The adiabatic or Born-Oppenheimer approximation is often used in molecular calculations to simplify the solution to the Schrodinger equation. The basis of the approximation is the large difference in the relative motions of the nuclei and electrons in the molecule-the electrons are able to respond almost instantly to the movements of the nuclei. Thus, the nuclei may be regarded as being fixed in a certain position and the Schrodinger equation can then be solved using the potential obtained by solving the electronic problem at fixed nuclear configuration. A similar argument can be used to decouple the angular and radial motions of many van der Waals complexes because, like nuclei in molecules, the radial motions in many van der Waals complexes are strongly localized. Fixing the radial separation between the atoms and molecules in the complex to a particular value results in a Schrodinger equation that is much simpler to solve because it is only dependent on angles. van der Waals complexes containing helium atoms, however, present a dilemma because the extremely weak interactions present also lead to large amplitude radial as well as angular motions. Because the basis of the adiabatic approximation is a large difference in time scale between the angular and radial motions, the validity of the adiabatic approximation for helium complexes is uncertain. In this thesis, the adiabatic separation of angular and radial motion is shown to be accurate for extremely floppy complexes of helium by demonstrating its use on the van der Waals molecule He-HCN. A major application of this method is expected to be the quick calculation of approximate wave functions for Diffusion Monte Carlo studies of the rotation of impurity molecules inside ultra-cold droplets of helium. The method presented here is significantly faster than other methods (e.g., Variational Monte Carlo) that have been used to calculate approximate wave functions for Diffusion Monte Carlo.

Precast concrete multistory buildings are used in an attempt to optimize the available construction space and reduce costs. However, little is known about predicting their capacity in a brittle response mode due to the sudden loss of a critical element that could induce a Progressive Collapse Scenario. Therefore, the National Institute for Standards and Technology (NIST) developed an explicit approach in the design of precast concrete systems that is intended to mitigate a progressive collapse by enhancing the rotational capacity of joints and the robustness of the structural system. A full-scale experiment was conducted to investigate the structural performance of a prototype design under a column-removal scenario. The test assembly frame, consisting of three columns and two beams, was subjected to a displacement controlled vertical force acting at the center to characterize the failure modes and collapse mechanisms. Brittleailures of critical structural elements were observed and significantly impacted the performance.

The development of acrylonitrile-butadiene-styrene (ABS) resins for use in rotational molding would provide a medium performance material, thus opening doors to new markets for the rotational molding industry. Unfortunately, ABS resins have shown serious problems during the rotational molding process, namely discoloration, bridging, and poor impact strength. It is believed that these effects are due to degradation of the carbon-carbon double bond in the butadiene, through attack by either oxygen or heat. Previous efforts have shown some success in addressing these issues. However, additional improvements are necessary to make ABS resins commercially viable to rotational molders. This study, fourth in a series of similar projects conducted though Brigham Young University, was focused on remediation of the ABS difficulties via two different approaches. First, a survey of several additives was performed with the intent of investigating four different strategies: increased protection from oxygen, decreased butadiene concentration, increased butadiene concentration, and promotion of flow. The best formulation was achieved when 15 wt % of a benzoate ester (XP-2280 available though ChemPoint) was blended into MAGNUM 342 EZ, an ABS resin (The Dow Chemical Company). This formulation showed the best balance between increased impact strength and improvement of cosmetic properties. Second, optimization of several rotational molding processing parameters was executed. These included particle size distribution of the resin, drying of the resin, internal mold atmosphere, and oven temperature. It was found that using coarse particle sizes (ground at 20-mesh rather than the industry standard of 35-mesh) increased the impact strength by about 19%. None of the other parameters proved to have a significant effect upon the system, except for the use of a nitrogen atmosphere, which lowered the impact strength. Final properties testing of this best formulation at the optimal processing conditions showed increased impact strength from 2 ft-lbs (the previous best value) to 8 ft-lbs. There was also a marginal decrease in surface hardness (95 to 78 on the Rockwell R scale) and yield tensile strength (3,900 psi to 3,300 psi). Larger differences were observed in flexural modulus (200,000 psi to 110,000 psi) and heat distortion temperature (95°C to 61°C). Therefore, these formulation and processing changes show a trade-off where stiffness and thermal stability (i.e. flexural modulus and heat distortion temperature) can be sacrificed for an increase in toughness and aesthetics, made manifest by increased impact strength, elimination of bridging, and eradication of discoloration.

In order to investigate the viability of friction stir welding for use in Naval construction, mode one elastic-plastic fracture toughness of friction stir processed HSLA-65 was determined using current ASTM 1820 and BS 7448 standards. Double-sided welds were used to achieve 12.7 mm thick samples. A constant feed rate of 100 mm/min was used for all welds. To explore the effect of weld parameters on toughness, welds were produced using two rotational speeds: 340 RPM and 490 RPM. The weld centerline, advancing side hardened region (ASHR), and TMAZ/HAZ regions were sampled, in addition to un-welded parent material. All elastic-plastic fracture toughness values were thickness dependent. For welds produced at 340 RPM, toughness ranged from 33% to 75% below parent material. By increasing the rotational speed to 490 RPM, weld toughness was likewise less than the parent material, but increased 12% to 50% relative to welds produced at 340 RPM. The lowest measured toughness was in the ASHR samples for both parameters. This region of the weld exhibited mixed mode stress-strain conditions and toughness 75% and 62% less than parent material. Toughness values for all samples failed to meet qualification requirements of both ASTM 1820 and BS 7448 due to non-uniform crack extension. Irregular crack extension was caused by the through thickness change in tensile properties due to welding and the affect this had on the plastic zone size compared to the thickness. Increased weld toughness from 340 RPM to 490 RPM was attributed to microstructural differences as a result of increased rotational speed. In addition, higher crack extensions were observed in the second weld pass relative to the first for both rotational speeds. This was attributed to weld tempering of the first pass by the second. The ASHR samples exhibited the highest crack extensions. In this location, the weld microstructure consisted of Widmanstatten ferrite, a microstructure known to be detrimental to toughness.

The purpose of this research is to investigate the use of compliant mechanisms in space applications and design, analyze, and test a compliant space mechanism. Current space mechanisms are already highly refined and it is unclear if significant improvements in performance can be made by continuing to refine current designs. Compliant mechanisms offer a promising opportunity to change the fundamental approach to achieving controlled motion in space systems and have potential for dramatic increases in mechanism performance given the constraints of the space environment. A compliant deployment hinge was selected for development after industry input was gathered. Concepts for large-displacement compliant hinges are investigated. A design process was developed that links the performance requirements of deployment to the design parameters of a deployment hinge. A large-displacement monolithic compliant rotational hinge, the Flex-16, is designed, analyzed, and tested. It was developed for possible application as a spacecraft deployment hinge and designs were developed using three different materials (polypropylene, titanium, and carbon nanotubes) and manufacturing processes (CNC milling, electron beam manufacturing metal rapid prototyping, and a carbon nanotube framework) on two size scales (macro and micro). A parametric finite element model allowed for prediction of prototype behavior before fabrication. The Flex-16 hinge is capable of 90 degrees of deflection without failure or contact and can be designed to meet industry requirements for space.

Capsule network (CapsNet) is a new and promising approach to computer vision. In the small amount of research published so far, it has shown to be good at generalizing complex objects and perform well even when the images are skewed or the objects are seen from unfamiliar viewpoints. This thesis further tests this ability of CapsNetby comparing it to convolutional networks (ConvNets) on the task to understand images of clothing in different rotational views. Even though the ConvNets have a higher classification accuracy than CapsNets, the results indicate that CapsNets are better at understanding the clothes when viewed in different rotational views. / Capsule network (CapsNet) är en ny typ av neuralt nätverk för datorseende, som framförallt presterar bra även då bilderna är förvrängda eller sedda från obekanta vinklar. Den här uppsatsen testar CapsNets förmåga att förstå klädesobjekt sedda ur olika synviklar genom att göra en jämförelse med ConvNets. Resultaten visar att, trots att ConvNets har en högre exakthet i sin klassificering, är CapsNets bättre på att förstå kläderna sedda från olika synvinklar.

Rotating machines such as motors, generators, turbines, etc. are crucial mechanical components of modern industrial and power generation facilities. For proper functioning of these facilities during and after an earthquake, it is essential that the rotating machines in these facilities also function as desired. The dynamics of a rotating machine is quite complex. It is further complicated by the presence of earthquake induced base motions. The response spectrum methods, which are now commonly used for calculating seismic design response of civil structures, cannot be used as such for calculating the design response of rotating machines. In this thesis, a response spectrum method which can be applied to the rotating machines is developed. To develop the response spectrum approach, a generalized modal superposition method is utilized. The random vibration analysis is applied to incorporate the stochastic characteristics of the seismic inputs. The applicability of the proposed response spectrum approach is verified by a simulation study where fifty sets of acceleration time histories are used. The proposed method considers the fact that earthquake induced base motions have several components, including rotational inputs. To define the correlation between the rotational and translational input components of the excitation, the correlation matrix and a travelling seismic wave approaches are used. The numerical results are obtained to evaluate the effect of rotational input components on the response of a rotating machine. It is observed that the rotational components are important only when they are very strong. In actual practice, such strong rotational inputs are not expected to excite rotors which are either directly placed on ground or are placed in common buildings. In the proposed spectrum approach, nevertheless, the effect of rotational input components can be easily incorporated if the correlation between various excitation components is specified. / Master of Science

Scope and Contents: A generalized pairing theory has been developed which diagonalizes matrix elements of the effective nucleon-nucleon interaction in a space of one, two and three-pair excitations from a Skyrme Hartree-Fock solution for deformed rotational nuclei. The "pairing" excitation energy for the configurations of time-reversed pairs of particles is obtained from the Hartree-Fock approximation as opposed to the conventional (BCS) residual interaction point of view. The effects of the finite-range character of the effective nucleon-nucleon interaction are studied in the single-particle structure they induce in the pairing matrix elements. Microscopic form factors for (p,t) and (t, p) reactions between states of the rotational bands built on the K^π=0^+ pairing solution band-head states are constructed in the cylindrical Harmonic-Oscillator basis in which the Hartree-Fock solution is expanded. These form factors are used in DWBA calculations for the differential cross-sections. Preliminary calculations for (p,t) and (t,p) transitions between states in 172Yb and 174Yb were performed. The calculations emphasize the effects of structure in the pairing matrix elements, and the necessity for a self-consistent calculation of the diagonal pairing matrix elements sing the Hartree-Fock equations. / Thesis / Doctor of Philosophy (PhD)

A formulation of a subspace identification method for multi-phase processes with applications to rotational moulding and suggestions for improvements and experimental applications. / This thesis focuses on the implementation of subspace identification (SSID) for nonlinear, chemical batch processes by introducing a model identification method for multi-phase processes. In this thesis, a multi-phase process refers to chemical or biological batch-like processes with properties that cause a change in the dynamics during the evolution of the process. This can occur, for example, when a process undergoes a change of state upon reaching a melting point. Existing SSID techniques are not designed to utilize any known, multiphase nature of a process in the model identification stage. The proposed approach, Multiphase Subspace Identification (MPSSID), is conducted by first splitting historical data into phases during the identification step and then building a subspace model for each phase. The phases are then connected via a partial least squares (PLS) model that transforms the states from one phase to the next. This approach makes use of existing SSID techniques that allow for model construction using batches of nonunifrom length. Here, MPSSID is applied to a uniaxial rotational moulding process. In rotational moulding, the dynamics switch as the process undergoes heating, melting, and sintering stages that are visibly distinct and recognizable upon a certain temperature (not time) being reached. Results demonstrate the ability of multiphase models to better predict the temperature trajectories and final product quality of validation batches. As an extension to this rotational moulding analysis, additional MPSSID methods of implementation are proposed and the results are compared. A MPSSID mixed integer linear program is then introduced for implementation within model predictive control. The applications to rotational moulding are presented within the context of plastics manufacturing and the impact of plastic on the global climate crisis, with suggestions for future work. / Thesis / Master of Applied Science (MASc) / The control of chemical processes is an important factor in achieving high quality products. To control a process well, the mathematical model of the system must be accurate. In the past, mathematical models for process control were designed based on engineering approximations. Now, with major advances in computing and sensor technology, it is possible to design a simulation of the entire process. These simulations can be designed using first-principles or black box approaches. First-principles approaches utilize rigorous models that are based on the complex chemical and physical formulas that govern a system. Black box approaches do not look at the first-principles dynamics. They only utilize the measured process inputs and outputs to form a model of the system. They are widely used because of their ease of implementation in comparison to first-principles approaches. In this thesis, a new black box process control model is proposed and is found to yield better theoretical results than existing techniques. This model is tested on data from a plastics manufacturing process called rotational moulding, which involves loading polymer powders into a mould that is simultaneously rotated and heated to yield seamless plastic parts. Lastly, a control framework that is compatible with the new black box model is proposed to be used for future experimental tests.

Halo currents (HCs) in post-disruption plasmas can be large enough to exert significant electromagnetic loads on structures surrounding the plasma. These currents have axisymmetric and non-axisymmetric components, both of which pose threats to the vacuum vessel and other components. However, the non-axisymmetric forces can rotate, amplifying the displacements they cause when the rotation is close to the structures’ resonant frequencies. A new physically motivated scaling law has been developed that describes the rotation frequencies of these HCs and has been validated against measurements on HBT-EP, Alcator C-Mod, and other tokamaks. This scaling law can describe the time-evolution of the asymmetric HC rotation throughout disruptions on HBT-EP as well as the time-averaged rotation on C-Mod. The scaling law can also be modified to include the edge safety factor at the onset of rotation (𝒒_𝑜𝑛𝑠𝑒𝑡), which significantly improves its validity when applied to machines like C-Mod, where 𝒒_𝑜𝑛𝑠𝑒𝑡 changes frequently. The 𝒒_𝑜𝑛𝑠𝑒𝑡 dependence is explained by the relationship between the poloidal structure of the HC asymmetries and the MHD instabilities that drive them, which has been observed experimentally for the first time using a novel set of current sensing limiter tiles installed on HBT-EP. The 1/𝑎² and 𝒒_𝑜𝑛𝑠𝑒𝑡-dependence of the rotation suggest that the HCs predominantly rotate poloidally. This remains consistent with the toroidal rotation observed on HBT-EP and other tokamaks through the “Barber Pole Illusion” and the direction of rotation’s dependence on the direction of 𝐼_𝑝. This scaling law is used to make projections for next generation tokamaks like ITER and SPARC, which predicts that rotation will be resonant on ITER. However, resonant effects can still be avoided if the duration of the disruption is kept short enough to prevent two rotations from being completed.