### Tuesday, July 14

## IP6

Macroscopic Models of Superconductivity

5:15 PM-6:00 PM

*Chair: Max Gunzburger, Iowa State University*

*Room: Convocation Hall *

There are many different models available to describe the phenomenon of superconductivity, ranging from the microscopic theory of Bardeen, Cooper & Schreiffer through the mesoscopic theories of London and Ginzburg & Landau, to the macroscopic critical state theories such as the Bean model. The aim of the talk is to show how it is possible to start with the Ginzburg-Landau theory and arrive at the Bean
critical state model by taking a series of suitable asymptotic limits.

The basic building block in deriving this hierarchy of models is the superconducting vortex, which is a thin core of nonsuperconducting material circled by a superconducting electric current. Similar line singularities are found in other systems, for example, line vortices in an inviscid fluid, or Volterra dislocations in an elastic crystal. Having demonstrated the hierarchy of models of superconductivity,
The speaker will describe briefly the analogous hierarchy of models in each of these other systems.

**S. Jonathan Chapman**

*Mathematical Institute*

*Oxford University, United Kingdom*

MMD Created: 3/30/98 Updated: 3/30/98