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Symmetry has played a crucial role in our understanding of physical systems. In this thesis, we review several works based on investigating the symmetry properties of theories. We examine and improve the Noether's theorem and the coset construction, both powerful tools when studying the symmetry aspects of a physical system. We manipulate the intrinsic ambiguities in the derivation of the stress-energy tensor using Noether's theorem to systematically compute, without any guesswork, the necessary ``improvement terms'' which make the tensor satisfy certain algebraic properties such as symmetry and tracelessness, even off-shell. We then construct a new type of coset construction, which can accommodate relativistic particles with arbitrary spins. This is the first work we know of to incorporate arbitrary spin degrees of freedom into coset construction. We then present two interesting examples of condensed matter systems described by effective field theories that come from spontaneous symmetry breaking. For the so-called framid, we present the peculiar behavior of its stress-energy tensor that it is Lorentz-invariant even though the system breaks Lorentz boosts spontaneously. An analogy is drawn to the cosmological constant problem since the vacuum energy there and the Lorentz-breaking terms here are all surprisingly zero. Lastly, we describe how the inflation of the universe can be driven by a solid. We focus on the icosahedral inflation model, where the isotropies of background evolution and scalar power spectrum are guaranteed although the system is anisotropic. We discuss some observational signatures of this model.

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A three-channel Frequency Response Function (FRF) estimator is discussed and statistical relations developed. Methods for estimating the variance of the FRF magnitude and levels of uncorrelated content in the test signals are developed. FRF magnitude variance estimates allow ’confidence bands’ to be placed on FRF magnitude estimates, giving an indication of the variability of the result. Uncorrelated content estimates indicate sources and magnitudes of noise in the measurement system. Both Monte Carlo simulations and experimental work are used to verify the statistical and uncorrelated content estimates. Relations to extend the three-channel FRF estimator to multiple input-multiple output measurements are developed and verified through simulations. / Ph. D.

Currently, many missile fire control systems use a three degree of freedom (3-DOF) trajectory model. The three degrees of freedom represent the linear motion of the missile in three dimensions. A 6-DOF model adds roll, pitch, and yaw, or angular motion in three dimensions to the first three degrees of freedom. Because more of the missile’s attributes are modeled, a 6-DOF model is more accurate than a 3-DOF model. For the same reason, a 3-DOF model is easier to develop and executes faster. Also, because a 3-DOF model ignores the seemingly random angular motion, the step sizes used to integrate 3-DOF models are larger. The goal of this project is to develop a 6-DOF re-entry model with the accuracy of a 6-DOF model with conventional equations of motion and computational speed at least comparable to the 3-DOF model. This can be achieved by transforming the equations that compute the effects of angular motion so that they are better conditioned. Essentially, this is done by fitting a sine wave to the oscillating state variables representing the orientation and angular rates, namely the quaternions and the angular velocity. This thesis shows the results of transforming the oscillating variables of the state vector. / Master of Science

Supercritical fluid chromatography (SFC) has been gaining much exposure over recent years. The characteristics inherent to SFC give it capabilities in separating nonvolatile, thermally labile compounds inseparable by GC, and with greater efficiency per unit time than HPLC. As in the past with the more conventional chromatographic methods, the need for higher information detectors, such as IR, exists for SFC. The interface of a Fourier Transform Infrared (FTIR) spectrometer to a packed column (analytical scale) SFC is demonstrated. Characterization of mobile phases for SFC-FTIR is presented. Also, parameters for the optimization of spectral sensitivity, such as mobile phase transparency and flow cell design, are discussed. Demonstrations are made via model mixture separations. Finally, the application of this technique to the analysis of free fatty acids is presented. Identification of carboxylic acids of carbon number 6-18 is made on several standard mixtures and on free fatty acids extracted from various complex samples. The spectral identification of the compounds as free fatty acids is presented, and spectral evidence for dimerization of the acids in CO 2 and the coelution of saturated and unsaturated carboxylic acids is shown. / Master of Science

Transformation induced plasticity was investigated in a model ceramic. The effect upon toughness of the martensitic transformation from the cubic (paraelectric) to the tetragonal ( ferroelectric) phase in BaTiO3 was determined. The K1C fracture toughness, as measured by the hardness indentation technique, exhibits a maximum within a temperature range approximately 50°C above the stress-free transformation temperature. Unlike the martensitic transformation associated with partially stabilized zirconia, there is no volume change during the cubic-to-tetragonal phase change in BaTi03. In addition, no evidence of microcracking was observed. The enhanced toughness in the vicinity of the transition temperature was attributed to limited plasticity at crack tips provided by the transformation shear strains. The effective strains at the crack tips required to produce the observed fracture toughness values are consistent with transformation strains calculated using the phenomenological theory of martensite. / Master of Science