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Existence theorems for 90o vortex-vortex scattering

Abdelwahid, Fawzi (1993) Existence theorems for 90o vortex-vortex scattering. Master of Science thesis, Dublin City University.

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Abstract

The scattering of magnetic flux tubes in superconductors is studied First, we introduce the Abehan-Higgs model, which describes vortices in a superconductor, and the Euler-Lagrange equations which minimize the energy density given by this model Static vortex solutions satisfying these equations are reviewed. A technique proposed by on Manton [1] in which slowly changing solutions are approximated by a special family of time-independent solutions is described. Time-dependent solutions over small intervals are also studied Then the existence and the symmetries of the time-dependent solutions are studied. This analysis rules out all cases other than 0°, 90° or 180° scattenng of two vortices The proof of the Cauchy-Kowalewskyi theorem for a system of first order quasi-linear partial differential equations of (n+1) independent variables and m unknown functions is given. The Taylor expansion of the initial data near the origin is studied. The Cauchy Kowalewskyi theorem is applied to find the solutions of the time-dependent Euler-Lagrange equations near the origin. This study proves that our solution describes 90° scattenng Mathematica programs to calculate the senes solutions are also supplied.

Item Type:Thesis (Master of Science)
Date of Award:1993
Refereed:No
Supervisor(s):Burzlaff, Jurgen
Uncontrolled Keywords:Scattering (Physics)
Subjects:Mathematics
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 3.0 License. View License
ID Code:18288
Deposited On:31 May 2013 10:39 by Celine Campbell . Last Modified 31 May 2013 10:39

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