Low symmetry patterns on magnetic fluids

Abstract

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 lattice, is studied using a perturbative energy minimization procedure. Moreover, the interplay between the anisotropy and the broken up-down symmetry of the system is quantitatively analyzed.