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Polystyrene samples prepared in emulsion at 55 C were carefully fractionated. The resulting fractions were in turn fractio­nated, combined in groups having similar intrinsic viscosities, and re-­fractionated. As the intrinsic viscosity of these fractions increased, the value of Huggins' k' in methyl ethyl ketone was found to increase a slightly ( from 0.39 to 0.41). Polystyrene samples prepared in exactly the same way except for the addition of small amounts of divinylbensene, a cross-linking agent, were similarly fractionated. The value of k' in methyl ethyl ketone for these fractions increased considerably (from 0.41 to 0.68) as the intrinsic viscosity increased, even though the amount of divinylbensene added was very small (from 0.003to 0.05%). Relations were then established for these cross-linked fractions between k' and the proportion of divinylbensene present, and between k' and the intrinsic viscosity of the fractions. It was concluded that polystyrene prepared in emulsion at 55 C. is essentially linear in structure, and that the value of Huggins' k* seems to provide a convenient and sensitive test for the presence of any appreciable branching that might occur in polystyrene. / Thesis / Master of Science (MS)

Yes / Bezier curves and surfaces are two very useful tools in Geometric Modeling, with many applications. In this paper, we will offer a new method to provide approximations of regular curves and surfaces by Bezier ones, with the corresponding examples.

If we adjoin the cube root of a cube free rational integer <i>m</i> to the rational numbers we construct a cubic field. If we adjoin the cube roots of distinct cube free rational integers <i>m</i> and <i>n</i> to the rational numbers we construct a bicubic field. The number theoretic invariants for the cubic fields and their normal closures are well known. Some work has been done on the units, classnumbers and other invariants of the bicubic fields and their normal closures by Parry but no method is available for calculating those invariants. This dissertation provides an algorithm for calculating the number theoretic invariants of the bicubic fields and their normal closure. Among these invariants are the discriminant, an integral basis, a set of fundamental units, the class number and the rank of the 3-class group. / Ph. D.

The experiments discussed in this thesis exploit parity violation in elastic electron proton scattering in order to measure properties of the nucleon. Both experiments make use of the high quality, highly polarized electron beam available at Thomas Jefferson National Accelerator Facility. Q_weak will measure the weak mixing angle, sin²θ_W, via a measurement of the weak charge of the proton, at a four-momentum transfer, Q² ~ 0.026 GeV²/c². The precision of this measurement gives Q_weak access to new physics at the scale of 2.3 TeV, making it a test of the standard model. The G⁰ experimental program provides the fully separated contributions of the strange quark to the charge and magnetization distributions of the nucleon at two different values of four-momentum transfer, Q² ~ 0.22 and 0.63 GeV²/c². The measurement of the strange quark content of the proton in the G⁰ experimental program and other parity-violating electron scattering experiments provides a measurement of the hadronic contribution to the asymmetry in Q_weak. In addition, G⁰ was able to measure the parity-conserving beam normal single spin asymmetries that provide a measurement of the imaginary part of two photon exchange. The measurement of this asymmetry is necessary to understand the systematic contribution to measurements of parity-violating asymmetries, but it is also an important physics result. Recent theoretical work has shown that higher order radiative effects, such as two photon exchange, may be able to explain discrepancies between experiments which measure the ratio of the electric and magnetic form factors of the proton. The measurement of the transverse or beam normal single spin asymmetries provides a benchmark for theories that estimate the size of radiative corrections that are important for precision electroweak scattering experiments such as those described in this thesis. The results of the measurement of the transverse asymmetries at backward angles in G⁰ are presented at the two values of Q² ~ 0.22 and 0.63 GeV²/c² for hydrogen. Results for deuterium, which can provide the first measurements of the beam normal single spin asymmetries on the neutron, are also presented. / Ph. D.

There is a need for a nonlinear flutter analysis method capable of predicting limit cycle oscillation in aeroelastic systems. A review is conducted of analysis methods and experiments that have attempted to better understand and model limit cycle oscillation (LCO). The recently developed method of nonlinear normal modes (NNM) is investigated for LCO calculation. Nonlinear normal modes were used to analyze a spring-mass-damper system with nonlinear damping and stiffness to demonstrate the ability and limitations of the method to identify limit cycle oscillation. The nonlinear normal modes method was then applied to an aeroelastic model of a pitch-plunge airfoil with nonlinear pitch stiffness and quasi-steady aerodynamics. The asymptotic coefficient solution method successfully captured LCO at a low relative velocity. LCO was also successfully modeled for the same airfoil with an unsteady aerodynamics model with the use of a first order formulation of NNM. A linear beam model of the Goland wing with a nonlinear aerodynamic model was also studied. LCO was successfully modeled using various numbers of assumed modes for the beam. The concept of modal truncation was shown to extend to NNM. The modal coefficients were shown to identify the importance of each mode to the solution and give insight into the physical nature of the motion. The quasi-steady airfoil model was used to conduct a study on the effect of the nonlinear normal mode's master coordinate. The pitch degree of freedom, plunge degree of freedom, both linear structural mode shapes with apparent mass, and the linear flutter mode were all used as master coordinates. The master coordinates were found to have a significant influence on the accuracy of the solution and the linear flutter mode was identified as the preferred option. Galerkin and collocation coefficient solution methods were used to improve the results of the asymptotic solution method. The Galerkin method reduced the error of the solution if the correct region of integration was selected, but had very high computational cost. The collocation method improved the accuracy of the solution significantly. The computational time was low and a simple convergent iteration method was found. Thus, the collocation method was found to be the preferred method of solving for the modal coefficients. / Ph. D.

A numerical study of a proposed innovative jet interaction configuration is presented. This work aimed at improving present-day jet interaction configurations in their applications as control thrusters on hypersonic vehicles. Jet thrusters are a useful control system for fast-moving vehicles flying in the upper layers of the atmosphere because of their effectiveness and responsiveness. They produce a strong and responsive lateral force on the vehicle through the interaction of two main mechanisms. The first mechanism comes from the momentum of the injectant itself, basically the thrust of the jet. The second and subtler contribution comes from the jet interaction flowfield, the interaction of the expanding injectant with the crossflow. This interaction produces areas of high pressure ahead of the injector and areas of low pressure in the region aft of the jet. The combination of the high-pressure regions in front of and low-pressure regions aft of the injector produces an undesirable nose-down pitching moment on the vehicle. In order to counterbalance the nose-down attitude, modern-day thruster designs include a large secondary injector far aft of the center of gravity of the vehicle. The thrust of this second injector acting far aft of the primary injector neutralizes the nose-down pitching moment. This is not an efficient method to obviate the problem since it requires the vehicle to be designed to carry two large thrusters and double the quantity of fuel necessary for one thruster. In light of these considerations, this study aimed at developing a jet interaction configuration that can dispense from the need of a large secondary injector to compensate for the nose-down pitching moment. The cases studied here were first a primary jet alone and then a primary jet with pairs of smaller jets. This configuration was based on the notion that the interaction of the secondary jets, conveniently located immediately aft of the thruster, with the barrel shock and the wake of the primary jet can drastically reduce the nose-down pitching moment. Because of the complexity of the jet interaction flowfield the investigation of the feasibility and the assessment of the efficiency of the new jet interaction configurations combined the present numerical effort with experimental studies of jet interaction flowfields performed in the supersonic wind tunnel at Virginia Tech. During the present numerical study the jet interaction flowfield associated with the sonic injection of a gas into a high-speed crossflow was simulated by numerically solving the Reynolds Averaged Navier Stokes (RANS) equations. Turbulence was modeled through a first-order model, the Wilcox's 1988 k-w turbulence model. The computations made use of the finite volume code General Aerodynamic Simulation Program (GASP) Version 4. For simplicity and to keep the study general, the jet interaction flowfield was studied on a flat plate instead of a body of revolution as on a vehicle. Calculations were run for a number of jet interaction configurations consisting of a primary jet alone, a primary jet and one pair of secondary jets, and a primary jet and two pairs of secondary jets. The flow conditions of the simulations ranged from a Mach number of 2.1 up to a Mach number of 4.5 and jet total pressure to freestream static pressure ratios of 14 to 680. A large effort was dedicated to the development of an efficient computational grid that could capture most of the flow-physics with a minimum number of cells. To this end , Chimera or overset grids were employed in the simulation of the secondary injectors. Grid convergence was shown to be achieved for the case of single injection by conducting a thorough convergence study. The discretization error was calculated through a modified Richardson extrapolation to be low. The numerical solutions were compared to the experimental results in order to assess the capability of RANS equations and of first-order turbulence models to properly simulate the complex flowfield. The k-w turbulence model proved to be reliable and robust and the results it provided for this type of flowfield were accurate enough from an engineering standpoint to make informed decisions about the configuration layout. In spite of the overall good performance, the k-w turbulence model failed to correctly predict the flow in the regions of strong adverse pressure gradients. Comparisons with experimental results showed that the separation region was often under-predicted thus highlighting the need to employ better turbulence models for more accurate results. The RANS equations were found accurate enough to provide physical mean-flow solutions. Further, the numerical simulations provided information about the detailed physics of the flowfield that is impossible to obtain through experimental work. The analysis of the numerical solutions highlighted the existence of a complex system of counter-rotating trailing vortices that are responsible for the mixing of the injectant with the freestream. The typical features of the flowfield created by an under-expanded jet exhausting in a quiescent medium were visible in the jet interaction flowfield with the difference of the existence of a crossflow and a non-uniform back-pressure. The region of low pressure aft of the injector was shown to be generated by the detachment of the barrel shock from the surface of the flat plate that leaves a large volume to be filled by the surrounding fluid. The simulations showed that the innovative configuration with one primary jet and an array of smaller secondary jets can effectively decrease the nose-down pitching moment by as much as 160%. In some cases, it also increased the total normal force acting on the flat plate (namely the thrust) by as much as 3%. This effect was found to be caused by the reduction in size and intensity of the low-pressure region aft of the primary injector. / Ph. D.

This dissertation proposes an approach for 3D micro-scale shape reconstruction using photometric stereo (PS) with surface normal integration (SNI). Based on the proposed approach, a portable cost-effective stationary system is developed to capture 3D shapes in the order of micrometer scale. The PS with SNI technique is adopted to reconstruct 3D microtopology since this technique is highlighted for its capability to reproduce fine surface details at pixel resolution. Furthermore, since the primary hardware components are merely a camera and several typical LEDs, the system based on PS with SNI can be made portable at low cost. The principal contributions are three folds. First, a PS method based on dichromatic reflectance model (DRM) using color input images is proposed to generalize PS applicable to a wider range of surfaces with non-Lambertian reflectances. The proposed method not only estimates surface orientations from diffuse reflection but also exploits information from specularities owing to the proposed diffuse-specular separation algorithm. Using the proposed PS method, material-dependent features can be simultaneously extracted in addition to surface orientations, which offers much richer information in understanding the 3D scene and poses more potential functionalities, such as specular removal, intrinsic image decomposition, digital relighting, material-based segmentation, material transfer and material classification. The second contribution is the development of an SNI method dealing with perspective distortion. The proposed SNI is performed on the image plane instead of on the target surface as did by orthographic SNI owing to the newly derived representation of surface normals. The motivation behind the representation is from the observation that spatially uniform image points are simpler for integration than the non-uniform distribution of surface points under perspective projection. The new representation is then manipulated to the so-called log gradient space in analogy to the gradient space in orthographic SNI. With this analogy, the proposed method can inherit most past algorithms developed for orthographic SNI. By applying the proposed SNI, perspective distortion can be efficiently tackled with for smooth surfaces. In addition, the method is PS-independent, which can keep the image irradiance equation in a simple form during PS. The third contribution is the design and calibration of a 3D micro-scale shape reconstruction system using the derived PS and SNI methods. This system is originally designed for on-site measurement of pavement microtexture, while its applicability can be generalized to a wider range of surfaces. Optimal illumination was investigated in theory and through numerical simulations. Five different calibrations regarding various aspects of the system were either newly proposed or modified from existing methods. The performances of these calibrations were individually evaluated. Efficacy of the developed system was finally demonstrated through comprehensive comparative studies with existing systems. Its capability for on-site measurement was also confirmed. / Ph. D.