abstract: Asymptotic and Numerical methods are popular in applied electromagnetism. In this work, the two methods are applied for collimated antennas and calibration targets, respectively. As an asymptotic method, the diffracted Gaussian beam approach (DGBA) is developed for design and simulation of collimated multi-reflector antenna systems, based upon Huygens principle and independent Gaussian beam expansion, referred to as the frames. To simulate a reflector antenna in hundreds to thousands of wavelength, it requires 1E7 - 1E9 independent Gaussian beams. To this end, high performance parallel computing is implemented, based on Message Passing Interface (MPI). The second part of the dissertation includes the plane wave scattering from a target consisting of doubly periodic array of sharp conducting circular cones by the magnetic field integral equation (MFIE) via Coiflet based Galerkin's procedure in conjunction with the Floquet theorem. Owing to the orthogonally, compact support, continuity and smoothness of the Coiflets, well-conditioned impedance matrices are obtained. Majority of the matrix entries are obtained in the spectral domain by one-point quadrature with high precision. For the oscillatory entries, spatial domain computation is applied, bypassing the slow convergence of the spectral summation of the non-damping propagating modes. The simulation results are compared with the solutions from an RWG-MLFMA based commercial software, FEKO, and excellent agreement is observed. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012

This analysis studies the phenomenon of the New Keynesian Phillips Curve - its inception from the RBC theory and DSGE modelling via incorporation of nominal rigidities, and its various specifications and empirical issues. The estimates on Czech macroeconomic data using the Generalised Method of Moments show that the hybrid New Keynesian Phillips Curve with the labour income share or the real unit labour cost as driving variables can be considered as an appropriate model describing inflation in the Czech Republic. Compared to other analyses, we show that the inflation process in the Czech Republic exhibits higher backwardness vis-a-vis other researchers' estimates based on US data.

Les modèles linéaires latents sont des modèles statistique puissants pour extraire la structure latente utile à partir de données non structurées par ailleurs. Ces modèles sont utiles dans de nombreuses applications telles que le traitement automatique du langage naturel et la vision artificielle. Pourtant, l'estimation et l'inférence sont souvent impossibles en temps polynomial pour de nombreux modèles linéaires latents et on doit utiliser des méthodes approximatives pour lesquelles il est difficile de récupérer les paramètres. Plusieurs approches, introduites récemment, utilisent la méthode des moments. Elles permettent de retrouver les paramètres dans le cadre idéalisé d'un échantillon de données infini tiré selon certains modèles, mais ils viennent souvent avec des garanties théoriques dans les cas où ce n'est pas exactement satisfait. Dans cette thèse, nous nous concentrons sur les méthodes d'estimation fondées sur l'appariement de moment pour différents modèles linéaires latents. L'utilisation d'un lien étroit avec l'analyse en composantes indépendantes, qui est un outil bien étudié par la communauté du traitement du signal, nous présentons plusieurs modèles semiparamétriques pour la modélisation thématique et dans un contexte multi-vues. Nous présentons des méthodes à base de moment ainsi que des algorithmes pour l'estimation dans ces modèles, et nous prouvons pour ces méthodes des résultats de complexité améliorée par rapport aux méthodes existantes. Nous donnons également des garanties d'identifiabilité, contrairement à d'autres modèles actuels. C'est une propriété importante pour assurer leur interprétabilité. / Latent linear models are powerful probabilistic tools for extracting useful latent structure from otherwise unstructured data and have proved useful in numerous applications such as natural language processing and computer vision. However, the estimation and inference are often intractable for many latent linear models and one has to make use of approximate methods often with no recovery guarantees. An alternative approach, which has been popular lately, are methods based on the method of moments. These methods often have guarantees of exact recovery in the idealized setting of an infinite data sample and well specified models, but they also often come with theoretical guarantees in cases where this is not exactly satisfied. In this thesis, we focus on moment matchingbased estimation methods for different latent linear models. Using a close connection with independent component analysis, which is a well studied tool from the signal processing literature, we introduce several semiparametric models in the topic modeling context and for multi-view models and develop moment matching-based methods for the estimation in these models. These methods come with improved sample complexity results compared to the previously proposed methods. The models are supplemented with the identifiability guarantees, which is a necessary property to ensure their interpretability. This is opposed to some other widely used models, which are unidentifiable.

The combustion of petroleum-based fuels leads to the formation of several pollutants. Among them, soot particles are particularly harmful due to their severe consequences on human health. Over the past decades, strict regulations have been placed on automotive and aircraft engines to limit these particulate matter emissions. This work is primarily focused on understanding the fundamental behaviour of soot particles and their formation. Though the focus of this work is on soot formation and growth pathways, the study of the gas-phase combustion process was also an integral part to validate the mechanism. A reduced mechanism is developed with retaining the larger PAH species till coronene from KAUST-ARAMCO mechanism. Counterflow diffusion flames had emphasized the simulation of canonical configuration where the reduced mechanism is validated and the soot growth pathways are evaluated. The importance of the significant contribution of larger PAH species on the soot growth pathways in both SF and SFO flames is evident in this analysis. The sensitivity of these flames with respect to strain rates, dilution, and at higher pressures are analysed. Direct Numerical Simulation (DNS) of two-dimensional counterflow diffusion flames is conducted to understand the impact of vortex interactions on soot characteristics. The results indicate that the larger PAH species contributes to the soot formation in the air-side perturbation regimes, whereas the soot formation is dominated by the soot transport in fuel-side perturbation. The study is extended to simulate and compare coflow laminar flame using different statistical moment methods MOMIC, HMOM and CQMOM.

Some methods for generating scenarios from multidimensional distribution assume we are able to generate scenarios from the one-dimensional distribution. We dedicate chapter 3 to this problem. At the end of the chapter, we provide references for applicable algorithms. Chapter 4 is focused on selected methods for generating scenarios from multidimensional distributions. In chapter 4.3, we introduce an algorithm for generating scenarios, which do not use any assumption about the distribution, except the first four moments and correlations to be specified. A method of generating scenarios based on approximation of multivariate normal distribution by the binomial distribution is described in chapter 4.5. Dimension reduction technique using principal components is presented in chapter 4.4. The algorithm is presented under the assumption of normal distribution. In chapter 4.6, we introduce the basics of the copula theory and a method for generating scenarios by C-vine copula. In chapter 5, we implement selected methods for generating scenarios for the estimation of daily value at risk for selected indexes and we discuss the results. Powered by TCPDF (www.tcpdf.org)

<div>Recently, researchers have pointed their attention toward Method of Moments (MoM)-based approaches to model low frequency magnetic devices (i.e. transformers and inductors). This has been prompted by the use of population-based design (PBD) methods wherein the performance of large numbers (on the order of millions) of candidate designs must be evaluated. MoM is attractive for such problems due to the fact that only the magnetic material is discretized. In addition, for the case in which the magnetic material is linear, only a surface mesh is required. In this research, point-matching and Galerkin-based MoM formulations are utilized for the design of electric machinery. In the formulations considered, the model inputs are the free currents of machine windings and the bound currents of permanent magnets. The unknowns are the magnetizations within the magnetic material which are used to compute winding inductance, electromagnetic torque, and core loss. </div><div><br></div><div>The proposed Galerkin formulation has been utilized in the PBD of a surface-mount permanent magnet machine with favorable results. Specifically, it is shown that a machine's performance can be evaluated on a time scale expected of a practical design tool. This is achieved in part through judicious exploitation of the periodic structure and excitation of machines to reduce the size of the system matrix. It is shown how the exploitation of periodic structure may be extended to the point-matching formulation for use in nonlinear analyses. Finally, alternative hybrid approaches that combine surface and volume meshing are explored for the analysis of an internal permanent magnet machine. It is shown that such a combination holds promise as a tool for rapid evaluation of machine performance.</div>

<div>In this research, the use of a Type-2 superconducting material (i.e. Yttrium Barium Copper Oxide) as a magnetic flux source within synchronous machines is considered. To do so, an analytical model is applied to predict the magnetic field and the currents that are induced within the material when it is magnetized to a mixed-state. These induced currents are then used to model the synchronous machine performance within a 2-dimensional Method of Moments (MoM) formulation. The MoM-based model is used in tandem with a thermal equivalent circuit to calculate the cooling required to keep the YBCO below its critical temperature. These are utilized within a genetic algorithm (GA) to evaluate the tradeoffs between mass and loss for several example electric drives ranging from 10 kW-20 MW. The expected mass and loss of the YBCO machines are compared to those of a standard permanent magnet synchronous machine (PMSM). Specifically, Pareto-optimal fronts are used to assess power levels where cryo-cooled YBCO materials may be warranted.<br></div>

Thesis advisor: Uzi Segal / The dissertation studies the property of transitivity in the social choice theory. I explain why we should care about transitivity in decision theory. I propose two social decision theories: redistribution regret and ranking regret, study their properties of transitivity, and discuss the possibility to find a best choice for the social planner. Additionally, in the joint work, we propose a general method to construct a consistent estimator given two parametric models, one of which could be incorrectly specified. In “Why Transitivity”, to explain behaviors violating transitivity, e.g., preference reversals, some models, like regret theory, salience theory were developed. However, these models naturally violate transitivity, which may not lead to a best choice for the decision maker. This paper discusses the consequences and the possible extensions to deal with it. In “Redistribution Regret and Transitivity”, a social planner wants to allocate resources, e.g., the government allocates fiscal revenue or parents distribute toys to children. The social planner cares about individuals' feelings, which depend both on their assigned resources, and on the alternatives they might have been assigned. As a result, there could be intransitive cycles. This paper shows that the preference orders are generally non-transitive but there are two exceptions: fixed total resource and one extremely sensitive individual, or only two individuals with the same non-linear individual regret function. In “Ranking Regret”, a social planner wants to rank people, e.g., assign airline passengers a boarding order. A natural ranking is to order people from most to least sensitive to their rank. But people's feelings can depend both on their assigned rank, and on the alternatives they might have been assigned. As a result, there may be no best ranking, due to intransitive cycles. This paper shows how to tell when a best ranking exists, and that when it exists, it is indeed the natural ranking. When this best does not exist, an alternative second-best group ranking strategy is proposed, which resembles actual airline boarding policies. In “Over-Identified Doubly Robust Identification and Estimation”, joint with Arthur Lewbel and Jinyoung Choi, we consider two parametric models. At least one is correctly specified, but we don't know which. Both models include a common vector of parameters. An estimator for this common parameter vector is called Doubly Robust (DR) if it's consistent no matter which model is correct. We provide a general technique for constructing DR estimators (assuming the models are over identified). Our Over-identified Doubly Robust (ODR) technique is a simple extension of the Generalized Method of Moments. We illustrate our ODR with a variety of models. Our empirical application is instrumental variables estimation, where either one of two instrument vectors might be invalid. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

The wireless industry is such that suppliers of antennas have to adapt their designs to requirement changes over a period of just a few months. In these short design cycles time is crucial. Radiation pattern testing of the antennas at various points in this design cycle are nowadays mostly done using spherical near-field techniques, where the tangential electric field is acquired over an imaginary sphere close to, and surrounding, the antenna under test, and this data then transformed into a far-zone radiation pattern. There are some applications where acquisition over a rotationally symmetric surface other than a spherical one would not only reduce test times, but allow equipment cost reductions as well. However, near-field to far-field transformations for finite non-spherical measurement surface shapes are not available. Such a transformation is proposed, implemented and validated in this thesis. It uses the method of moments, customized to a rotationally symmetric surface (body of revolution) to effect this transformation.

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