Year

2026

Season

Spring

Paper Type

Master's Thesis

College

College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)

Department

Mathematics & Statistics

NACO controlled Corporate Body

University of North Florida. Department of Mathematics and Statistics

Committee Chairperson

Dr. Kening Wang

Second Advisor

Dr. Mahbubur Rahman

Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

Third Advisor

Dr. Mei-Qin Zhan

Department Chair

Dr. Richard F. Patterson

College Dean

Dr. Kaveri Subrahmanyam

Abstract

Ginzburg and Landau have provided a set of equations that relate superconductivity to magnetic fields. Through a transformation process, Zhan has derived what are now called the phase-lock equations. A stability analysis of the spatially-independent phase-lock equations is the purpose of this presentation. This simplification is significant since it allowed for the analytical determination of equilibria, their stability, and the influence of a periodic forcing function. Through the use of an original code, numerical simulations are shown to corroborate the analytical results described above.

This analysis includes novel Lyapunov functions that allowed for the analytical determination of the instability region. This presentation will address a perturbation of the equations in the form of a periodic forcing function. By determining the asymptotic behavior of part of the variables, the limiting behavior of the forcing function is described.

The exact amplitude of the oscillations induced by a periodic forcing function. Finally, a numerical implementation has been conducted to corroborate the analytical results described in this project. The novel results derived in the analysis contribute to understanding the long-term stability of superconductivity for various materials.

In the unperturbed system, the stability of all equilibria has been established and a region of instability has been analytically described.

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