Year: 2003
Type: preprint
Abstract: 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 transform of the surface profile. The resulting third order amplitude equation describing the slow modulation of the basic pattern is shown to be purely local.
Source: arXiv (Cornell University)
Authors: Friedrichs, Rene, Engel, Andreas
Institutions: ABB (Germany), Otto-von-Guericke-Universität Magdeburg
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1558566974