Amplitude Equation for the Rosensweig Instability(Non Equilibrium Soft Matter)

概要

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The Rosensweig instability is a prominent example for a surface driven instability, where the deformation of the surface is amplified by an external generalized force, the normal magnetic field, and finally settles at a spatial pattern of spike deformations. This property has so far prohibited the derivation of an amplitude equation by means of the standard weakly nonlinear analysis. Here we give a derivation of the appropriate amplitude equation based on the hydrodynamic equations and the appropriate boundary conditions. We stress the fact, that even though the final pattern does not involve flow, the system has to be treated dynamically. The observed static pattern has to be interpreted as the limiting case of a frozen-in characteristic mode. The amplitude equation finally obtained contains first, for the ferrogel case also second order, time derivatives as well as quadratic (for the hexagonal case) and cubic nonlinearities in the amplitudes.
理論物理学刊行会の論文
2008-12-05