Leapfrogging vortex rings in the Landau-Lifshitz equation
Abstract
Vortex rings are ubiquitous in fluids, with smoke rings being a familiar example. The interaction of multiple vortex rings produces complex dynamical behaviour, such as the leapfrogging motion first analysed by Helmholtz more than a century and a half ago. Here we report on numerical investigations of vortex ring dynamics in a different setting from fluids, namely, as solutions of the Landau-Lifshitz equation that models the evolution of the local magnetization in a ferromagnetic medium. We present the results of the first study on the dynamics of interacting magnetic vortex rings and provide a novel link between fluids and magnetism, by showing that a range of phenomena familiar in fluids are reproduced in ferromagnets. This includes the leapfrogging motion of a pair of vortex rings and evidence for the chaotic dynamics of a trio of rings.
Keywords
Cite
@article{arxiv.1402.6165,
title = {Leapfrogging vortex rings in the Landau-Lifshitz equation},
author = {Antti J. Niemi and Paul Sutcliffe},
journal= {arXiv preprint arXiv:1402.6165},
year = {2015}
}
Comments
18 pages, 9 figures. Version to appear in Nonlinearity