Making Mountains out of Magnets: Localised Patterns on the Surface of a Ferrofluid

Dan Hill, University of Surrey, will be presenting at this event.

Part of the Leeds Applied Nonlinear Dynamics seminar series.

Abstract: 

Localised patterns, where a finite patch of heterogeneous solution is surrounded by a homogeneous flat state, are observed in many experiments and numerical simulations. However, our analytical understanding of such structures remains extremely limited, especially in two dimensions (and higher). In 2005, localised axisymmetric spots were observed on the  surface of a magnetic fluid, known as a ferrofluid, after a uniform magnetic field was applied vertically through the ferrofluid. Using these experimental results as motivation, we study the existence of small-amplitude localised radial patterns in the ferrofluid experiment.

In this talk, I will introduce some of the techniques required in proving the existence of localised radial patterns for the Swift-Hohenberg equation, and then discuss how we extend this approach for the ferrofluid experiment. Finally, I will also present some recent work regarding the existence of localised cellular patterns -- such as hexagons, squares, rhomboids -- in the Swift-Hohenberg equation.