Die Bevorzugung hexagonaler Strukturen bei symmetrischen Oberflächenformen magnetischer Flüssigkeiten

Abstract

A magnetic ideal fluid under the influence of a vertical homogeneous magnetic field is considered. Over rhombic lattices with arbitrary angle equilibrium configurations of the free surface are determined. Especially, for some lattice length $l_c$ the bifurcation equations are solved and over regular hexagonal lattices with lattice length $I>l_c$ solutions of the bifurcation equations are given. The regular hexagonal structures, in an interval depending on physical parameters, have smallest energy.