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

Adrian Lange
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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.

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Adrian Lange. 2002-04-09. The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids. https://doi.org/10.1142/s0217979202010105

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