University of Macau / Faculty of Science and Technology. / Department of Mathematics

Sun, Lei = 利用梯度超穎材料實現對電磁場的操控 / 孫磊. / "October 2010." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 64-74). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Sun, Lei = Li yong ti du chao ying cai liao shi xian dui dian ci chang de cao kong / Sun Lei.

by Suen Wai Mo. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1980. / Bibliography: leaves 96-99.

Fazemos uma análise das teorias de campos escalar e vetorial na correspondência AdS/CFT. Começamos apresentando as propriedades básicas das teorias conformes e dos espaços AdS. Então, estudamos em detalhe os problemas da estabilidade e quantização do campo escalar acoplado com espaços assintóticamente AdS, seguindo o trabalho de Breitenlohner e Freedman [1]. Mostramos que existem dois tipos de modos normalizáveis: os \"regulares\" e os \"irregulares\" . No caso dos modos \'\'\'regulares\'\', a energia é positiva e finita para qualquer valor do coeficiente de acoplamento do campo com o fundo e para massa do campo satisfazendo o vínculo m POT.2 > -d POT.2/4, onde d + 1 é a dimensão do espaço-tempo. No caso dos modos \"irregulares\", a energia é positiva e finita para -d POT.2/4 < m POT.2 < 1 -d POT.2/4 e para valores particulares do coeficiente de acoplamento do campo com o fundo. A seguir estudamos o problema de reproduzir esses resultados na correspondência AdS / CFT. Trabalhamos com ações estacionárias perante condições de contorno de Dirichlet, Neumann e mistas, onde as últimas fixam na borda do espaço AdS o valor de combinações lineares do campo e sua derivada normal. Mostramos que os resultados são consistentes com a condição de unitariedade do campo escalar, que o formalismo fixa a normalização das ações na borda, e que são reproduzidas as teorias conformes correspondentes às condições \"regulares\" e \"irregulares\". Finalmente, consideramos teorias de campo vetorial em três dimensões e contendo um termo de Chern-Simons. Encontramos as funções de dois pontos na borda correspondentes às teorias de Proca-Chern-Simons e Maxwell-Chern-Simons. No caso do modelo Auto-Dual, adicionamos um termo de superfície que faz com que a ação seja estacionária, e que fornece funções de dois pontos na borda que são consistentes com a equivalência do modelo Auto-Dual com a teoria de Maxwell-Chern-Simons. / We consider scalar and vector field theories in the AdS/CFT correspondence. We begin by describing conformai field theories and AdS spaces. Then, we follow the work by Breitenlohner and Freedman [1] and study in detail the problems of stability and quantization of a: scalar field coupled to an asymptotically AdS space. We show that there exist two different kinds of normalizable modes, namely the regular and the irregular ones. In the case of the regular modes the energy is positive and finite for any value of the coupling coefficient between the field and the background and for m2 > -d2/4 where m is the mass of the scalar field and d + 1 is the dimension of the space-time. In the case of the \'irregular\' modes the energy is positive and finite for - d2/4 < m2 < 1- d2/4 and for particular values ofthe coupling coefficient between the field and the background. Then, we consider the problem of reproduzing these results in the AdS/CFT correspondence context. We analize actions which are stationary under Dirichlet, Neumann and mixed boundary conditions on the field where the mixed boundary conditions are a combination of the Dirichlet and Neumann ones. We show that our results are consistent with the unitarity bound for the scalar field, that the formalism fixes the normalization of the actions at the bounelary anel that we reproduce the conformal field theories corresponding to the regular and irregular conditions. Finally, we consider vector field theories in three dimensional AdS spaces and including a Chern-Simons term. We find the boundary two-point functions corresponding to the Proca-Chern-Simons and Maxwell-Chern-Simons theories. In the case of the Self-Dual model we add a surface term which makes the action stationary and which gives rise to boundary two-point functions which are consistent with the equivalence between the Self-Dual model and the Maxwell-Chern-Simons theory.

by Tsang, Yuk-fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 67-68). / by Tsang, Yuk-fai. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- Uniform accelerated charge radiation --- p.7 / Chapter 2.1 --- An old paradox: Radiate or not? --- p.7 / Chapter 2.2 --- Uniform Accelerating Charge(UAC) --- p.8 / Chapter 2.3 --- EM fields of UAC --- p.9 / Chapter 2.4 --- Radiation of UAC --- p.13 / Chapter 2.5 --- Energy conservation: acceleration energy --- p.14 / Chapter 3 --- Numerical calculation of EM field energy --- p.18 / Chapter 3.1 --- EM fields of UAC --- p.19 / Chapter 3.2 --- Comparison of total EM field energy --- p.23 / Chapter 3.3 --- Results --- p.28 / Chapter 4 --- Modification of the paradox --- p.30 / Chapter 4.1 --- Uniformly accelerated frame (UAF) --- p.30 / Chapter 4.2 --- Radiation in UAF --- p.32 / Chapter 4.3 --- The paradox in another situation --- p.34 / Chapter 5 --- The rotating frame --- p.37 / Chapter 5.1 --- The reference frames --- p.37 / Chapter 5.2 --- Geometric properties of co-rotating frame --- p.38 / Chapter 5.3 --- Maxwell equations in non-inertial frame --- p.41 / Chapter 6 --- Transformation of radiation fields to rotating frame --- p.42 / Chapter 6.1 --- EM fields of a moving charge --- p.43 / Chapter 6.2 --- Dipole radiation --- p.44 / Chapter 6.3 --- Dipole radiation of a rotating charge --- p.45 / Chapter 7 --- Tr ansformation of the complete fields to rotating frame --- p.49 / Chapter 7.1 --- Lienard-Wiechert Fields --- p.49 / Chapter 7.2 --- Determination of R --- p.54 / Chapter 7.3 --- Radiation is a frame-dependent phenomenon --- p.58 / Chapter 7.4 --- Transformation of static field --- p.59 / Chapter 8 --- Conclusions --- p.62 / Chapter 8.1 --- Comparison of the transformation of EM fields / Chapter 8.2 --- Radiation is a frame-dependent phenomenon --- p.64 / Chapter 8.3 --- The concept of photon --- p.65 / Chapter 8.4 --- Problems left --- p.65 / Reference --- p.67

Orientador: José Márcio Machado / Banca: Manoel Ferreira Borges / Banca: Angelo Passaro / Resumo: O método element-free Galerkin (EFG) com a abordagem interpolante e combinado com a técnica de truncamento de domínio provou ser uma fácil e eficiente técnica para o tratamento de descontinuidades físicas na equação de Poisson. Uma boa acurácia para esta abordagem é alcançada quando a discretização nas linhas das interfaces materiais são apropriadamente refinadas. Este trabalho trata o estudo de parâmetros os quais servem de ajuste para um cálculo mais refinado da descontinuidade em problemas eletromagnéticos, para uma combinação de diferentes materiais com diferentes discretizações / Abstract: The element free-Galerkin (EFG) method with the interpolating approach and combined with the domain truncation technique proved to be an easy and efficient method for the treatment of physical discontinuities in Poisson's equation. A good accuracy for this approach is achieved when the discretization on the lines of the material interfaces are properly refined. This work deals with the study of parameters which serve as the setting for a more refined calculation of the discontinuity in electromagnetic problems, with a combination of different materials with different discretizations / Mestre

Kwok, Tsz Chiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 43-45). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Historical remarks and main results --- p.6 / Chapter 1.2 --- Structure of the thesis --- p.8 / Chapter 2 --- Basic properties --- p.10 / Chapter 2.1 --- Existence of infinite convolution --- p.10 / Chapter 2.2 --- Properties --- p.16 / Chapter 2.3 --- Law of pure type --- p.17 / Chapter 3 --- Some results related to pure singularity --- p.20 / Chapter 3.1 --- The Pisot-Vijayaraghavan numbers --- p.20 / Chapter 3.2 --- The Salem numbers --- p.22 / Chapter 3.3 --- The weak separation condition --- p.23 / Chapter 4 --- A proof of almost everywhere absolute continuity --- p.30 / Chapter 5 --- Other results and problems --- p.37 / Chapter 5.1 --- Entropy of Bernoulli convolutions --- p.37 / Chapter 5.2 --- Dimensions --- p.40 / Chapter 5.3 --- Non PV numbers with bad behavior --- p.41 / Chapter 5.4 --- Open problems --- p.41 / Bibliography --- p.43

Fung, Tai Hang = 利用梯度超材料控制電場 / 馮泰恆. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 56-58). / Abstracts in English and Chinese. / Fung, Tai Hang = Li yong ti du chao cai liao kong zhi dian chang / Feng Taiheng. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- What are metamaterials? --- p.1 / Chapter 1.2 --- Negative refraction --- p.1 / Chapter 1.3 --- Transformation media --- p.2 / Chapter 1.4 --- Objectives of the thesis --- p.3 / Chapter 2 --- Mathematical formalism --- p.6 / Chapter 2.1 --- Boundary value problem of anisotropic media in spherical coordinates --- p.6 / Chapter 2.2 --- Boundary value problem of anisotropic media in cylindrical coordinates --- p.9 / Chapter 2.3 --- Anisotropic differential effective multipole moment theory --- p.11 / Chapter 2.4 --- Numerical solution of the radial equation for arbitrary profiles --- p.12 / Chapter 3 --- Perfect cloaking --- p.14 / Chapter 3.1 --- A review on Pendry´ةs cloaking model --- p.14 / Chapter 3.2 --- Perfect spherical cloak --- p.16 / Chapter 3.2.1 --- Perfect spherical cloak in uniform E-field --- p.16 / Chapter 3.2.2 --- Perfect spherical cloak and a point charge --- p.19 / Chapter 3.3 --- Perfect cylindrical cloak --- p.21 / Chapter 3.3.1 --- Perfect cylindrical cloak in uniform E-field --- p.22 / Chapter 3.3.2 --- Perfect cylindrical cloak and an infinite line charge --- p.24 / Chapter 3.4 --- ADEMMT analysis on perfect cloaking model --- p.27 / Chapter 3.4.1 --- Multipole factors of a perfect spherical cloak --- p.27 / Chapter 3.4.2 --- Equivalent dielectric constants of a perfect spherical cloak --- p.28 / Chapter 3.5 --- Remark --- p.29 / Chapter 4 --- Imperfect cloaking --- p.30 / Chapter 4.1 --- Designing cloaking materials via spectral representation theory --- p.31 / Chapter 4.2 --- Electric field distribution of an imperfect cloak --- p.32 / Chapter 4.3 --- ADEMMT analysis on imperfect cloaking model --- p.35 / Chapter 5 --- Confining electric fields spatially by graded metamaterials --- p.37 / Chapter 5.1 --- Graded solid cylinder --- p.38 / Chapter 5.1.1 --- Formalism --- p.38 / Chapter 5.1.2 --- Electric field distribution in graded cylinder --- p.40 / Chapter 5.1.3 --- Discussion --- p.43 / Chapter 5.2 --- Graded cylindrical shell --- p.44 / Chapter 5.3 --- Conclusion --- p.47 / Chapter 6 --- Future problems --- p.48 / Chapter A --- General coordinate transformation --- p.50 / Chapter A.1 --- The invariance of Maxwell´ةs equations --- p.50 / Chapter A.2 --- Scaling of ε and μ --- p.51 / Chapter B --- Designing cloaking model via spectral representation theory --- p.53 / Bibliography --- p.56

The magnetic (B) field is ubiquitous throughout the Milky Way. Several fundamental questions about the B-field in the cool, star-forming interstellar medium (ISM) remain unanswered. In this dissertation, near-infrared (NIR) polarimetric observations are used to study the large-scale Galactic B-field in the cool ISM in a spiral arm and to determine the role of B-fields in the formation of Infrared Dark Clouds (IRDCs). NIR polarimetry of 31 star clusters, located in and around the Perseus spiral arm, were obtained to determine the orientation of the plane-of-sky B-field in the outer Galaxy, and whether the presence of a spiral arm influenced B-field properties. Cluster distances, which provide upper limits to the B-field probed by observations, were estimated by developing a maximum likelihood method to fit theoretical stellar isochrones to stars in cluster color-magnitude diagrams (CMDs). Using the distance estimates, the cluster locations relative to the Perseus arm were found. The cluster polarization percentages and orientations were compared between clusters foreground to the arm and clusters inside or behind the arm. The cluster polarization orientations are predominantly parallel to the Galactic plane. Clusters inside and behind the arm have larger polarization percentages, likely a result of more polarizing material along the line of sight. The cluster polarization data were also compared to optical, inner Galaxy NIR, and Planck submm polarimetry data, and showed agreement with all three data sets. The polarimetric properties of one IRDC, G28.23, were determined using deep NIR observations. The polarization orientations relative to the cloud major axis were found to change directions with distance from the cloud axis. The B-field strength was estimated to be 10 to 100uG. Despite these large inferred B-field strengths, the B-field was found not to be the dominant force in the formation of the IRDC, though the B-field morphology was influenced by the cloud. Using NIR observations, the B-field of 27 IRDCs were studied. The relative polarization orientations with respect to the cloud major axes were found. No preferential relative orientation was found, implying that the B-field did not greatly influence the formation of this sample of IRDCs.

The effect of pulsed electric fields on cell membranes were studied to investigate the effects of an electric field, per se, on biological systems, without the densometric and other technical problems associated with other forms of nonionizing radiation. Exposure of mouse splenocytes to a high voltage pulse resulted in an increase in membrane permeability to K+ that was dependent on both the electric field strength and the pulse duration. Exposure to a 2 μsec, 3.0 kV/cm pulse elicited a 50% loss of intracellular K+ indicating that the critical transmembrane potential (Vm) at breakdown was 1.26 volts for the membrane of mouse spleen cells. These results agreed with previous studies on erythrocytes and micro-organisms. Effects of a pulsed electric field on a cell's functional integrity were assessed by measuring 3H-thymidine incorporation by lymphocytes cultured in the presence and absence of various mitogens following exposure to an electrical pulse. No statistically significant effects on the response of mouse spleen lymphocytes to Con-A, PHA, or LPS were observed following exposure to a 2 usec electric pulse. Exposure to 10 μsec pulses ≥ 2.4 kV/cm produced a statistically significant reduction in the response of lymphocytes to LPS stimulation. While not statistically significant, results from both 2 and 10 usec experiments consistently indicated that exposure to pulses at sublethal electric field strengths may have a stimulatory effect on mouse spleen lymphocytes. This result is discussed and an experiment to resolve this issue is presented. Exposure of Ehrlich ascites tumor cells to 2 μsec electrical pulses produced no statistically significant alterations in the tumorigenicity of these cells. K+ release data indicated these cells are unusually resistant to the effects of pulsed electric fields having a high breakdown potential, Vm = 2.37 volts.