Event image

Experiments involving a plate of magnetic fluid in the presence of a magnetic field have shown that it is possible for stable localised spots on the surface of the magnetic to exist. Building on work analysing localised patterns in reaction –diffusion equations, we try to explain the nucleation of such spots for the magnetic fluid and some of their properties away from onset. In particular, I will show that the equations governing the free-surface of the magnetic fluid obey an energy principle. Furthermore, an approximate Hamiltonian formulation can be found near onset that simplifies a centre-manifold reduction for patterns in the one-dimensional case. Finally, we show some numerical continuation results for 2D and 3D localised Ferropatterns and relate the results to work on reaction-diffusion systems in the presence of a conserved quantity.