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FDTD can successfully simulate various kinds of phenomena of electromagnetic waves. Mainly, we use orthogonal Cartesian coordinate in general situations when we deal with the electromagnetic problems, but the curved geometry of the problem makes it difficult to obtain accurate results using conventional FDTD algorithm because of staircasing. To analyze curved geometry using Conformal FDTD can improve this shortcoming. The Conformal FDTD uses the regular FDTD equation for updating the magnetic field by using the electric field values along the distorted contours, that are appropriately weighted with lengths of the contours. The Conformal FDTD technique is well suited for handling such curved geometries. The moment method is used to convert the integral equation into a matrix equation.The major drawback of moment method (MoM) is the full matrix generation and huge computation time. The CFDTD directly approximates the differential operators in the Maxwell curl equation, and avoids using more mathematic formulae. This thesis uses Conformal FDTD to simulate RCS value of the cylinder and sphere and compare Conformal FDTD with Moment Method. We know that Conformal FDTD will save memory requirement and CPU time even more than Moment Method in layered structure.

It is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier’s law for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, the It is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier's law for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, the study of rarefied flows is extremely important. This dissertation includes two main parts. First, we look into the heat transport in solids when the mean free path for phonons are comparable with the length scale of the flow. A set of macroscopic moment equations for heat transport in solids are derived to extend the validity of Fourier's law beyond the hydrodynamics regime. These equations are derived such that they remain valid at room temperature, where the MEMS devices usually work. The system of moment equations for heat transport is then employed to model the thermal grating experiment, recently conducted on a silicon wafer. It turns out that at room temperature, where the experiment was conducted, phonons with high mean free path significantly contribute to the heat transport. These low frequency phonons are not considered in the classical theory, which leads to failure of the Fourier's law in describing the thermal grating experiment. In contrast, the system of moment equations successfully predict the deviation from the classical theory in the experiment, and suggest the importance of considering both low and high frequency phonons at room temperature to capture the experimental results. In the second part of this study, we look into the gas-surface interactions for conventional gas dynamics when the gas flow is rarefied. An extension to the well-known Maxwell boundary conditions for gas-surface interactions are obtained by considering velocity dependency in the reflection kernel from the surface. This extension improves the Maxwell boundary conditions by providing an extra free parameter that can be fitted to the experimental data for thermal transpiration effect in non-equilibrium flows. The velocity dependent Maxwell boundary conditions are derived for the Direct Simulation Monte Carlo (DSMC) method and the regularized 13-moment (R13) equations for conventional gas dynamics. Then, a thermal cavity is considered to test and study the effect of these boundary conditions on the flow formation in the slip and early transition regime. It turns out that using velocity dependent boundary conditions allows us to change the size and direction of the thermal transpiration force, which leads to marked changes in the balance of transpiration forces and thermal stresses in the flow. / Graduate

Modelling of laminar multiphase flow is extremely important in a wide range of engineering and scientific applications. The particle phases are often difficult to model, especially when particles display a range of sizes and velocities at each location in space. Lagrangian methods can be too expensive and many Eulerian methods, though often computationally more affordable, suffer from model deficiencies and mathematical artifacts that lead to non-physical results. For example, efficient Eulerian models that can accurately predict the crossing of multiple streams of non-interacting particles in laminar flow have traditionally been lacking. The predictive capabilities of modern techniques from the kinetic theory of gases to the treatment of disperse multiphase flows are investigated. In particular, several moment-methods, including a recently proposed fourteen-moment approximation to the underlying kinetic equation describing particle motion, are considered and their abilities to predict particle-stream crossing are assessed. Furthermore, a new polydisperse model has been proposed for treatment of flows that display a range of particles sizes. The proposed model is an extension of the well-known maximum-entropy ten-moment model from rarefied gas dynamics with an addition for the treatment of a range of particle diameters. This model allows for anisotropic variance of particle velocities in phase space and directly treats correlations between particle diameter and velocity. The derivation and mathematical structure, of the proposed models are presented. A fine-volume discretization solution procedure for the resulting moment equations is described and used for performing numerical experiments. Results for flow problems that are designed to demonstrate the fundamental behaviour of each model are presented. It is shown that the new models offer clear advantages in terms of accuracy as compared to traditional Eulerian models for multiphase flows.

Yes / In this paper, the gyrotropic bi-anisotropy of the chiral medium in substrate constitutive parameters (ξc and ηc) of a rectangular microstrip patch antenna is introduced in order to observe its effects on the complex resonant frequency, half-power bandwidth and input impedance. Numerical calculations and analysis based on the dominant mode are carried out to show that the latter is directly related to the former. This paper is based on the Moment Method as full-wave spectral domain approach using sinusoidal basis functions. Two new results, namely the appearance of the difference (ξc-ηc) and sum (ξc+ηc) of the two magneto-electric elements are obtained in the electric transverse components and Green tensor expressions, respectively. These new results can be considered as a generalisation form of the previously published work.

Approved for public release; distribution is unlimited / The Linearly Tapered Slot Antenna (LTSA) had been investigated and developed experimentally; its applications have primarily been based on empirical designs. An accurate theoretical model based on Moment Methods (MM) is developed here to study the radiation characteristics of the LTSA. Using the MM solutions to the reaction integral equation, this thesis presents an analysis to model and explain the LTSA behavior. The effects of variable design parameters on radiation patterns are studied. Discussion is augmented by relating predicted radiation patterns to calculated current distributions on the antenna surface. Conclusions are made regarding optimum designs for the LTSA. Relevant observations are made concerning the extensive computational tasks and the computer resources required for the MM model. / http://archive.org/details/modelingbehavior00kell / Major, United States Army

[pt] Neste trabalho, o Método dos Momentos é aplicado na análise de antenas microfita excitadas por cabo coaxial, utilizando Funções de Green no modelamento dos campos no interior da camada de dielétrico, o que permite considerar as ondas de superfície excitadas no substrato. Para obter a impedância de entrada da antena microfita, foi implementado um algoritmo numérico para a solução do problema. Neste trabalho, atenção especial é dada à análise de singularidades e ao comportamento assintótico dos integrandos envolvidos na solução numérica do problema. A validação do algoritmo é feita através da comparação com resultados apresentados em referências. Os resultados fornecidos pelo Método dos Momentos são comparados com os obtidos na aplicação de outros métodos na solução do problema. Para esta comparação, são utilizados dois programas comerciais de simulação eletromagnética, o Ansoft HFSS e o CST. São feitas simulações com a variação dos parâmetros de entrada do problema, com o objetivo de assegurar a convergência dos resultados e permitir a comparação com os resultados obtidos pelo Método dos Momentos. São apresentadas diferenças entre os resultados obtidos pelos diversos métodos e analisadas as possíveis causas das discrepâncias. / [en] In the present work, the Method of Moments is applied to the analysis of probe fed antennas. The approach uses Green Functions to model the fields within the dielectric layer, which allows to take into account the surface waves excited in the substrate. A numerical algorithm was implemented in order to obtain the microstrip antenna input impedance. The latter is then verified through the comparison with results presented in references. Special attention is given to the analysis of singularities and to the asymptotic behavior of the integrands involved in the numerical solution. A comparison is drawn between the results obtained with the Method of Moments and those obtained with other methods by employing two electromagnetic simulation commercial softwares, Ansoft HFSS and CST. Simulations with different input parameters are performed in order to ensure convergence of the results and allow comparison with results obtained by the Method of Moments. The differences among the results obtained by the several methods addressed in the analysis are presented and the potential causes of them are analyzed.

[pt] Neste estudo faz-se uma análise do desempenho de antenas cônicas compactas para operar em largas bandas de freqüência. Esta análise será feita observando o comportamento da impedância da antena. Serão, primeiramente, consideradas as estruturas convencionais formadas por cones e cones sobrepostos próximos a um plano condutor. Posteriormente, será considerada uma estrutura cônica onde o arredondamento das bordas resulta em um comportamento mais uniforme para a impedância de entrada com variações da freqüência, conferindo um aumento na banda para esta configuração. / [en] The discone antenna is well known as an easy to build multioctave broadband antenna with a omnidirectional radiation pattern in the H-plane, It comprises a plane conductive disc element spaced close to and axially aligned with a conductive cone element. For applications in the UHF and microwave ranges, high performance antennas have been designed to operate from 0.5 to 5 GHz with a VSWR of about 3.5:1 or less. If the length is finite, the impedance still strongly dependent on apex angle as long as the cone is longer than about quarter of wavelength and the apex angle is relatively larger. A problem that is experienced with these antenna designs is the relatively large size required to operate at the low frequencies. In applications where utilization of this antenna. In this work, the analysis and design of these antenna is obtained by employing a rigorous formulation of the electromagnetic scattering problem. As a design tool, we employ Method of Moments for the analysis of rotationally symmetric structures excited by TEM mode. To properly account the variations in driven-point impedance with frequency, the coaxial waveguide used to feed the antenna is also included in the analysis. The excitation is simulated by a distribution of equivalent electric and magnetic currents placed inside the coaxial cable, over a cross-section plane. These currents are defined such that only excite the mode TEM towards the cable-antenna junction. These numerical tool is employed in the shaping the metallic surfaces involved in the discone-type antennas in order to obtain more compact structures. Simple solutions can be easily obtained making the center fed cone and the disc element with radially outer edge portions rolled backwardly and away from each other to form donut-shaped configurations. The ruled edges not only reduce the diameter of the antenna but also permit the current to flow around them smoothly and without reflections that degrade the VSWR at low end of the frequency band.

[pt] Estuda-se o espalhamento de ondas eletromagnéticas por condutores elétricos perfeitos com simetria de revolução. A formulação envolve a solução da Equação Integral para o Campo Elétrico (EFIE), aplicável a superfícies fechadas ou abertas, utilizado-se o Método dos Momentos com funções teste iguais às funções base (alternativa de Galerkin). São empregadas três diferentes classes de funções base: locais (triângulos e retângulos), globais (senos e cossenos) e limitadas em banda (funções sampling-like). Os resultados da análise (determinação da densidade de corrente elétrica induzida por uma onda plana axialmente incidente) de diversos tipos de objetos canônicos (esferas, discos e cone-esferas) ao utilizar-se as duas primeiras classes são comparados com aqueles encontráveis na literatura. Em seguida, analisa-se (determinação da corrente induzida, do campo espalhado e do campo irradiado com uma fonte esférica pontual situada no foco) refletores axialmente simétricos (parabolóides e hiperbolóides) com diâmetro entre 10 e 20 (lambda) empregando-se as três classes. É feita uma comparação entre os resultados variando-se o número de funções base por comprimento de onda para cada classe e os resultados obtidos ao empregar-se a Ótica Física (PO). / [en] The problem of electromagnetic scattering from perfectly conducting circularly symmetric bodies is considered. The mathematical formulation herein employed uses the Electrical Field Integral Equation (EFIE), which is applicable to either open or closed surfaces. The solution is effected by the Method of Moments. Test functions are chosen to be equal to basis functions (Galerkin´s alternative). Three different classes of basis functions are studied: local (pulses and triagles), global (sines and cossines) and band-limited ones (sampling-like functions). Results from the analysis (i. E., determination of induced electric currents)of different Kinds of cononical scatters (spheres, discs and cone-spheres) illuminated by an axially incident plane wave, using local and global functions, are compared with results found in the literature. In addition, circularly symmetric reflector antennas (paraboloids and hyperboloids with diameters between 10-20 lambda) are analyzed using the three different classes. The analysis involves the determination of induced currents, scattered and radiated fielsd. A comparision is made among the results obtained when employing different numbers of basis funcions and with the ones derived from Physical Optics (PO) approxomation.

Cette thèse est constituée de deux parties indépendantes. La première partie concerne l'étude des vecteurs propres de matrices aléatoires de type Wigner. Dans un premier temps, nous étudions la distribution des vecteurs propres de matrices de Wigner déformées, elles consistent en une perturbation d'une matrice de Wigner par une matrice diagonale déterministe. Si les deux matrices sont du même ordre de grandeur, il a été prouvé que les vecteurs propres se délocalisent complètement et les valeurs propres rentrent dans la classe d'universalité de Wigner-Dyson-Mehta. Nous étudions ici une phase intermédiaire où la perturbation déterministe domine l'aléa: les vecteurs propres ne sont pas totalement délocalisés alors que les valeurs propres restent universelles. Les entrées des vecteurs propres sont asymptotiquement gaussiennes avec une variance qui les localise dans une partie explicite du spectre. De plus, leur masse est concentrée autour de cette variance dans le sens d'une unique ergodicité quantique. Ensuite, nous étudions des corrélations de différents vecteur propres. Pour se faire, une nouvelle observable sur les moments de vecteurs propres du mouvement brownien de Dyson est étudiée. Elle suit une équation parabolique close qui est un pendant fermionique du flot des moments de vecteurs propres de Bourgade-Yau. En combinant l'étude de ces deux observables, il est possible d'analyser certaines corrélations.La deuxième partie concerne l'étude de la distribution des valeurs propres de modèles non-linéaires de matrices aléatoires. Ces modèles apparaissent dans l'étude de réseaux de neurones aléatoires et correspondent à une version non-linéaire de matrice de covariance dans le sens où une fonction non-linéaire, appelée fonction d'activation, est appliquée entrée par entrée sur la matrice. La distribution des valeurs propres convergent vers une distribution déterministe caractérisée par une équation auto-consistante de degré 4 sur sa transformée de Stieltjes. La distribution ne dépend de la fonction que sur deux paramètres explicites et pour certains choix de paramètres nous retrouvons la distribution de Marchenko-Pastur qui reste stable après passage sous plusieurs couches du réseau de neurones. / This thesis consists in two independent parts. The first part pertains to the study of eigenvectors of random matrices of Wigner-type. Firstly, we analyze the distribution of eigenvectors of deformed Wigner matrices which consist in a perturbation of a Wigner matrix by a deterministic diagonal matrix. If the two matrices are of the same order of magnitude, it was proved that eigenvectors are completely delocalized and eigenvalues belongs to the Wigner-Dyson-Mehta universality class. We study here an intermediary phase where the deterministic perturbation dominates the randomness of the Wigner matrix : eigenvectors are not completely delocalized but eigenvalues are still universal. The eigenvector entries are asymptotically Gaussian with a variance which localize them onto an explicit part of the spectrum. Moreover, their mass is concentrated around their variance in a sense of a quantum unique ergodicity property. Then, we consider correlations of different eigenvectors. To do so, we exhibit a new observable on eigenvector moments of the Dyson Brownian motion. It follows a closed parabolic equation which is a fermionic counterpart of the Bourgade-Yau eigenvector moment flow. By combining the study of these two observables, it becomes possible to study some eigenvector correlations.The second part concerns the study of eigenvalue distribution of nonlinear models of random matrices. These models appear in the study of random neural networks and correspond to a nonlinear version of sample covariance matrices in the sense that a nonlinear function, called the activation function, is applied entrywise to the matrix. The empirical eigenvalue distribution converges to a deterministic distribution characterized by a self-consistent equation of degree 4 followed by its Stieltjes transform. The distribution depends on the function only through two explicit parameters. For a specific choice of these parameters, we recover the Marchenko-Pastur distribution which stays stable after going through several layers of the network.