Scholarly Communications Project


A Study of Inhomogeneities and Anisotropies in Superconductors via Ginzburg-Landau Type Models

by

Jennifer Marie Deang

PhD Dissertation submitted to the Faculty of the Virginia Tech in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in

Mathematics

Approved

Max D. Gunzburger, Chair
John A. Burns
Eugene M. Cliff
Terry L. Herdman
Janet S. Peterson

March 14, 1997
Blacksburg, Virginia


Abstract

Superconductivity continues to be of great theoretical and practical interest and remains a challenging area of scientific inquiry. Most superconductors of practical utility are of type-II, i.e., they allow the penetration of magnetic fields in the form of tubes of flux that are referred to as ``vortices.'' Motion of these vortices due to, e.g., applied currents, induce a loss of perfect conductivity. Knowing how vortices move and arrange themselves in lattice structures, how their movement is suppressed by pinning mechanisms, and how their movement is affected by thermal fluctuations is critical to understanding how to maintain resistanceless current flow. We study a variety of Ginzburg-Landau type models for superconductivity that can account for inhomogeneous and anisotropy materials, grain boundaries, and thermal fluctuations. We develop robust, accurate, and efficient numerical codes and apply them to numerous studies of how vortex motions are affected by the various mechanisms mentioned above. We also examine some analytical aspects of type-II superconductors under the influence of thermal fluctuations.

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