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To accurately solve the general nuclear spin state function in Nuclear Magnetic Resonance (NMR), a rotation wave approach was employed, allowing the reference frame to rotate in sync with the oscillating magnetic field. The spin state system was analogously treated as a Rubik's Cube, ensuring the diagonalization of only the time-dependent part of the state function. Although Gottfried's equation (1966) aligns with transitions between specific spin states m and m′, his second rotation contradicts the conservation of angular momentum, resulting in inaccuracies for spin states with initial phase shifts or entangled states. Contrarily, Schwinger (1937) efficiently computed the coefficients for each spin state in a frequency range opposite to the Larmor frequency, using an unorthodox approach in quantum mechanics, which unfortunately led to the oversight of his work in subsequent citations. This methodology was also applied to derive the general electron spin state function in Nuclear Magnetic Resonance (NMR) and Electron Paramagnetic Resonance (EPR), enabling the construction of a doubly rotated ground state for time-dependent perturbation theory. This was particularly relevant as the Hamiltonians for magnetic dipole, electric quadrupole, and magnetic octupole moments incorporate powers of I · J terms, necessitating the calculation of sub-state energy levels for perturbation, including those of molecules 14N7 and 7Li3. Furthermore, the study expanded to the general Lie group for 3D rotations along three linearly independent axes, resulting in 12 distinct methods to achieve rotations in any arbitrary direction using these axes, yielding wave function with only one spin operator in each exponent. The ongoing research is now concentrated on generating NMR spectra for 14N7 in amino acids, furthering the understanding of nuclear spin dynamics in complex molecular systems.

Harmonic oscillatory tests for a fighter aircraft using the Dynamic Plunge--Pitch--Roll model mount at Virginia Tech Stability Wind Tunnel are described. Corresponding data reduction methods are developed on the basis of multirate digital signal processing. Since the model is sting mounted, the frequencies associated with sting vibration are included in balance readings thus a linear filter must be used to extract out the aerodynamic responses. To achieve this, a Finite Impulse Response (FIR) is designed using the Remez exchange algorithm. Based on the reduced data, a state–space model is developed to describe the unsteady aerodynamic characteristics of the aircraft during roll oscillations. For this model, we chose to separate the aircraft into panels and model the local forces and moments. Included in this technique is the introduction of a new state variable, a separation state variable which characterizes the separation for each panel. This new variable is governed by a first order differential equation. Taylor series expansions in terms of the input variables were performed to obtain the aerodynamic coefficients of the model. These derivatives, a form of the stability derivative approach, are not constant but rather quadratic functions of the new state variable. Finally, the concept of the model was expanded to allow for the addition of longitudinal motions. Thus, pitching moments will be identified at the same time as rolling moments. The results show that the goal of modeling coupled longitudinal and lateral–directional characteristics at the same time using the same inputs is feasible. / Master of Science

Three end-plate moment connection configurations are prequalified for special moment frames for seismic applications in AISC 358-10. The eight bolt extended stiffened connection is the strongest of the three configurations, but it can only develop approximately 30 percent of currently available hot-rolled beam sections. The strength of this configuration is limited by bolt strength. There is a need for a stronger end-plate moment connection, hence the reason for the development and validation of a twelve bolt configuration. Equations were developed for the design procedure using various analytical methods, which included yield line analysis and an effective tee stub model. An experimental program was conducted, which consisted of the full-scale cyclic testing of four end-plate moment connections. The intention of the testing was to develop and validate the design procedure, and prequalify a new twelve bolt configuration. A displacement-controlled loading protocol was applied according to AISC 341-10. The experimental results showed that the model for thick end-plate behavior is conservative by 6.7%, the model for end-plate yielding is conservative by 8.8%, and the model for bolt tension rupture with prying conservatively predicts by 18.5%. The specimens that were designed to form a plastic hinge in the beam fractured in a brittle manner. The deep beam specimen fractured in the first 2% story drift cycle, and the shallow beam specimen fractured in the second 3% story drift cycle. The fracture of the prequalification specimens was determined to have been caused by stiffeners of high yield stress relative to the beam yield stress. / Master of Science

A comparison of two methods to deal with allocating controls for unattainable moments in an aircraft was performed using a testbed airframe that resembled an F/A-18 with a large control effector suite. The method of preserving the desired moment direction to deal with unattainable moments is currently used in a specific control allocator. A new method of prioritizing the pitch axis is compared to the moment-direction preservation. Realtime piloted simulations are completed to evaluate the characteristics and performance of these methods. A direct comparison between the method of preserving the moment direction by scaling the control solution vector and prioritizing the pitching moment axis is performed for a specific case. Representative maneuvers are flown with a highly unstable airframe to evaluate the ability to achieve the specific task. Flight performance and pilot interpretation are used to evaluate the two methods. Pilot comments and performance results favored the method of pitch-axis prioritization. This method provided favorable flight characteristics compared to the alternative method of preserving the moment direction for the specific tasks detailed in this paper. NOTE: An updated copy of this ETD was added on 09/28/2010. / Master of Science

This diploma thesis is about the basics of satellite systems, about their sorting, usage and technologies. An important part is the description of the principles controlling and stabilization of the small experimental CubeSat type satellites. The main point is the proposition and construction of the laboratory model of the CubeSat type satellite that should simulate the chosen methods of controlling and stabilization in laboratory conditions. The thesis describes the construction of the electronic parts of the model, the controlling software of the satellite’s processor and user software for easy controlling by PC.

Abstract The studies of the deformed nucleus for the Pb isotopes in the A~190 re- gion has been carried out by using the P.S.M. The comparison between the theoretical calculation of the transition energy, kinetic moment of ine- rtia, dynamic moment of inertia, paring gap, rotational energy, quadrupole moment, and B(M1)/B(E2) and the experiment observations are presented. We found that the kinetic moment of inertia is increased as the spin incre- ase for the even-even nuclei. This rise has been interpreted as being due to the combined alignment of the quasiparticles in the high-N intruder or- bit. And the kinetic moment of inertia is constant function of spin in the odd-even nuclei. It is interpreted as been due to the Pauli blocking of odd -quasineutron in the high-N intruder orbit.

Master of Science / Architectural Engineering and Construction Science / Donald J. Phillippi / Special steel moment frames are one of the most common systems used to resist high seismic forces. Well-proportioned moment resisting connections are essential. Special steel moment frame connections must be capable of transferring moment and shear forces that are developed in the beams to the column. These connections must be designed as a highly ductile element in order to dissipate extensive energy thus undergo inelastic deformations. Doubler plates and continuity plates have been recommended by several design codes and standards in order to strengthen the column web and prevent the inelastic deformation of the panel zone due to high shear stress concentrations. However, doubler plates and continuity plates are very expensive due to the large amount of detailing and welding requirements. Furthermore, the extensive welding may affect the properties of the steel in which it may cause shrinkage, lower potential notch toughness and cracking. In any of these cases, there is high potential of losing the desirable inelastic performance required for these SMF. This report investigates the design of the special steel moment frame connections thus eliminating the use of doubler and continuity plates in these connections. Tables are provided that show all steel W-Shape beam sizes with all the adequate steel W-Shape column sizes used in special steel moment frames without the use of doubler and continuity plates in frame connections.

Hydraulic tomography has been tested at the field scale, lab scale and in synthetic experiments. Recently Illman and Berg have conducted studies at the lab scale. Using their data hydraulic tomography can be compared to homogeneous anisotropic solutions using one pumping well or multiple pumping wells. It has been found that hydraulic tomography out performs homogenous methods at predicting hydraulic head for validation pumping experiments. Also it has been shown in this study that homogenous anisotropic tests exhibit scenario dependent behavior. Additional tests performed to further validate the conclusions made in this experiment include spatial moment analysis, response surface analysis, and synthetic hydraulic tomography and show consistent results providing additional validation of these findings. Additional study examining the principle of reciprocity has proven inconclusive.