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No description available.

Broadband scanning arrays require small element spacing over a broad frequency band to achieve the desired scan capabilities. Previous research has concentrated on the development of small broadband elements to meet the demands of broadband arrays. However, mutual coupling between elements in a tightly spaced array can change the operating frequency and bandwidth from that of the single isolated element. Several research efforts have focused on minimizing the mutual coupling to maintain the frequency response of the single isolated element. This dissertation focuses on using the strong coupling between Foursquare antennas to obtain the broadband frequency response while maintaining a small element spacing. The isolated Foursquare antenna was modeled using an in-house FDTD code. The modeled current distribution over the frequency band of operation revealed how the antenna achieved a broadband frequency response. Because of this understanding of the single element, the downward shift in the frequency response of the Foursquare antenna in a fully active array could be anticipated. Furthermore, the infinite array models of the Foursquare revealed an increase in bandwidth. Both are desirable characteristics for a broadband scanning array. Therefore, through this research using the Foursquare element, it has been shown that the strong mutual coupling in a tightly spaced array can have advantages if initially taken into consideration when designing the array. / Ph. D.

Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. Specifically, we study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet. The equation for stability is derived and solved numerically using the Chebyshev collocation spectral method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability. The numerical solutions are compared with the analysis of the long wave limit and excellent agreement is shown between the analytical and the numerical solutions. We found flows which are long wave stable, but nevertheless unstable to wave numbers in a certain finite range. While elasticity is ultimately stabilizing, this effect is not monotone; there are instances where a small amount of elasticity actually destabilizes the flow. The linear stability in the short wave limit of shear flows bounded by two parallel free surfaces is investigated. Unlike the plane Couette flow which has no short wave instability, we show that plane Poiseuille flow has two unstable eigenmodes localized near the free surfaces which can be combined into an even and an odd eigenfunctions. The derivation of the asymptotics of these modes shows that our numerical eigenvalues are in agreement with the analytic formula and that the difference between the two eigenvalues tends to zero exponentially with the wavenumber. / Ph. D.

This thesis poses and solves a distribution free learning problem with consensus that arises in the study of estimation and control strategies for distributed sensor networks. Each node i for i = 1, . . . , n of the sensor network collects independent and identically distributed local measurements {z i} := {z i j}j∈N := {(x i j , yi j )}j∈N ⊆ X × Y := Z that are generated by the probability measure ρ i on Z. Each node i for i = 1, . . . , n of the network constructs a sequence of estimates {f i k }k∈N from its local measurements {z i} and from information functionals whose values are exchanged with other nodes as specified by the communication graph G for the network. The optimal estimate of the distribution free learning problem with consensus is cast as a saddle point problem which characterizes the consensus-constrained optimal estimate. This thesis introduces a two stage learning dynamic wherein local estimation is carried out via local least square approximations based on wavelet constructions and information exchange is associated with the Lagrange multipliers of the saddle point problem. Rates of convergence for the two stage learning dynamic are derived based on certain recent probabilistic bounds derived for wavelet approximation of regressor functions. / Master of Science

This thesis generalizes and interprets Kesten\'s Incipient Infinite Cluster (IIC) measure in two ways. Firstly we generalize Járai\'s result which states that for planar lattices the local configurations around a typical point taken from crossing collection is described by IIC measure. We prove in Chapter 2 that for backbone, lowest crossing and set of pivotals, the same hold true with multiple armed IIC measures. We develop certain tools, namely Russo Seymour Welsh theorem and a strong variant of quasi-multiplicativity for critical percolation on 2-dimensional slabs in Chapters 3 and 4 respectively. This enables us to first show existence of IIC in Kesten\'s sense on slabs in Chapter 4 and prove that this measure can be interpreted as the local picture around a point of crossing collection in Chapter 5.

In der vorliegenden Arbeit wird ein Programmcode zur numerischen Modalanalyse dreidimensionaler Fluide in komplexen akustischen Systemen, speziell in Resonatoren, entwickelt. Mit diesem Code ist es möglich, turbulente Strömungen im Rahmen der Modalanalyse zu berücksichtigen. Hierzu wird ein realistisches Strömungsprofil, ermittelt mithilfe eines 3D-Navier-Stokes-Lösers, verwendet. Der Hauptteil der Arbeit befasst sich mit der Herleitung der für die Berechnung notwendigen Galbrun-Gleichung und deren Aufbereitung zur numerischen Analyse. Für die numerische Umsetzung kommt die Methode der finiten Elemente in Verbindung mit komplex konjugierten, infiniten Astley-Leis Elementen zur Anwendung. Die infiniten Elemente werden genutzt, um in den betrachteten Außenraumproblemen die Abstrahlung in das Fernfeld abzubilden. Nach der Anwendung des entwickelten Programmcodes auf einfachere Modelle erfolgen Untersuchungen zur Intonation einer Blockflöte. Hierzu wird das Fluid innerhalb und im Nahfeld des Instruments unter Berücksichtigung des turbulenten Strömungsprofils, welches sich beim Spielen der Blockflöte ausbildet, betrachtet. Im Ergebnis stehen die Eigenwerte des Instruments in Abhängigkeit von der gewählten Griffkombination. Zur Evaluierung der Ergebnisse und zur Untersuchung des Einflusses der Strömung auf den Klang erfolgt der Vergleich mit den exakten Eigenfrequenzen. Die Galbrun-Gleichung wurde bereits von anderen Autoren untersucht und auf akustische Problemstellungen angewendet. Im Rahmen dieser Arbeit erfolgt jedoch erstmalig die Anwendung der Galbrun-Gleichung auf Eigenwertprobleme. Darüber hinaus sind der Autorin keine Arbeiten bekannt, die sich mit dreidimensionalen Modellen befassen. In der vorliegenden Arbeit werden somit erstmals komplexe dreidimensionale Modelle unter Anwendung der Galbrun-Gleichung untersucht.

We consider the set of all spacelike embeddings of the circle S1 into a spacetime R1 × S1 with a metric globally conformal to the Minkowski metric. We identify this set and the group of conformal isometries of this spacetime as quotients of semidirect products involving diffeomorphism groups and give a transitive action of the conformal group on the set of spacelike embeddings. We provide results showing that the group of conformal isometries is a topological group and that its action on the set of spacelike embeddings is continuous. Finally, we point out some directions for future research.

A subfield of artificial intelligence, machine learning (ML), is concerned with the development of algorithms that allow computers to &ldquo / learn&rdquo / . ML is the process of training a system with large number of examples, extracting rules and finding patterns in order to make predictions on new data points (examples). The most common machine learning schemes are supervised, semi-supervised, unsupervised and reinforcement learning. These schemes apply to natural language processing, search engines, medical diagnosis, bioinformatics, detecting credit fraud, stock market analysis, classification of DNA sequences, speech and hand writing recognition in computer vision, to encounter just a few. In this thesis, we focus on Support Vector Machines (SVMs) which is one of the most powerful methods currently in machine learning. As a first motivation, we develop a model selection tool induced into SVM in order to solve a particular problem of computational biology which is prediction of eukaryotic pro-peptide cleavage site applied on the real data collected from NCBI data bank. Based on our biological example, a generalized model selection method is employed as a generalization for all kinds of learning problems. In ML algorithms, one of the crucial issues is the representation of the data. Discrete geometric structures and, especially, linear separability of the data play an important role in ML. If the data is not linearly separable, a kernel function transforms the nonlinear data into a higher-dimensional space in which the nonlinear data are linearly separable. As the data become heterogeneous and large-scale, single kernel methods become insufficient to classify nonlinear data. Convex combinations of kernels were developed to classify this kind of data [8]. Nevertheless, selection of the finite combinations of kernels are limited up to a finite choice. In order to overcome this discrepancy, we propose a novel method of &ldquo / infinite&rdquo / kernel combinations for learning problems with the help of infinite and semi-infinite programming regarding all elements in kernel space. This will provide to study variations of combinations of kernels when considering heterogeneous data in real-world applications. Combination of kernels can be done, e.g., along a homotopy parameter or a more specific parameter. Looking at all infinitesimally fine convex combinations of the kernels from the infinite kernel set, the margin is maximized subject to an infinite number of constraints with a compact index set and an additional (Riemann-Stieltjes) integral constraint due to the combinations. After a parametrization in the space of probability measures, it becomes semi-infinite. We analyze the regularity conditions which satisfy the Reduction Ansatz and discuss the type of distribution functions within the structure of the constraints and our bilevel optimization problem. Finally, we adapted well known numerical methods of semiinfinite programming to our new kernel machine. We improved the discretization method for our specific model and proposed two new algorithms. We proved the convergence of the numerical methods and we analyzed the conditions and assumptions of these convergence theorems such as optimality and convergence.

This thesis generalizes and interprets Kesten\''s Incipient Infinite Cluster (IIC) measure in two ways. Firstly we generalize Járai\''s result which states that for planar lattices the local configurations around a typical point taken from crossing collection is described by IIC measure. We prove in Chapter 2 that for backbone, lowest crossing and set of pivotals, the same hold true with multiple armed IIC measures. We develop certain tools, namely Russo Seymour Welsh theorem and a strong variant of quasi-multiplicativity for critical percolation on 2-dimensional slabs in Chapters 3 and 4 respectively. This enables us to first show existence of IIC in Kesten\''s sense on slabs in Chapter 4 and prove that this measure can be interpreted as the local picture around a point of crossing collection in Chapter 5.