Thesis (M.S.)--Brigham Young University. Dept. of Physics and Astronomy, 2003. / Includes bibliographical references (p. 73).

Thesis (Ph. D.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on March 4, 2008) Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 64-65).

Thesis (Ph.D.)--Baylor University, 2009. / Subscript in abstract: n and n=0 in {Pn([alpha],[beta])(x)} [infinity] n=0, [mu] in (f,g)[mu], and R in [integral]Rfgd[mu]. Superscript in abstract: ([alpha],[beta]) and [infinity] in {Pn([alpha],[beta])(x)} [infinity] n=0. Includes bibliographical references (p. 115-119).

A one dimensional analysis of the boundary conditions of the electron energy eigenfunc-tion at a sharp interface between two crystals was made. An attempt to evaluate these conditions in terms of known band structure was made. It was concluded that this cannot be done in general. It was shown, however, that if the interface has the proper symmetry properties, the boundary conditions can be expressed in terms of only one unknown, energy-dependent parameter. It was concluded that setting this parameter equal to one gives boundary conditions which, though more general, are equivalent to the commonly used effective mass boundary conditions when they are applicable. It was concluded from numerical results for the transmission coefficient of the symmetric interface, that in general, these boundary conditions, which depend only on known band structure, do not give a good approximation to the exact answer. Since the energy dependence of the parameter mentioned above is described quite well qualitatively using the nearly free electron approximation or the tight-binding approximation, the applicability of any boundary conditions depending only on band structure can be predicted using these simple theories. The exact numerical results were calculated using the transfer matrix method. It was also concluded that the presence of symmetry in the interface either maximizes or minimizes the transmission coefficient. A tight-binding calculation showed that the transmission coefficient depends on an interface parameter which is independent of band structure. The transmission coefficient is maximized when this parameter is ignored. It was concluded that the effective mass equation is of little use when applied to this problem. Some transfer matrix results pertaining to the barrier and the superlattice were obtained. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.

Propriedades do primeiro autovalor e da primeira autofunção do operador laplaciano em variedades riemannianas são estudadas. Para variedades em que se pode estimar o laplaciano de funções distância, estimativas explícitas para o primeiro autovalor do laplaciano em domínios duplamente conexos são obtidas. Então observamos que hipóteses sobre as curvaturas da variedade e do bordo do domínio permitem estimar o laplaciano da distância. Além disso, autofunções em domínios não compactos do espaço hiperbólico EI" são estudadas. Mostramos que donn'nios contidos em horobolas não admitem autofunções limitadas associadas ao autovalor A(HIn), mas se o fecho assintótico do domínio contém um aberto de (9ooIHIn, então ele admite uma autofunção positiva que se anula em dfí U dooQ. A existência e o perfil de autofunções de autovalor A(IHI") em EI", em IHIn\Sr(o), em horobolas, em hiperbolas e no complementar de horobolas são analisados. Para alguns desses domínios apresentamos uma expressão explícita para a autofunção que depende apenas da distância à fronteira. Finalmente, técnicas de simetrização de Schwarz são adaptadas para variedades permitindo-nos obter estimativas para normas de autofunções. Primeiro um argumento de comparação demonstra que variedades mais simétricas maximizam certas normas. Obtenios também uma estimativa diretamente da função isoperimétrica da variedade. / Some properties of the first eigenvalue A and the first eigenfunction of the Laplace operator in a Riemannian manifold are studied. Assuming a bound for the Laplacian of the distance function, exphcit estimates for the first eigenvalue of a doubly counected domain are presented. Then some assumptions on the curvatures of the manifold and its boundary are made in order to have an estimate for the Laplacian of the distance function. Furthermore eigenfunctions of non compact domains in the hyperbohc space EIn are studied. We prove that a domain contained in a horoball does not admit a bounded eigenfunction of eigenvalue A(lHIn), but if the closure of the domain contains an open set of then it admits a positive eigenfunction that vanishes on dQ U daoíl. The existence and the profile of eigenfunctions of eigenvalue A(E[n ) in H71, in H [ r i \ 5 r ( o ) , in horoballs, hiperballs and in the complement of a horoball are analysed. For some of these domains we present an explicit expression for the eigenfunction that depends only on the distance to the boundary. Finally Schwarz symmetrization techniques are adapted for manifolds implying in estimates for the norm of the eigenfunctions. First a comparison argument proves that highly symmetric manifolds maximize some norm and then an estimated obtained directly from the isoperimetric function of the manifold is presented.

Propriedades do primeiro autovalor e da primeira autofunção do operador laplaciano em variedades riemannianas são estudadas. Para variedades em que se pode estimar o laplaciano de funções distância, estimativas explícitas para o primeiro autovalor do laplaciano em domínios duplamente conexos são obtidas. Então observamos que hipóteses sobre as curvaturas da variedade e do bordo do domínio permitem estimar o laplaciano da distância. Além disso, autofunções em domínios não compactos do espaço hiperbólico EI" são estudadas. Mostramos que donn'nios contidos em horobolas não admitem autofunções limitadas associadas ao autovalor A(HIn), mas se o fecho assintótico do domínio contém um aberto de (9ooIHIn, então ele admite uma autofunção positiva que se anula em dfí U dooQ. A existência e o perfil de autofunções de autovalor A(IHI") em EI", em IHIn\Sr(o), em horobolas, em hiperbolas e no complementar de horobolas são analisados. Para alguns desses domínios apresentamos uma expressão explícita para a autofunção que depende apenas da distância à fronteira. Finalmente, técnicas de simetrização de Schwarz são adaptadas para variedades permitindo-nos obter estimativas para normas de autofunções. Primeiro um argumento de comparação demonstra que variedades mais simétricas maximizam certas normas. Obtenios também uma estimativa diretamente da função isoperimétrica da variedade. / Some properties of the first eigenvalue A and the first eigenfunction of the Laplace operator in a Riemannian manifold are studied. Assuming a bound for the Laplacian of the distance function, exphcit estimates for the first eigenvalue of a doubly counected domain are presented. Then some assumptions on the curvatures of the manifold and its boundary are made in order to have an estimate for the Laplacian of the distance function. Furthermore eigenfunctions of non compact domains in the hyperbohc space EIn are studied. We prove that a domain contained in a horoball does not admit a bounded eigenfunction of eigenvalue A(lHIn), but if the closure of the domain contains an open set of then it admits a positive eigenfunction that vanishes on dQ U daoíl. The existence and the profile of eigenfunctions of eigenvalue A(E[n ) in H71, in H [ r i \ 5 r ( o ) , in horoballs, hiperballs and in the complement of a horoball are analysed. For some of these domains we present an explicit expression for the eigenfunction that depends only on the distance to the boundary. Finally Schwarz symmetrization techniques are adapted for manifolds implying in estimates for the norm of the eigenfunctions. First a comparison argument proves that highly symmetric manifolds maximize some norm and then an estimated obtained directly from the isoperimetric function of the manifold is presented.

Propriedades do primeiro autovalor e da primeira autofunção do operador laplaciano em variedades riemannianas são estudadas. Para variedades em que se pode estimar o laplaciano de funções distância, estimativas explícitas para o primeiro autovalor do laplaciano em domínios duplamente conexos são obtidas. Então observamos que hipóteses sobre as curvaturas da variedade e do bordo do domínio permitem estimar o laplaciano da distância. Além disso, autofunções em domínios não compactos do espaço hiperbólico EI" são estudadas. Mostramos que donn'nios contidos em horobolas não admitem autofunções limitadas associadas ao autovalor A(HIn), mas se o fecho assintótico do domínio contém um aberto de (9ooIHIn, então ele admite uma autofunção positiva que se anula em dfí U dooQ. A existência e o perfil de autofunções de autovalor A(IHI") em EI", em IHIn\Sr(o), em horobolas, em hiperbolas e no complementar de horobolas são analisados. Para alguns desses domínios apresentamos uma expressão explícita para a autofunção que depende apenas da distância à fronteira. Finalmente, técnicas de simetrização de Schwarz são adaptadas para variedades permitindo-nos obter estimativas para normas de autofunções. Primeiro um argumento de comparação demonstra que variedades mais simétricas maximizam certas normas. Obtenios também uma estimativa diretamente da função isoperimétrica da variedade. / Some properties of the first eigenvalue A and the first eigenfunction of the Laplace operator in a Riemannian manifold are studied. Assuming a bound for the Laplacian of the distance function, exphcit estimates for the first eigenvalue of a doubly counected domain are presented. Then some assumptions on the curvatures of the manifold and its boundary are made in order to have an estimate for the Laplacian of the distance function. Furthermore eigenfunctions of non compact domains in the hyperbohc space EIn are studied. We prove that a domain contained in a horoball does not admit a bounded eigenfunction of eigenvalue A(lHIn), but if the closure of the domain contains an open set of then it admits a positive eigenfunction that vanishes on dQ U daoíl. The existence and the profile of eigenfunctions of eigenvalue A(E[n ) in H71, in H [ r i \ 5 r ( o ) , in horoballs, hiperballs and in the complement of a horoball are analysed. For some of these domains we present an explicit expression for the eigenfunction that depends only on the distance to the boundary. Finally Schwarz symmetrization techniques are adapted for manifolds implying in estimates for the norm of the eigenfunctions. First a comparison argument proves that highly symmetric manifolds maximize some norm and then an estimated obtained directly from the isoperimetric function of the manifold is presented.

by Chong, Cheung-Yu = 開放球腔中波動之二分量理論 / 莊翔宇. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 84-87). / Text in English; abstracts in English and Chinese. / by Chong, Cheung-Yu = Kai fang qiu qiang zhong bo dong zhi er fen liang li lun / Zhuang Xiangyu. / Abstract --- p.i / Acknowledgments --- p.iii / Contents --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Open Cavities and Quasinormal Modes --- p.1 / Chapter 1.2 --- Completeness of Quasinormal Modes --- p.3 / Chapter 1.3 --- Objective and Outline of this Thesis --- p.5 / Chapter 2 --- Waves in One-Dimensional Open Cavities I: Completeness --- p.6 / Chapter 2.1 --- Quasinormal Modes of One-Dimensional Open Cavities --- p.6 / Chapter 2.2 --- Green's Function Formalism --- p.7 / Chapter 2.2.1 --- Construction of the Green's Function --- p.8 / Chapter 2.2.2 --- Conditions for Completeness --- p.9 / Chapter 2.2.3 --- Quasinormal Mode Expansion of the Green's Function --- p.10 / Chapter 2.3 --- Two-Component Formalism --- p.11 / Chapter 2.3.1 --- Overcompleteness --- p.11 / Chapter 2.3.2 --- Two-Component Expansion --- p.11 / Chapter 2.3.3 --- Linear Space Structure --- p.13 / Chapter 3 --- Waves in One-Dimensional Open Cavities II: Time-Independent Problems --- p.16 / Chapter 3.1 --- Perturbation Theory --- p.16 / Chapter 3.1.1 --- Formalism I: Green's Function Formalism --- p.17 / Chapter 3.1.2 --- Formalism II: Two-Component Formalism --- p.20 / Chapter 3.2 --- Diagonalization Method --- p.23 / Chapter 3.2.1 --- Formalism I: One-Component Expansion --- p.24 / Chapter 3.2.2 --- Formalism II: Green's Function Formalism --- p.25 / Chapter 3.2.3 --- Formalism III: Two-Component Formalism --- p.28 / Chapter 3.2.4 --- Numerical Example --- p.29 / Chapter 4 --- Waves in Open Spherical Cavities I: Completeness --- p.34 / Chapter 4.1 --- Quasinormal Modes of Open Spherical Cavities --- p.34 / Chapter 4.2 --- Green's Function Formalism --- p.36 / Chapter 4.2.1 --- Construction of the Green's Function --- p.37 / Chapter 4.2.2 --- Conditions for Completeness --- p.37 / Chapter 4.2.3 --- Quasinormal Mode Expansion of the Green's Function --- p.38 / Chapter 4.3 --- Two-Component Formalism --- p.39 / Chapter 4.3.1 --- Evolution Formula --- p.40 / Chapter 4.3.2 --- Two-Component Expansion --- p.48 / Chapter 4.3.3 --- Outgoing-Wave Boundary Condition --- p.49 / Chapter 4.3.4 --- Numerical Example --- p.51 / Chapter 4.3.5 --- Linear Space Structure --- p.52 / Chapter 5 --- Waves in Open Spherical Cavities II: Time-Independent Prob- lems --- p.57 / Chapter 5.1 --- Perturbation Theory --- p.57 / Chapter 5.1.1 --- Formalism I: Green's Function Formalism --- p.57 / Chapter 5.1.2 --- Formalism II: Two-Component Formalism --- p.60 / Chapter 5.2 --- Diagonalization Method --- p.61 / Chapter 5.2.1 --- Formalism I: One-Component Expansion --- p.61 / Chapter 5.2.2 --- Formalism II: Green's Function Formalism --- p.63 / Chapter 5.2.3 --- Formalism III: Two-Component Formalism --- p.64 / Chapter 5.2.4 --- Numerical Example --- p.65 / Chapter 6 --- Numerical Evolution of Outgoing Waves in Open Spherical Cav- ities --- p.73 / Chapter 6.1 --- Formulation of the Problem --- p.74 / Chapter 6.2 --- Derivation of the Boundary Condition --- p.75 / Chapter 6.3 --- Boundary Condition without High Derivatives --- p.76 / Chapter 6.4 --- Numerical results --- p.78 / Chapter 6.5 --- Discussion --- p.79 / Chapter 7 --- Conclusion --- p.82 / Chapter 7.1 --- Summary of Our Work --- p.82 / Chapter 7.2 --- Future Developments --- p.83 / Bibliography --- p.84