René Friedrichs

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The formation of patterns of peaks on the free surface of a magnetic fluid subject to a magnetic field normal to the undisturbed interface is investigated theoretically. The relative stability of ridge, square, and hexagon planforms is studied using a perturbative energy minimization procedure. Extending previous studies the finite depth of the fluid layer(More)
The pattern formation on the free surface of a magnetic fluid subjected simultaneously to a vertical and a horizontal magnetic field is investigated theoretically. In this anisotropic system planforms less symmetric then squares and hexagons arise. The relative stability of parallel ridges and asymmetric patterns, periodic on a rectangular or a rhombic(More)
Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field, the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a(More)
– We derive a closed equation for the shape of the free surface of a magnetic fluid subject to an external magnetic field. The equation is strongly non-local due to the long range character of the magnetic interaction. We develop a systematic multiple scale perturbation expansion in which the non-locality is reduced to the occurrence of the Hilbert(More)
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