddy dominated regime. Solitons Fract. 4:1994;1091-1110.
20. Ponomarenko Y.B., Theory of the hydromagnetic generator. J. Appl. Mech. Tech. Phys. 14:1973;775-778.
21. G.R. Sell, Y. You, Dynamics of Evolutionary Equations, Springer, New York, 2002.
22. R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, 2nd ed., SIAM, Philadelphia, PA, 1995.
23. F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer, Berlin, 1990.
24. V.I. Yudovich, The Linearization Method in Hydrodynamical Stability Theory, AMS Translations of Mathematical Monographs, AMS, Providence, 1989.
25. Ya.B. Zeldovich, A.A. Ruzmaikin, D.D. Sokoloff, Magnetic fields in astrophysics, in: The Fluid Mechanics of Astrophysics and Geophysics, vol. 3, Gordon and Breach, London, 1983.