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dc.contributor.advisorPalaniappan, Devanayagam
dc.contributor.authorAlarki, Rabab Abdulwahed
dc.date.accessioned2017-11-02T19:21:34Z
dc.date.available2017-11-02T19:21:34Z
dc.date.issued2017-05
dc.identifier.urihttp://hdl.handle.net/1969.6/5628
dc.descriptionA thesis Submitted in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE in MATHEMATICS from Texas A&M University-Corpus Christi from Corpus Christi, Texas.en_US
dc.description.abstractIn this thesis, two phase models in a magnetostatics context using the Maxwell-Maxwell (MM) model and the Maxwell-London (ML) model are investigated. The vector equations are transformed in terms of scalar potentials leading to mixed boundary value problems for Laplace-Laplace and Laplace Helmholtz equations in the respective cases. Exact analytic solutions for the exterior and interior potentials Fe(r;q;f) and Fi(r;q;f), where r;q;f are the spherical coordinates, are obtained as infinite series and in closed forms for the MM model. The general solutions are found as a theorem. Several illustrative examples for specific externally imposed magnetic fields including a magnetic monopole and dipole are discussed based on our analytic solutions. It is shown that the magnetic permeability parameter k = me me+mi , where me and mi are magnetic permeabilities in the exterior and interior phases, has a significant impact on the magnetic induction fields and the forces acting on the sphere. A new relation for the multipole coefficients of the external phase is derived as well. Exact solutions for the ML model involving a superconducting sphere are derived in terms of the magnetic flux density functions Ye(r;q) and Yi(r;q) in the respective phases. The general solutions are established as a theorem for this model as well. The non-dimensional penetration depth parameter l is found to dictate the induction fields in ML model. Our results are of interest in various topics in mathematical physics where two phase models are used.en_US
dc.format.extent64 pages.en_US
dc.language.isoen_USen_US
dc.rightsThis material is made available for use in research, teaching, and private study, pursuant to U.S. Copyright law. The user assumes full responsibility for any use of the materials, including but not limited to, infringement of copyright and publication rights of reproduced materials. Any materials used should be fully credited with its source. All rights are reserved and retained regardless of current or future development or laws that may apply to fair use standards. Permission for publication of this material, in part or in full, must be secured with the author and/or publisher.en_US
dc.titleCalculation of laplace and helmholtz potentials in two-phase problemsen_US
dc.typeTexten_US
dc.rights.holderAlarki, Rabab Abdulwahed
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorTexas A & M University--Corpus Christien_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Scienceen_US
dc.contributor.committeeMemberSadovski, Alexey
dc.contributor.committeeMemberZimmer, Beate
dc.description.departmentMathematics and Statisticsen_US
dc.description.collegeCollege of Science and Engineeringen_US
dc.type.genreThesisen_US


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