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Uniform asymptotic approximation of solutions to the conductivity problem with thin open filaments
Descriptive
TitleInfo
Title
Uniform asymptotic approximation of solutions to the conductivity problem with thin open filaments
Name
(type = personal)
NamePart
(type = family)
Charnley
NamePart
(type = given)
Matthew
NamePart
(type = date)
1990-
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Matthew Charnley
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author
Name
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Vogelius
NamePart
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Michael
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Michael Vogelius
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Advisory Committee
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chair
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NamePart
(type = family)
Han
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Zheng-Chao
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Zheng-Chao Han
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Advisory Committee
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internal member
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Cakoni
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Fioralba
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Fioralba Cakoni
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Advisory Committee
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internal member
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Bryan
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Kurt
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Kurt Bryan
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Advisory Committee
Role
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Rutgers University
Role
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degree grantor
Name
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School of Graduate Studies
Role
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school
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Text
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theses
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2019
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2019-05
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English
Abstract
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The asymptotic approximation of solutions to the conductivity problem with thin filaments is analyzed. While filaments with a closed mid-curve have been looked at previously, this thesis pays particular attention to the case of an open mid-curve, focusing on the extra singularities that can develop around the endpoints of this curve. The argument relies on a primal and dual energy argument as well as an explicit representation for the most singular part of the solution around each of the endpoints of the mid-curve. After proving the energy closeness of the reduced problem to the full problem for a constant conductivity in the inhomogeneity, related problems including those with variable conductivities, anisotropic conductivities, and curved inhomogeneities are all discussed briefly. Finally, numerical simulations are shown for many of the situations in this thesis, illustrating the convergence that has been proven here, as well as convergence that it may be possible to prove in the future.
Subject
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Topic
Differential equations, Partial
Subject
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Topic
Mathematics
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Rutgers University Electronic Theses and Dissertations
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ETD_9666
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1 online resource (ix, 180 pages)
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Ph.D.
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Includes bibliographical references
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School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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doi:10.7282/t3-444h-3v53
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ETD doctoral
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Rights
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The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Charnley
GivenName
Matthew
Role
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Permission or license
DateTime
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2019-04-02 17:51:38
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Matthew Charnley
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Affiliation
Rutgers University. School of Graduate Studies
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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2019-05-31
DateTime
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2020-05-30
Detail
Access to this PDF has been restricted at the author's request. It will be publicly available after May 30th, 2020.
Copyright
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Copyright protected
Availability
Status
Open
Reason
Permission or license
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