Master of Science / Particulate ingestion has been an ongoing issue in the aviation industry as aircraft are required to operate in hostile environments. Ingesting particulates such as sand or dust can erode and damage engine components. This damage will affect the life cycle of parts and compromise the safety of the aircraft. This issue is very costly and dangerous. In order to combat these issues, a particle sensor with the ability to monitor in-stream particulate size, shape, and mass flow rate is necessary. Our team with the Advanced Propulsion and Power Laboratory developed a non-intrusive optical sensor that is able to characterize non-spherical particles. This sensor has been used in various applications through the years; however, most recently, the sensor has been demonstrated at the Virginia Tech M250 engine inlet. This was the first time that the sensor was directly attached to an engine's inlet and subjected to engine conditions. For this validation, highly erosive, coarse quartz was used. Utilizing laser and cameras, the sensor is able to deduce the particles' average shape and size distributions. From those measurements, the mass flow rate of the particle can be calculated. The works provided in the thesis show that particle ingestion rates can be measured to an acceptably high accuracy. In contrast, refinement of the processing techniques can provide spatially resolved measurements of particle characteristics as well.

Bandwidth enhancement of low-profile omnidirectional, electrically-small antennas has evolved from the design and construction of AM transmitter towers eighty years ago to current market demand for battery-powered personal communication devices. Electrically-small antenna theory developed with well-known approximations for characterizing radiation properties of antenna structures that are fractions of the radiansphere. Current state-of-the-art wideband small antennas near kaH1 have achieved multiple-octave impedance bandwidths when utilizing volume-efficient designs. Significant advances in both the power and miniaturization of microelectronics have created a second possible approach to enhance bandwidth. Frequency agility, via switch tuning of reconfigurable structures, offers the possibility of the direct integration of high-speed electronics to the antenna structure. The potential result would provide a means to translate a narrow instantaneous bandwidth across a wider operating bandwidth. One objective of the research was to create a direct comparison of the passive- multi-resonant and active-reconfigurable approaches to enhance bandwidth. Typically, volume-efficient, wideband antennas are unattractive candidates for low-profile applications and conversely, active electronics integrated directly antenna elements continue to introduce problematic loss mechanisms at the proof-of-concept level The dissertation presents an analysis method for wide bandwidth self-resonant antennas that exist in the 0.5dkad1.0 range. The combined approach utilizes the quality factor extracted directly from impedance response data in addition to near-and-far field modal analyses. Examples from several classes of antennas investigated are presented with practical boundary conditions. The resultant radiation properties of these antenna-finite ground plane systems are characterized by an appreciable percentage of radiated power outside the lowest-order mode. Volume-efficient structures and non-omnidirectional radiation characteristics are generally not viable for portable devices. Several examples of passive structures, representing different antenna classes are investigated. A PIN diode, switch-tuned low-profile antenna prototype was also developed for the comparison which demonstrated excessive loss in the physical prototype. Lastly, a passive, low-profile multi-resonant antenna element with monopole radiation is introduced. The structure is an extension of the planar inverted-F antenna with the addition of a capacitance-coupled parasitic to enhance reliable operation in unknown environments. / Ph. D.

In Chapter 1 we introduce the Yokonuma-Hecke Algebra and a Yokonuma-Hecke Algebra-module. In Chapter 2 we determine that the possible eigenvalues of particular elements in the Yokonuma-Hecke Algebra acting on the module. In Chapter 3 we find determine module subspaces and eigenspaces that are isomorphic. In Chapter 4 we determine the structure of the q-eigenspace. In Chapter 5 we determine the spherical elements of the module. / Master of Science / The Yokonuma-Hecke Algebra-module is a vector space over a particular field. Acting on vectors from the module by any element of the Yokonuma-Hecke Algebra corresponds to a linear transformation. Then, for each element we can find eigenvalues and eigenvectors. The transformations that we are considering all have the same eigenvalues. So, we consider the intersection of all the eigenspaces that correspond to the same eigenvalue. I.e. vectors that are eigenvectors of all of the elements. We find an algorithm that generates a basis for said vectors.

No / Aspheric intraocular lenses (IOLs) are designed to correct spherical aberration in pseudophakic eyes. We predict the benefit from correcting spherical aberration based on simulations and aberrometry of pseudophakic eyes implanted with spherical IOLs. METHODS Ray tracing was performed through a model eye with an equi-biconvex spherical IOL and with a spherical aberration-correcting aspheric IOL. The IOLs were increasingly tilted and/or displaced, and the resulting transverse aberrations of 169 rays were transformed into Zernike coefficients for different pupil sizes. The benefit from correcting spherical aberration at individual mesopic pupils was investigated by canceling in the sets of Zernike coefficients for 41 eyes implanted with a spherical IOL. RESULTS Both the model eye and the real eye data predict that age-related miosis reduces spherical aberration in the eye implanted with a spherical IOL to approximately 1/3 of the spherical aberration at a 6-mm pupil. A reduction of similar magnitude occurs when spherical aberration-induced non-paraxial defocus is corrected by a spectacle lens. For natural mesopic pupils, canceling the Zernike coefficient improved the objective image quality at a rate similar to changing defocus by 0.05 diopters. Average centration and tilt levels diminish the lead of aspheric IOLs over spherical IOLs, depending on the direction of decentration. CONCLUSIONS The benefit from correcting spherical aberration in a pseudophakic eye is limited for some or all of the following reasons: wearing glasses, age-related miosis, tilt and decentration of IOL, small contribution of spherical aberration to all aberrations, and intersubject variability

In this thesis, the parallel performance of the finite element-spherical harmonics (FE-PN) method implemented in the general-purpose radiation transport code EVENT is studied both analytically and empirically. EVENT solves the coupled set of space-angle discretized FE-PN equations using a parallel block-Jacobi domain decomposition method. As part of the analytical study, the thesis presents complexity results for EVENT when solving for a 3D criticality benchmark radiation transport problem in parallel. The empirical analysis is concerned with the impact of the main algorithmic factors affecting performance. Firstly, EVENT supports two solution strategies, namely MOD (Moments Over Domains) and DOM (Domains Over Moments), to solve the transport equation in parallel. The two strategies differ in the way they solve the multi-level space-angle coupled systems of equations. The thesis presents empirical evidence of which of the two solution strategies is more efficient. Secondly, different preconditioners are used in the Preconditioned Conjugate Gradient (PCG) inside EVENT. Performance of EVENT is compared when using three preconditioners, namely diagonal, SSOR(Symmetric Successive Over-Relaxation) and ILU. The other two factors, angular and spatial resolutions of the problem affect both the performance and precision of EVENT. The thesis presents comparative results on EVENTs performance as these two resolutions are increased. From the empirical performance study of EVENT, a bottleneck is identified that limits the improvement in performance as number of processors used by EVENT is increased. In some experiments, it is observed that uneven assignment of computational load among processors causes a significant portion of the total time being spent in synchronization among processors. The thesis presents two indicators that identify when such inefficiency occur; and in such a case, a load rebalancing strategy is applied that computes a new partition of the problem so that each partition corresponds to equal amount of computational load.

In indoor environment, the multi-sensor system has been proved to be an efficient solution for target locating process in terms of lower estimation cost. However, the placement of designed multi-sensor has great impact on the location performance in an indoor environment. Based on the time difference of arrival (TDOA), closed-form least-square location methods, including the spherical-interpolation (SI) and the spherical-intersection (SX) methods, are used in the estimation of target locations. The two methods are apart from the usual process of iterative and nonlinear minimization. Consequently, under the influence of noise interference, the performance of the two methods also produce different results. In addition to the above issues, the limitation of these methods will also be examined. The geometric dilution of precision (GDOP) effects of TDOA location on location performance of both inside and outside of the multi-sensor environment in the 2-D scenario have been studied in the past. This thesis aims to further advance the performance of GDOP in 3-D scenarios, analyze the differences, and propose the suitable needs. Programmed 3-D scenario simulations are used in this research, designed according to multiple sensor arrays and the moving latitude of a target. The Setup interprets the degree of multi-sensor separation, and distances from targets to the sensor array. A suitable location algorithm and optimal multi-sensor deployments in an indoor environment were proposed according to the simulation results.

<p>Spherical agglomerates of benzoic acid crystals have been successfully prepared by drowning-out crystallization in three solvent partial miscible mixtures. Benzoic acid is dissolved in ethanol, bridging liquid is added and this mixture is fed to the agitated crystallizer containing water. Fine crystals are produced by crystallization of the substance, and the crystals are agglomerated by introduction of an immiscible liquid called the bridging liquid. The concentration of solute, agitation rate, feeding rate, amount of bridging liquid and temperature are found to have a significant influence on the physico-mechanical properties of the product. The product particle characterization includes the particle size distribution, morphology and mechanical strength.</p><p>Many of the solvents such as chloroform, toluene, pentane, heptane, cyclo hexane, diethyl ether and ethyl acetate were used as bridging liquids. Among the selected solvents ethyl acetate and di ethyl ether could not form the spherical agglomerates. Characteristics of the particles are changing with the bridging liquid used. Range of the operation for spherical agglomeration is very narrow and was shown that only at certain conditions the spherical agglomerates are produced. Increased amount of bridging liquid, decrease in feeding rate and temperature causes the particle size to increase. Particle morphology depends on the bridging liquid used, amount of bridging liquid and the temperature. Particles look completely spherical from the experiments where toluene is used as bridging liquid. </p><p>The mechanical strength of single agglomerates has been determined by compression in a materials testing machine, using a 10N load cell. For single particle compression an approximate estimation of the true stress is presented. Compression characteristics for single agglomerates are compared with data on particle bed compression. Low elastic recovery and high compressibility of the single particles and of bed of particles reveals that the spherical agglomerates prepared in this work have a plastic behavior which is expected to be favorable for direct tabletting. Some of the stress–strain curves are J-shaped with no clear fracturing of the particles, and are well correlated by an exponential–polynomial equation. </p>

The area of particle characterization is expansive; it contains many technologies and methods of analysis. Light spectroscopy techniques yield information on the joint property distribution of particles, comprising the chemical composition, size, shape, and orientation of the particles. The objective of this dissertation is to develop a hybrid scattering-absorption model incorporating Mie and Rayleigh-Debye-Gans theory to characterize submicron particles in suspension with multiwavelength spectroscopy.Rayleigh-Debye-Gans theory (RDG) was chosen as a model to relate the particles joint property distribution to the light scattering and absorption phenomena for submicron particles. A correction model to instrument parameters of relevance was implemented to Rayleigh-Debye-Gans theory for spheres. Behavior of nonspherical particles using RDG theory was compared with Mie theory (as a reference). A multiwavelength assessment of Rayleigh-Debye-Gans theory for spheres was conducted where strict adherence to the limits could not be followed. Reported corrections to the refractive indices were implemented to RDG to try and achieve Mies spectral prediction for spheres.The results of studies conducted for RDG concluded the following. The angle of acceptance plays an important role in being able to assess and interpret spectral differences. Multiwavelength transmission spectra contains qualitative information on shape and orientation of non-spherical particles, and it should be possible to extract this information from carefully measured spectra. There is disagreement between Rayleigh-Debye-Gans and Mie theory for transmission simulations with spherical scatterers of different sizes and refractive indices.

Diffusion MRI (dMRI) measurements allow us to infer the microstructural properties of white matter and to reconstruct fiber pathways in-vivo. High angular diffusion imaging (HARDI) allows for the creation of more and more complex local models connecting the microstructure to the measured signal. One of the challenges is the derivation of meaningful metrics describing the underlying structure from the local models. The aim hereby is to increase the specificity of the widely used metric fractional anisotropy (FA) by using the additional information contained within the HARDI data. A local model which is connected directly to the underlying microstructure through the model of a single fiber population is spherical deconvolution. It produces a fiber orientation density function (fODF), which can often be interpreted as superposition of multiple peaks, each associated to one relatively coherent fiber population (bundle). Parameterizing these peaks one is able to disentangle and characterize these bundles. In this work, the fODF peaks are approximated by Bingham distributions, capturing first and second order statistics of the fiber orientations, from which metrics for the parametric quantification of fiber bundles are derived. Meaningful relationships between these measures and the underlying microstructural properties are proposed. The focus lies on metrics derived directly from properties of the Bingham distribution, such as peak length, peak direction, peak spread, integral over the peak, as well as a metric derived from the comparison of the largest peaks, which probes the complexity of the underlying microstructure. These metrics are compared to the conventionally used fractional anisotropy (FA) and it is shown how they may help to increase the specificity of the characterization of microstructural properties. Visualization of the micro-structural arrangement is another application of dMRI. This is done by using tractography to propagate the fiber layout, extracted from the local model, in each voxel. In practice most tractography algorithms use little of the additional information gained from HARDI based local models aside from the reconstructed fiber bundle directions. In this work an approach to tractography based on the Bingham parameterization of the fODF is introduced. For each of the fiber populations present in a voxel the diffusion signal and tensor are computed. Then tensor deflection tractography is performed. This allows incorporating the complete bundle information, performing local interpolation as well as using multiple directions per voxel for generating tracts. Another aspect of this work is the investigation of the spherical harmonic representation which is used most commonly for the fODF by means of the parameters derived from the Bingham distribution fit. Here a strong connection between the approximation errors in the spherical representation of the Dirac delta function and the distribution of crossing angles recovered from the fODF was discovered. The final aspect of this work is the application of the metrics derived from the Bingham fit to a number of fetal datasets for quantifying the brain’s development. This is done by introducing the Gini-coefficient as a metric describing the brain’s age.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O principal objetivo deste trabalho foi estudar, em triângulos construídos sobre uma superfície esféerica, versões para resultados conhecidos da geometria euclidiana plana e da trigonometria nos triângulos planos. Inicialmente apresentam-se os conceitos fundamentais da geometria esférica e alguns elementos de trigonometria triangular esférica. Para isso, iniciou-se com uma breve revisão de alguns desses resultados e também com algumas definições da geometria plana necessárias para a construção de resultados da geometria esférica. Feito isso, foram construídas, em um triângulo esférico, versões para a lei dos senos, a lei dos cossenos e outros resultados da trigonometria triangular plana. Também foi visto o Teorema de Girard, onde pode-se estudar a área de um triângulo construído sobre a superfície de uma esfera de raio R e a soma de seus ângulos internos, que ao contrário do que ocorre nos triângulos planos inscritos em um círculo de raio r, não é constante. Foi apresentado um contraexemplo, neste ambiente, em que o famoso teorema de Pitagoras não vale. Ao longo do texto são apresentados alguns exemplos com a utilização das relações trigonométricas estudadas, bem como alguns conceitos elementares de coordenadas geograficas e aplicações práaticas da trigonometria esférica na aviação e na geografia. Finalmente, observa-se que esse trabalho utiliza fortemente a matemática do Ensino Básico, facilitando assim a compreensão e o acesso de alunos e professores do Ensino Médio, bem como profissionais que fazem uso da matematica. / The main objective of this work was to study in triangles constructed on a spherical surface, versions of known results of the plane euclidean geometry and trigonometry in plans triangles. Initially it presents the fundamental concepts of spherical geometry and some elements of spherical triangular trigonometry. For this, begins with a brief review of some of these results and also with some denitions of plane geometry required for the construction of spherical geometry results. That done, are build, in a spherical triangle, versions for the law of sines, law of cosines and other results of the plane triangular trigonometry. Was also seen is the theorem of Girard, where can study the area of a triangle built on the surface of a sphere of radius R and the sum of its internal angles, which is not constant unlike what occurs in triangles plans built on disc of radius r. The Pythagorean theorem is not true in this environment and a counter-example will be presented. Throughout the text will be presented some examples with the use of trigonometric relations, as well as some elementary concepts of geographical coordinates and practical applications of spherical trigonometry in aviation and geography. Finally it is observed that this work strongly uses the mathematics of basic education, facilitating the understanding of the said theory, of students and teachers of basic education, as well as of the professionals who use math.