PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Becky Halpenny.

Title:"Asymptotic analysis of Ginzburg-Landau superconductivity model"
Seminar:Ph.D. Thesis Defense
Speaker:Oleksandr Misiats, Adviser: Leonid Berlyand, Penn State
Abstract Link:http://
Abstract:
The thesis is devoted to variational problems and PDEs related to the Ginzburg-Landau superconductivity theory and consists of two parts. In the first part we establish the existence of minimizers of the magnetic Ginzburg-Landau energy functional with prescribed degrees and unit modulus on the boundary (so called semi-stiff boundary conditions) in both simply connected and doubly connected domains. In simply connected domains we show that the vortices of these minimizers are located strictly inside the domain for certain values of Ginzburg-Landau parameter, while in doubly connected domains we have nearboundary vortices in the same parameter regime. We also establish the necessary conditions for the existence of local minimizers of the simplified Ginzburg-Landau functional in doubly connected domains with semi-stiff boundary conditions. The second part of the thesis studies vortex pinning (i.e., fixing the positions of vortices), which is done through introducing inclusions into a homogeneous superconductor. We use the homogenization techniques to model a composite superconductor obtained by introducing a large number of superconducting inclusions in superconducting media. Next, we focus on modeling a superconductor with finitely many small superconducting inclusions in the vortex state. We show that even the inclusions of negligibly small size (e.g. shrinking to single points) capture the vortices of minimizers, and therefore, the problem of finding the locations of the vortices of minimizers may be reduced to a discrete minimization problem for a finite-dimensional functional.

Room Reservation Information

Room Number:MB106
Date:08 / 03 / 2012
Time:11:00am - 01:00pm