The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids

Details The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids

2002-04-09

arxiv.org/abs/cond-mat/0204198v1

Int. J. Modern Phys. B 16 (2002) 1155-1170

Physics

Condensed Matter

Soft Condensed Matter

11 pages, 1 figure

Scientific paper

10.1142/S0217979202010105

The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities of the Rosensweig instability are entirely triggered by the properties of a deformed and a priori unknown surface. The resulting problems in defining an adjoint operator for such nonlinearities are illustrated. The implications concerning amplitude equations for pattern forming systems with a deformed surface are discussed.

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