Description
If you put a certain type of material (called a superconductor) in a magnetic field then the magnetic field concentrates in a region and forms an object called a magnetic vortex.
The project involves studying the mathematical model that describes this system, called the Ginzburg-Landau model, and finding the magnetic vortex solutions of the differential equations that follow from this theory.
Properties of the vortices, such as whether a pair of vortices attract or repel each other, depend on the kind of material being considered, and this can be studied by changing the values of parameters in the theory.
The same vortex appears in theories of cosmology, where it is known as a cosmic string, although the dynamics is different in the two contexts.
A small amount of python programming will be required, mainly to plot the solutions and create images of the magnetic vortex.
Prerequisites
Mathematical Physics II and Special Relativity and Electromagnetism II are prerequisites.Resources
Topological solitons, by Manton and Sutcliffe, Chapter 7.Cosmic strings and other topological defects, by Vilenkin and Shellard.