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.

This study aims to deduce an appropriate shape and density for an electronic free-cell that could be placed into a silo so that position and other desired physical parameters could be recorded. To determine how density and shape affects the trajectory and displacement of free cells, the trajectory and displacement of cylindrical, cuboid and triangular prism free-cells of equivalent volume was investigated in a discharging quasi 3D silo slice. The free-cells were placed at twelve different starting positions spread evenly over one half of the 3D slice. Tests were conducted using a monosized batch of spherical particles with a diameter of approximately 5 mm. Tests were also conducted in a binary mixture consisting of particles of different sizes (5 mm/4 mm) and the same density (1.28 g/cm3) and a binary mixture consisting of particles of different size (6 mm/5 mm) and different densities (1.16 g/cm3/1.28 g/cm3).The rotation of the free cells was also briefly discussed.Computer simulations were conducted using the Discrete Element Method (DEM). The simulation employed the spring-slider-dashpot contact model to represent the normal and tangential force components and the modified Euler integration scheme was applied to calculate the particle velocities and positions at each time step. One trial of each of the metal and plastic, cylindrical, cuboid and triangular prism free cells was compared with the average of three experimental trials. The trajectory and displacement of a representative particle positioned at the same starting position as the free cell was also obtained from DEM simulation and compared with the path and displacement of each of the free cells to determine which free cell followed the particle most closely and hence to determine a suitable free cell that would move with the rest of the grains. Spherical particles are idealised particles. Therefore tests were also conducted with a small number of polyhedral particles, to deduce their flow rate and the critical orifice width at which blockages were likely to form. Simulations were also conducted to test the feasibility of the DEM in modelling the behaviour of these polyhedral particles.Results indicate that for a free cell to move along the same trajectory and have the same displacement and velocity as an equivalent particle in the batch it should have a similar density to the majority of the other particles. A cylindrical free cell of similar density to the particles was found to follow the path of the representative particle more closely than the cuboid or triangular prism. Polyhedral particles were found to have a greater flow rate than spherical particles of equivalent volume.

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. 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. 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. / QC 20101119

No / Following aberroscopy, aspheric front surface soft contact lenses (SCLs) were custom-made to correct spherical refractive error and ocular spherical aberration (SA) of 18 myopic and five hypermetropic subjects (age, 20.5 . 5 yr). On-eye residual aberrations, logMAR visual acuity, and contrast sensitivity were compared with the best-correcting spectacle lens, an equally powered standard SCL, and an SCL designed to be aberration free in air. Custom-made and spherical SCLs reduced SA ( p . 0.001; p . 0.05) but did not change total root-meansquare (rms) wave-front aberration (WFA). Aberration-free SCLs increased SA ( p . 0.05), coma ( p . 0.05), and total rms WFA. Visual acuity remained unchanged with any of the SCL types compared with the spectacle lens correction. Contrast sensitivity at 6 cycles/degree improved with the custom-made SCLs ( p . 0.05). Increased coma with aspheric lens designs and uncorrected astigmatism limit the small possible visual benefit from correcting ocular SA with SCLs.

ITC/USA 2015 Conference Proceedings / The Fifty-First Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2015 / Bally's Hotel & Convention Center, Las Vegas, NV / To determine the tracking abilities of a Telemetry (TM) antenna control unit (ACU) requires 'truth data' to analyze the accuracy of measured, or observed tracking angles. This requires we know the actual angle, i.e., that we know where the target is above the earth. The positional truth is generated from target time-space position information (TSPI), which implicitly places the target's global positioning system (GPS) as the source of observational accuracy. In this paper we present a model to generate local look-angles (LA) and line-of-sight (LoS) distance with respect to (w.r.t.) target global GPS. We ignore inertial navigation system (INS) data in generating relative position at time T; thus we model the target as a global point in time relative to the local tracker's global fixed position in time. This is the first of three companion papers on tracking This is the first of three companion papers on tracking analyses employing Statistically Defensible Test & Evaluation (SDT&E) methods.

Call number: LD2668 .T4 1964 C15 / Master of Science

An important aspect for precision guidance, navigation, and control for lunar operations is environmental modeling. In particular, consider gravity field modeling. Available gravity field models for the Moon reach degree and order 165 requiring the use and storage of approximately 26,000 spherical harmonic coefficients. Although the high degree and order provide a means by which to accurately predict trajectories within the influence of the Moon's gravitational field, the size of these models makes using them computationally expensive and restricts their use in design environments with limited computer memory and storage. It is desirable to determine reduced complexity realizations of the gravitational models to lower the computational burden while retaining the structure of the original gravitational field for use in rapid design environments. The extended Kalman filter and the unscented Kalman filter are used to create reduced order models and are compared against a simple truncation based reduction method. Both variations of the Kalman filter out perform the truncation based method as a means by which to reduce the complexity of the gravitational field. The extended Kalman filter and unscented Kalman filter were able to achieve good estimates of position while reducing the number of spherical harmonic coefficients used in gravitational acceleration calculations by approximately 5,400, greatly increasing the speed of the calculations while reducing the required computer allocation. / text

Carbon dioxide reforming, or drying reforming, of methane can now be used in new applications such as landfill gas utilization where CO and CH need to be converted to a mixture of CO and H, called synthesis gas or syn-gas. A novel Ni-Co/AlMgO bimetallic powder catalyst was developed in previous research for dry reforming of methane (DRM) process which can eliminate carbon deposition. But it is difficult242x to apply this loose-powder catalyst in industrial scale. The procedure of making spherical Ni-Co/AlMgOx bimetallic catalyst supported on BASF CSS-350 alumina balls (BASF Catalysts LLC) using impregnation method with different impregnation steps and calcination steps is explained in this thesis. For every batch of preparation, the concentration of metal solution was calculated based on different impregnation steps. BET (Brunauer-Emmett-Teller) analysis, compressive strength test, XANES (X-ray Absorption Near-Edge Structure) measurement and ICP-MS (Inductively Coupled Plasma Mass Spectrometry) analysis are conducted to understand the physical and chemical properties of the catalyst. It is found that both impregnation steps and calcination steps have great influence on the performance of the prepared catalyst samples. Among all the catalysts prepared, BF-4-0.25(MgNiCo)-C, which was made by using 4 impregnation-calcination cycles, shows the best activity and stability for 160 h time-on stream (TOS) under the reaction condition of 0.10 g catalyst loading, 750 oC, ambient pressure, GHSV=100,000 ml/gc·h, and CH4/CO2/N2 = 1/1/1. The CH4 conversion started at 66.7% and slowly dropped to 52.8% after 160 hours. I I BF-4-0.25(MgNiCo)-C spherical catalyst shows lower reaction rate compared to the loose powder format but shows compatible or higher activity to other two reported catalysts in similar compositions. Most importantly, it is a shaped catalyst ready for industrial use.

A significant component of recent space exploration has been unmanned mission to comets and asteroids. The increase in interest for these bodies necessitates an increase in demand for higher fidelity trajectory simulations in order to assure mission success. Most available methods for simulating trajectories about asymmetric bodies assume they are of uniform density. This thesis examines a hybrid method that merges a mass concentration ("mascon") model and a spherical harmonic model using the "Brillouin sphere" as the interface. This joint model will be used for simulating trajectories about variable density bodies and, in particular, contact binary asteroids and comets. The scope of this thesis is confined to the analysis and characterization of the spherical harmonic modeling method in which three bodies of increasing asymmetrical severity are used as test cases: Earth, asteroid 101955 Bennu, and asteroid 25143 Itokawa. Since the zonal harmonics are well defined for Earth, it is used as the initial baseline for the method. Trajectories in the equatorial plane and inclined to this plane are simulated to analyze the dynamical behavior of the environment around each of the three bodies. There are multiple degrees of freedom in the spherical harmonic modeling method which are characterized as follows: (1) The radius of the Brillouin sphere is varied as a function of the altitude of the simulated orbit, (2) The truncation degree of the series is chosen based upon the error incurred in the acceleration field on the chosen Brillouin sphere, and (3) The gravitational potential and acceleration field are calculated using the determined radial location of the Brillouin sphere and the truncation degree. An ideal Brillouin sphere radius and truncation degree are able to be determined as a function of a given orbit where the error in the acceleration field is locally minimized. The dual-density model for a contact binary is found to more accurately describe the dynamical environment around Asteroid 25143 Itokawa compared to the single density model.

Doctor of Philosophy / Department of Civil Engineering / Hayder A. Rasheed / Spherical shells are widely used in aerospace, mechanical, marine, and other industrial applications. Accordingly, the accurate determination of their behavior becomes more and more important. One of the most important problems in spherical shell behavior is the determination of buckling loads either experimentally or theoretically. Therefore, in this study some elastic and plastic buckling problems associated with spherical shells are investigated. The first part of this research study presents the analytical, numerical, and experimental results of moderately thick and thin hemispherical metal shells into the plastic buckling range illustrating the importance of geometry changes on the buckling load. The hemispherical shell is rigidly supported around the base circumference against horizontal translation and the load is vertically applied by a rigid cylindrical boss (Loading actuator) at the apex. Kinematics stages of initial buckling and subsequent propagation of plastic deformation for a rigid-perfectly plastic shell models are formulated on the basis of Drucker- Shield's limited interaction yield condition. The effect of the radius of the boss used to apply the loading, on the initial and subsequent collapse load is studied. In the numerical model, the material is assumed to be isotropic and linear elastic perfectly plastic without strain hardening obeying the Tresca or Von Mises yield criterion. Finally, the results of the analytical solution are compared and verified with the numerical results using ABAQUS software and experimental findings. Good agreement is observed between the load-deflection curves obtained using three different fundamental approaches. In the second part, the Southwell’s nondestructive method for columns is analytically extended to spherical shells subjected to uniform external pressure acting radially. Subsequently finite element simulation and experimental work shown that the theory is applicable to spherical shells with an arbitrary axi-symmetrical loading too. The results showed that the technique provides a useful estimate of the elastic buckling load provided care is taken in interpreting the results. The usefulness of the method lies in its generality, simplicity and in the fact that, it is non-destructive. Moreover, it does not make any assumption regarding the number of buckling waves or the exact localization of buckling