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Asymptotic perturbation formulas for the effect of scattering by small objects:

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TypeOfResource
Text
TitleInfo (ID = T-1); (type = )
Title
Asymptotic perturbation formulas for the effect of scattering by small objects:
SubTitle
an analysis over a broad band of frequencies
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17136
Identifier
ETD_732
Language
LanguageTerm (authority = ISO639-2)
eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Mathematics
Subject (ID = SBJ-1); (authority = ETD-LCSH)
Topic
Perturbation (Mathematics)
Subject (ID = SBJ-1); (authority = ETD-LCSH)
Topic
Electromagnetic theory
Subject (ID = SBJ-1); (authority = ETD-LCSH)
Topic
Mathematical physics
Abstract
This thesis is a study of the asymptotic perturbation formulas that result from electromagnetic (or acoustic) wave scattering by small, penetrable objects. The ultimate purpose of these formulas is to aid in solving the inverse problem of reconstructing small inhomogeneities embedded within an otherwise known background medium.
For simplicity, we consider the time-harmonic, transverse magnetic setting, in which case the scalar electric field satisfies a two-dimensional Helmholtz equation.
We first derive, in the case of fixed frequency, a rigorous asymptotic formula for the boundary field perturbation caused by small inhomogeneities of arbitrary shape within a bounded domain.
We then derive formal asymptotic formulas in the
case where frequency is allowed to grow as the size of a single, smooth inhomogeneity tends to zero.
For high frequencies, we use the technique of geometric optics to derive an integral formula for the scattered field, which we then simplify by a stationary phase analysis. The resulting asymptotic formula is ripe with geometric information to aid in solving the inverse problem.
In a step toward a rigorous proof of this high frequency asymptotic formula, we prove an estimate of a Sobolev norm of the scattered field in the case of a penetrable, though conducting, circular scatterer.
PhysicalDescription
Extent
vi, 190 pages
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application/pdf
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Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 183-189).
Name (ID = NAME-1); (type = personal)
NamePart (type = family)
Hansen
NamePart (type = given)
Derek J.
NamePart (type = date)
1976-
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Derek J. Hansen
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Vogelius
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Michael
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chair
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Advisory Committee
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Michael S Vogelius
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Nussbaum
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Roger
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Advisory Committee
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Roger Nussbaum
Name (ID = NAME-4); (type = personal)
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Falk
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Richard
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internal member
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Advisory Committee
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Richard Falk
Name (ID = NAME-5); (type = personal)
NamePart (type = family)
Weinstein
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Michael
Role
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outside member
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Advisory Committee
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Michael Weinstein
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB); (type = )
degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB); (type = )
school
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artist
OriginInfo
DateCreated (point = ); (qualifier = exact)
2008
DateOther (qualifier = exact); (type = degree)
2008-01
Location
PhysicalLocation (authority = marcorg)
NjNbRU
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Identifier (type = doi)
doi:10.7282/T36M375F
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
Copyright
Status
Copyright protected
Availability
Status
Open
AssociatedEntity (AUTHORITY = rulib); (ID = 1)
Name
Derek Hansen
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
RightsEvent (AUTHORITY = rulib); (ID = 1)
Type
Permission or license
Detail
Non-exclusive ETD license
AssociatedObject (AUTHORITY = rulib); (ID = 1)
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License
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Author Agreement License
Detail
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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