Approved for public release; distribution is unlimited / This thesis investigates the viability of a new method for numerically computing the input impedance and the currents on simple antenna structures. This technique considers the antenna between two ground planes and uses multiregion cylindrical harmonic expansions with tangential field continuity to obtain the surface currents and input impedance. The computed results are compared to the results obtained from the Numerical Electromagnetics Code for various physical parameters to assess computational accuracy. / http://archive.org/details/computationofmon00hurl / Lieutenant, United States Navy

In mathematical physics, Laplace's equation plays an especially significant role. It is fundamental to the solution of problems in electrostatics, thermodynamics, potential theory and other branches of mathematical physics. It is for this reason that this investigation concerns the development of some general properties of continuous solutions of this equation.

In treating the motion of a fluid mathematically, it is convenient to make some simplifying assumptions. The assumptions which are made will be justifiable if they save long and laborious computations in practical problems, and if the predicted results agree closely enough with experimental results for practical use. In dealing with the flow of air about an airfoil, at subsonic speeds, the fluid will be considered as a homogeneous, incompressible, inviscid fluid.

This research was mainly focused on the design and optimization of aperture-based structures to achieve the greatest third harmonic conversion efficiency. It was discovered that by tuning the localized surface plasmon resonance to the fundamental beam wavelength, and by tuning the propagating surface plasmons resonance to the Bragg resonance of the aperture arrays, both the directivity and conversion efficiency of the third harmonic signal were enhanced. The influence of the gap plasmon resonance on the third harmonic conversion efficiency of the aperture arrays was also investigated. The resulted third harmonic generation (THG) from an array of annular ring apertures as a closed loop structure were compared to arrays of H-shaped, double nanohole and rectangular apertures as open-loop structures. The H-shaped structure had the greatest conversion efficiency at approximately 0.5 %. Moreover, it was discovered that the maximum THG did not result from the smallest gap; instead, the gap sizes where the scattering and absorption cross sections were equal, led to the greatest THG. The finite difference time domain (FDTD) simulations based on the nonlinear scattering theory were also performed. The simulation results were in good agreement with the experimental data. Moreover, a modified quantum-corrected model was developed to study the electron tunneling effect as a limiting factor of the THG from plasmonic structures in the sub-nanometer regime. / Graduate / 0544 / 0794 / 0752 / 0756 / mrnezami@gmail.com

A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Master of Science. Johannesburg, 2013 / Many of the problems in mathematics have very elegant solutions. As complex, real–world geometries come into play, however, this elegance is often lost. This is particularly the case with meshes of physical, real–world problems. Domain mapping helps to move problems from some geometrically complex domain to a regular, easy to use domain. Shape transformation, specifically, allows one to do this in 2D domains where mesh construction can be difficult. Numerical methods usually work over some mesh on the target domain. The structure and detail of these meshes affect the overall computation and accuracy immensely. Unfortunately, building a good mesh is not always a straight forward task. Finite Element Analysis, for example, typically requires 4–10 times the number of tetrahedral elements to achieve the same accuracy as the corresponding hexahedral mesh. Constructing this hexahedral mesh, however, is a difficult task; so in practice many people use tetrahedral meshes instead. By mapping the geometrically complex domain to a regular domain, one can easily construct elegant meshes that bear useful properties. Once a domain has been mapped to a regular domain, the mesh can be constructed and calculations can be performed in the new domain. Later, results from these calculations can be transferred back to the original domain. Using harmonic functions, source domains can be parametrised to spaces with many different desired properties. This allows one to perform calculations that would be otherwise expensive or inaccurate. This research implements and extends the methods developed in Voruganti et al. [2006 2008] for domain mapping using harmonic functions. The method was extended to handle cases where there are voids in the source domain, allowing the user to map domains that are not topologically equivalent to the equivalent dimension hypersphere. This is accomplished through the use of various boundary conditions as the void is mapped to the target domains which allow the user to reshape and shrink the void in the target domain. The voids can now be reduced to arcs, radial lines and even shrunk to single points. The algorithms were implemented in two and three dimensions and ultimately parallelised to run on the Centre for High Performance Computing clusters. The parallel code also allows for arbitrary dimension genus-0 source domains. Finally, applications, such as remeshing and robot path planning were investigated and illustrated.

Master of Science - Science / The theoretical investigation of the Optical Kerr Effect (OKE) and Third- Harmonic Generation (THG) of Au-VO2 nanocomposite thin-films undertaken in this project is motivated by the potential use of the Au-VO2 nanocomposite in nonlinear optical (NLO) devices. NLO devices are a driving force in today fs high technology industry. In this thesis the OKE is estimated and computed and will be compared later to the measured OKE using the Z-scan interferometric laser technique [47]. This is a simple yet highly sensitive single-beam experimental technique used to determine the real part of the dielectric susceptibility. The study of the OKE in these composites has shown that it has a high value, comparable to that found in Au-SiO2, Au-TiO2 and Au-Al2O3 thin-films [29, 33]. This is despite the fact that the Au volumetric concentration in the Au-VO2 composites considered here is 10 percent at most, whereas in the other above mentioned composite thin-films the volumetric concentration range was between 5 − 60 percent. Moreover, it has been demonstrated that the OKE is thermally tunable in the Au-VO2 thin-films, owing to the thermally tunable optical properties of the VO2 [8, 38]. It is found that the magnitude of the OKE is of the order of 10−6 esu when the composite is below 68 0C and it is of the order of 10−7 esu when the nanocomposite thin-film is above 68 0C. The large enhancement of the OKE is due to the surface plasmon resonance (SPR) of the nanogold particles. Its fast response, which is of the order of few picoseconds [4, 6, 7], makes the Au-VO2 nanocomposite a good candidate as a fast thermally tunable optical switch or modulator. The modelling here of high-order harmonic generation in strongly absorbing media, as regards the amplitude of the primary beam, takes into account pump attenuation only, due to the absorption of light by the media. It is not concerned with pump depletion which is a consequence of the transfer of energy to the harmonics and which is small by comparison with attenuation in absorbing media. The modelling is applied to the so-called transmission and reflection configurations. The former refers to the case in which the high-order harmonic wave is monitored in the same direction as the input fundamental wave, whereas the latter describes the situation in which the fundamental wave is in the opposite direction to the high-order harmonic one. To analyse high-order harmonic generation one has to relate the high-order harmonic intensity to the fundamental intensity [1, 9, 10, 34-36]. In so doing, a general formula for analysing high-order harmonic generation is obtained and reduced to the particular case pertaining to THG in strongly absorbing media. The ratio of the third-harmonic intensity to the fundamental intensity is termed the conversion coefficient or the conversion efficiency, and it is denoted by ƒÅ [23, 34]. It is useful in the sense that it expresses quantitatively the amount of input light of frequency ƒÖ converted into light of frequency nƒÖ, where n is the order of nonlinear polarisation [1]. It is found that the THG conversion coefficient is higher the higher the laser intensity. It is thus advantageous to use a pulsed laser, which achieved very high intensities for short periods, separated by long off periods. The net harmonic output in this case is much higher than one would obtain with a continous laser of the same average output. It is found here that ƒÅ is greater in the reflection configuration compared to the transmission one above and below Tt in the photon energy range 1.0 − 3.0 eV, see Fig. 5.1 to 5.8. However, the conversion efficiency for THG in the Au-VO2 nanocomposites for the picoseconds laser illumination we have considered, is still extremely low, and it is difficult to see a potential use for this system as a tunable frequency converter. The situation would become more favorable with the use of femtosecond laser pulses, where for the same pulse energy the intensity is much greater. The laser pulse energy must be limited to avoid excessive heating of the thin-film. The heat generated as a consequence of the illumination of the thin-film by the laser [23] may be controlled by using a simple cooling device which consists of a substrate on which the thin-film is deposited. The choice of such a substrate depends on whether THG is monitored in the transmission or reflection configuration. In the former a transparent substrate must be used (for example diamond) whereas in the latter an opaque substrate may be used (for example Ag). Calculations pertaining to the removal of heat from the illuminated film are reported, and show that thermal control is manageable but only within limits. To avoid a temperature rise of more than 5 0K the peak laser intensity we found must not exceed 7.4 ~105Wcm−2 with a pulse duration of 5 ps.

Orientador: João Antônio Pereira / Banca: Fabio Roberto Chavarette / Banca: Adailton Silva Borges / Resumo: O objetivo motivacional deste trabalho é estudar a possibilidade de desenvolvimento de um material a base de bagaço de cana com um maior valor agregado, propondo assim, outra função e/ou utilização para o bagaço da cana de açúcar. Para isso, foi desenvolvido um aglomerado de fibra de cana (compósito) com diferentes proporções de fibra de cana e aglutinante, e posteriormente foram estudadas algumas características acústicas destes diferentes compósitos, avaliando assim, o potencial de uso da fibra como material de absorção acústica. Os coeficientes de absorção acústica do aglomerado foram estimados com base na teoria e conceitos de acústica utilizando o tubo de impedância, tendo como base a norma ISO10534-1(1996). Os resultados obtidos do coeficiente de absorção acústica dos compósitos analisados mostraram que a fibra da cana pode ser utilizada como um material de absorção acústica, dependendo da composição do compósito, o mesmo se mostrou equivalente a alguns materiais do mercado de absorvedores acústico / Abstract: The motivational goal of this work is to study the possibility of developing a material basis of bagasse with a higher added value, thus suggesting another function and / or use for bagasse from sugar cane. For this, we developed a cluster of sugarcane (composite) with different proportions of sugar and binder fiber and fiber were subsequently studied some acoustic characteristics of different composites, thus assessing the potential use of fiber as sound absorption material. The sound absorption coefficients of the cluster were estimated based on the theory and concepts of acoustic, using the impedance tube, based on the standard ISO10534-1 (1996). The results of the sound absorption coefficient of the analysis showed that the composite fiber rod can be used as an acoustic absorption material, depending on the composition of the composite, it was equivalent to some of the noise absorbing materials market / Mestre

by Lei Ka Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 70-71). / Abstracts in English and Chinese. / Chapter 0 --- Introduction --- p.5 / Chapter 1 --- Dirichlet Problem at infinity --- p.9 / Chapter 1.1 --- The Geometric Boundary --- p.9 / Chapter 1.2 --- Dirichlet Problem --- p.15 / Chapter 2 --- The Martin Boundary --- p.29 / Chapter 2.1 --- The Martin Metric --- p.30 / Chapter 2.2 --- The Representation Formula --- p.31 / Chapter 2.3 --- Uniqueness of Representation --- p.36 / Chapter 3 --- The Geometric boundary and the Martin boundary --- p.42 / Chapter 3.1 --- Estimates for harmonic functions in cones --- p.42 / Chapter 3.2 --- A Harnack Inequality at Infinity --- p.49 / Chapter 3.3 --- The kernel function --- p.54 / Chapter 3.4 --- The Main Theorem --- p.55 / Chapter 4 --- Positive Harmonic Functions on Product of Manifolds --- p.61 / Chapter 4.1 --- Splitting Theorem --- p.61 / Chapter 4.2 --- Riemannian Halfspace and the parabolic Martin boundary --- p.62 / Chapter 4.3 --- Splitting of parabolic Martin kernels --- p.63 / Chapter 4.4 --- Proof of theorem 4.1 --- p.66 / Bibliography

To Chi Wing = 具非線性光學性質客體-主體聚合物系統的極化動力學研究 / 杜志榮. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 102-104). / Text in English; abstracts in English and Chinese. / by To Chi Wing = Ju fei xian xing guang xue xing zhi ke ti-zhu ti ju he wu xi tong de ji hua dong li xue yan jiu / Du Zhirong. / Table of contents / Acknowledgements --- p.ii / Abstract --- p.iii / Chinese Abstract --- p.iv / Table of Contents --- p.v / List of Figures --- p.viii / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Fundamental of nonlinear optics --- p.2 / Chapter 1.2 --- Centrosymmetry and even-order nonlinear susceptibilities --- p.4 / Chapter 1.3 --- Generation of second harmonic radiation --- p.5 / Chapter 1.4 --- Tensor properties of the nonlinear susceptibilities --- p.7 / Chapter 1.5 --- Relationship between macroscopic and microscopic nonlinear susceptibility for a poled polymer --- p.8 / Chapter 1.6 --- Outline of the thesis --- p.12 / Figures --- p.13 / Chapter Chapter 2 --- Poling and Relaxation of Guest-host Polymeric System --- p.15 / Chapter 2.1 --- Guest-host nonlinear optical polymeric systems --- p.15 / Chapter 2.1.1 --- Photoisomerization of Azobenzene --- p.16 / Chapter 2.1.2 --- Disperse Red-1 --- p.17 / Chapter 2.1.3 --- Poly (methyl methacrylate) --- p.18 / Chapter 2.2 --- Poling techniques --- p.19 / Chapter 2.2.1 --- Thermal Assisted Electric-field Poling --- p.19 / Chapter 2.2.2 --- Photo-assisted Electric-field poling --- p.22 / Chapter 2.2.3 --- All-Optical Poling --- p.25 / Chapter 2.3 --- Relaxation of poled nonlinear optical polymers --- p.27 / Figures --- p.31 / Chapter Chapter 3 --- Experimental Methods --- p.36 / Chapter 3.1 --- Sample Preparation --- p.36 / Chapter 3.2 --- Experimental Setup --- p.38 / Chapter 3.2.1 --- Laser system --- p.38 / Chapter 3.2.2 --- The reference arm --- p.39 / Chapter 3.2.3 --- The sample arm --- p.40 / Chapter 3.2.4 --- Data acquisition (DAQ) system --- p.41 / Chapter 3.2.5 --- Temperature control --- p.42 / Chapter 3.3 --- Poling and the erasing of thermal history --- p.43 / Chapter 3.3.1 --- All Optical Poling --- p.43 / Chapter 3.3.2 --- Eecteic Poling --- p.44 / Chapter 3.3.3 --- Erasure of thermal history --- p.45 / Figures --- p.46 / Chapter Chapter 4 --- Experimental results and discussions --- p.51 / Chapter 4.1 --- Reliability and reproducibility --- p.51 / Chapter 4.2 --- Features of different poling techniques --- p.52 / Chapter 4.2.1 --- Sub-Tg electric Poling --- p.53 / Chapter 4.2.2 --- Thermal assisted electric Poling --- p.54 / Chapter 4.2.3 --- Photo assisted electric Poling --- p.55 / Chapter 4.3 --- Relaxation of poling induced x(2) --- p.56 / Chapter 4.4 --- Effect of physical aging on the relaxation of PAP induced x{2) --- p.58 / Chapter 4.4.1 --- Origin of physical aging and its effect on relaxation --- p.58 / Chapter 4.4.2 --- Effect of aging on the relaxation of a PAP sample --- p.59 / Chapter 4.5 --- Onset studies of photo-induced free volume --- p.61 / Chapter 4.6 --- Comparative studies of TAP and PAP induced x{2) --- p.62 / Chapter 4.6.1 --- Secondary Poling --- p.63 / Chapter 4.6.1.1 --- Model for describing the temporal behavior of secondary poling --- p.65 / Chapter 4.6.1.2 --- Experimental details of the secondary poling measurement --- p.68 / Chapter 4.6.1.3 --- Results and Discussion on secondary poling of sample poled by TAP or PAP --- p.69 / Chapter 4.6.2 --- Onset of second harmonic signal during electric poling --- p.71 / Chapter 4.7 --- Charge injection studies --- p.73 / Figures --- p.77 / Chapter Chapter 5 --- Conclusion --- p.98 / References --- p.101

We provide an L² theory for the local double Hilbert transform along an analytic surface (s, t ,φ(s, t )) in the Heisenberg group H¹, that is operator f ↦ Hφ f (x) := p.v.∫∣s∣,∣t∣≤1 f (x ∙ (s, t ,φ(s, t ))-¹) ds/s dt/t, where ∙ denotes the group operation in H1. This operator combines several features: it is amulti-parameter singular integral, its kernel is supported along a submanifold, and convolution is with respect to a homogeneous group structure. We reprove Hφ is always L²(H¹)→L²(H¹) bounded (a result first obtained in [Str12]) to illustrate the method and then refine it to characterize the largest class of polynomials P of degree less than d such that the operator HP is uniformly bounded when P ranges in the class. Finally, we provide examples of surfaces that can be treated by our method but not by the theory of [Str12].