Ph.D. Tezi Görüntüleme

Student:	Zafer CAKIR
Supervisor:	Prof.Dr. Erhan COSKUN
Department:	Mathematics
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University, Turkey

Title of the Thesis:	TEMPERATURE AND TIME-DEPENDENT GINZBURG-LANDAU MODEL
Level:	Ph.D.
Acceptance Date:	14/4/2006
Number of Pages:	138
Registration Number:	di535

Summary:

In this work we investigate electromagnetic and thermodynamic properties of a thin film superconductor subject to a tangential magnetic field using both steady and time-dependent Ginzburg-Landau (GL) models, as well as the variants introduced herein.

In Section 2.1. we derive the steady GL model using variational principles from free energy functional for a thin film superconductor.

In Section 2.2. we investigate the GL system with respect to the variation of parameters GL, H, L. In Section 2.3. we nondimensionalize the free energy functional using a nonstandard set of scales in order to preserve the temperature dependence of the original system, and thus obtain a Temperature and Time-Dependent GL (TTDGL) system. We provide some theoretical properties for the TTDGL system.

In Section 2.4. we investigate both theoretical and numerical properties of TTDGL system with respect to the variation of parameters GL, H, L, temperature. In particular, we emphasize the existence of hysteresis with respect to variations in temperature parameter . Later on, we determine the dependence of critical fields on temperature, and thus the phase transition boundaries for both Type I and Type II superconductors

In Section 2.5., employing both finite step length integration methods and also some of those in MATLAB ODE SUITE, we perform a comparative performance analysis among the solvers. Furthermore, performing a stability analysis for the Euler scheme applied to TDGL system, we observe that the maximum time step length provided by the stability analysis is indeed a practical one.

In Section 2.6, we introduce a generalized functional by adding a suitably formulated thermodynamic energy functional to the GL energy functional. Thus, obtain a heat-coupled TDGL (HTDGL) model as a gradient flow. We investigate some properties of solution to HTDGL system and perform numerical simulations emphasizing some thermal characteristics of superconductors. In section 2.7, we investigate Josephson junctions with TDGL.

Key Words: Superconductivity, Ginzburg-Landau Model, Hysteresis, Heat-coupled Ginzburg-Landau Model, Josephson Junction