Nucleation of Localised Ferro-patterns

Monday, June 3, 2013 - 2:00pm - 2:30pm
Keller 3-180
David Lloyd (University of Surrey)
Ferro-solitons and patches of localised patterns have been observed experimentally on the surface of a magnetic fluid in the presence of a uniform vertical magnetic field by Richter and Barashenkov (PRL 2005). In this talk, I will present some recent experimental results of Richter and link these with some analysis and numerical results of the equations governing the free-surface. It turns out that the system possesses an energy formulation and for the linear magnetisation law case a Hamiltonian formulation exists. This Hamiltonian formulation is then used to do Normal form analysis for one-dimensional interfacial localised patterns. We then present numerical results for these patterns and trace-out a two-parameter bifurcation diagram depicting the existence of one-dimensional interfacial localised patterns. Finally, we present some preliminary results looking at a general nonlinear magnetisation law and two-dimensional interfacial localised patterns.
MSC Code: