The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids
arXiv:cond-mat/0204198 · doi:10.1142/S0217979202010105
Abstract
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.
11 pages, 1 figure