Second project report of two. Part A is available at http://hdl.handle.net/11375/17551 / <p> The design, construction, and initial operation of an ultra high vacuum testing system was undertaken. The final UHV system is equipped with a residual gas analyser (RGA). </p> <p> The system was used to test a National Research Council of Canada magnetron pump-gauge. The pumping action of the device was adequate with speeds of litres/second for hydrogen and other chemically active species. A speed of ≃0.3 L/S was measured for methane (CH₄). The pressure measuring capabilities of this particular pump may be in question due to the presence of surface leakage currents. </p> / Thesis / Master of Engineering (ME)

No description available.

No description available.

<p>Let $p>5$ be a prime and $X_0$ a simply-connected $4$-manifold with boundary the Poincar\'e homology sphere $\Sigma(2,3,5)$ and even negative-definite intersection form $Q_=\text_8$ . We obtain restrictions on extending a free $\bZ/p$-action on $\Sigma(2,3,5)$ to a smooth, homologically-trivial action on $X_0$ with isolated fixed points. It is shown that for $p=7$ there is no such smooth extension. As a corollary, we obtain that there does not exist a smooth, homologically-trivial $\bZ/7$-equivariant splitting of $\#^8 S^2 \times S^2=E_8 \cup_ \overline$ with isolated fixed points. The approach is to study the equivariant version of Donaldson-Floer instanton-one moduli spaces for $4$-manifolds with cylindrical ends. These are $L^2$-finite anti-self dual connections which asymptotically limit to the trivial product connection.</p> / Doctor of Philosophy (PhD)

This thesis studies N=(2,2) gauged linear sigma models (GLSMs) and three-dimensional N=2 Chern-Simons-matter theories and their mathematical applications. After a brief review of GLSMs, we systematically study nonabelian GLSMs for symplectic and orthogonal Grassmannians, following up a proposal in the math community. As consistency checks, we have compared global symmetries, Witten indices, and Calabi-Yau conditions to geometric expectations. We also compute their nonabelian mirrors following the recently developed nonabelian mirror symmetry. In addition, for symplectic Grassmannians, we use the effective twisted superpotential on the Coulomb branch of the GLSM to calculate the ordinary and equivariant quantum cohomology of the space, matching results in the math literature. Then we discuss 3d gauge theories with Chern-Simons terms. We propose a complementary method to derive the quantum K-theory relations of projective spaces and Grassmannians from the corresponding 3d gauge theory with a suitable choice of the Chern-Simons levels. In the derivation, we compare to standard presentations in terms of Schubert cycles, and also propose a new description in terms of shifted Wilson lines, which can be generalized to symplectic Grassmannians. Using this method, we are able to obtain quantum K-theory relations, which match known math results, as well as make predictions. / Doctor of Philosophy / In this thesis, we study two specific models of supersymmetric gauge theories, namely two-dimensional N=(2,2) gauged linear sigma models (GLSMs) and three-dimensional N=2 Chern-Simons-matter theories. These models have played an important role in quantum field theory and string theory for decades, and generated many fruitful results, improving our understanding of Nature by drawing on many branches in mathematics, such as complex differential geometry, intersection theory, quantum cohomology/quantum K-theory, enumerative geometry, and many others. Specifically, this thesis is devoted to studying their applications in quantum cohomology and quantum K-theory. In the first part of this thesis, we systematically study two-dimensional GLSMs for symplectic and orthogonal Grassmannians, generalizing the study for ordinary Grassmannians. By analyzing the Coulomb vacua structure of the GLSMs for symplectic Grassmannians, we are able to obtain the ordinary and equivariant quantum cohomology for these spaces. A similar methodology applies to 3d Chern-Simons-matter theories and quantum K-theory, for which we propose a new description in terms of shifted Wilson lines.

Quantization and renormalization of non-Abelian gauge fields is studied. Yang-Mills theory is renormalized up to two-loops using the background field method retaining arbitrary value of the gauge parameter. The result confirms the expectations for calculations performed in background field gauge. Namely, the counter-term depending on the background field only is a renormalization constant times the square of the field strength of the background field, and the constant upon renormalization of the gauge parameter is independent of the gauge parameter. Finally, the three-loop contribution to the renormalization group β function of pure Yang-Mills theory is calculated in the background field gauge. / Ph. D.

Accurate theoretical predictions of optical rotation are of substantial utility to the chemical community enabling the determination of absolute configuration without the need for poten- tially lengthy total synthesis. The requirements for robust calculation of gas-phase optical rotation are well understood, but too expensive for routine use. In an effort to reduce this cost we have examined the performance of the LPol and ORP basis sets, created for use in density functional theory calculations of optical rotation, finding that at the coupled cluster level of theory they perform the same or better than comparably sized general basis sets that are often used. We have also examined the performance of a perturbational approach to inclusion of explicit solvent molecules in an effort to extend the calculation of response properties from the gas phase to the condensed phase. This N-body approach performs admirably for interaction energies and even dipole moments but breaks down for optical rotation, exhibiting large basis set superposition errors and requiring higher-order terms in the expansion to provide reasonable accuracy. In addition, we have begun the process of implementing a gauge invariant version of coupled cluster response properties to address the fundamentally unphysical lack of gauge invariance in coupled cluster optical rotations. Correcting this problem, which arises from the non- variational nature of the coupled cluster wavefunction, involves reformulating the response amplitude and function expressions and solving for all necessary amplitudes simultaneously. / Ph. D.

The U.S. Army has recently developed cutting edge designs for gun barrels, projectiles, and propellants that require testing. This includes measuring the internal pressure during fire. There are concerns with the current method of drilling to mount pressure transducers near the breech and chamber of the gun barrel where pressure is highest. An alternative, non-intrusive strain measurement method is introduced and discussed in the present work. This focuses on determining the feasibility and accuracy of relating tangential strain along the sidewall of a gun barrel to the drastic internal pressure rise created during combustion. A transient structural, numerical modal was created using ANSYS of a 155 mm gun barrel. The pressure gradient was derived using a method outline in IBHVG2 (Interior Ballistics of High Velocity Guns, version 2), and the model was validated using published experimental tangential strain testing data from a gun of the same caliber. The model was used to demonstrate the ideal location for strain measurement along the sidewall of the chamber. Furthermore, three different pressure ranges were simulated in the model. The behavior of the tangential strain in each case indicates a similar trend to the internal pressure rise and has oscillation due to a dominant frequency of the barrel. A method to predict internal pressure from external tangential strain was developed. The internal pressure predicted is within 4% of the pressure applied in the model. A sensitivity study was performed to determine the primary factors affecting tangential strain. The study specifically looked at material properties and geometry of the gun barrel. The thickness and elastic modulus of the gun barrel were determined the most relevant. Overall, the present work helps to understand tangential strain behavior on the sidewall of a large caliber gun barrel and provides preliminary work to establish an accurate prediction of internal pressure from external tangential strain. / Master of Science / Innovative technology for large gun systems require testing to evaluate safety and performance. The most recent designs from the U.S. Army for long range artillery require higher pressures. Currently, large gun barrels are drilled to mount pressure transducers for internal pressure testing, but the new generation of weapons require a way to measure internal pressure of the gun without introducing these high stress locations. External strain offers a means to measure displacement of the barrel caused by the internal pressure change with minimal alteration to the gun barrel. The present work focuses on modelling a large gun barrel using finite elements to understand the behavior of strain on the external surface due to internal pressure during fire. Measurements were taken near the chamber of the gun barrel model. The strain behavior is comprised of two components, a linear change due to a pressure increase and vibrations introduced due to the sharp pressure increase over a short amount of time. Three cases were evaluated at different pressure ranges and a method was developed to predict internal pressure from the tangential strain with a maximum error of 4% for all cases studied. The model also indicates that the strain results are most sensitive to a change in thickness and the elastic modulus of the gun barrel material.

The Virginia Tech Transportation Institute is recognized for being a pioneer in naturalistic driving studies. These studies determine driving behavior, and its correlation to safety critical events, by equipping participant's vehicles with data acquisition systems and recording them for a period of time. The driver's habits and responses to certain scenarios and events are analyzed to determine trends and opportunities to improve overall driver safety. One of these studies installed strain gauges on the front and rear brake levers of motorcycles to record the frequency and magnitude of brake presses. The recorded data was sampled at 10 hertz and had a significant amount of noise introduced from temperature and electromagnetic interference. This thesis proposes a peak detection algorithm, written in MATLAB, that can parallel process the 40,000 trips recorded in this naturalistic driving study. This algorithm uses an iterative LOWESS regression to eliminate the offset from zero when the strain gauge is not stressed, as well as a cumulative sum and statistical concepts to separate brake activations from the rest of the noisy signal. This algorithm was verified by comparing its brake activation detection to brake activations that were manually identified through video reduction. The algorithm had difficulty in accurately identifying activations in files where the amplitude of the noise was close to the amplitude of the brake activations, but this only described 2% of the sampled data. For the rest of the files, the peak detection algorithm had an accuracy of over 90%. / Master of Science / The Virginia Tech Transportation Institute is recognized for being a pioneer in naturalistic driving studies. In these studies, participants are recorded with cameras and other sensors for a period of time. Researchers then look at this data and find the habits that tended to distract the drivers, like using their phones while driving, and other characteristics that bring insight on what causes crashes and unsafe driving behavior. One of these studies installed strain gauges on the front and rear brake levers of motorcycles to record how hard the brakes were pressed, as well as how often. The strain gauge was sampled ten times a second, and had a significant amount of variation in the signal from temperature changes and interference from other electronic systems on the bike. This thesis proposes a method, written in MATLAB, that can quickly find all the brake activations in the 40,000 trips recorded in this naturalistic driving study. This program uses an iterative LOWESS regression, cumulative sum, and other statistical concepts to determine the brake activations in the signal. This program was verified by comparing its brake activation it found to brake activations that were manually identified through video reduction. The algorithm had difficulty in accurately identifying activations in files where the peaks of the noise were close to the peaks of the brake activations, but this only described 2% of the sampled data. For the rest of the files, the program had an accuracy of over 90%.

[pt] A magnetostricção é a propriedade dos materiais ferromagnéticos de se deformarem pela presença de um campo magnético externo. Trata-se de uma propriedade inerente ao material, que não muda com o tempo. Materiais que apresentam deformações da ordem de 10-3 são conhecidos como materiais de magnetostricção gigante (GMM). Esta dissertação de mestrado estuda a aplicação destes materiais em sensores de deslocamento onde não há contacto entre o elemento cursor (um ímã) e o elemento sensor (GMM). O princípio de funcionamento consiste em aplicar um gradiente de campo magnético ao GMM que está fixo. O gradiente de campo magnético é gerado por um ímã preso ao componente ou estrutura na qual se quer medir o deslocamento. As variações no campo magnético no material GMM originados pelo deslocamento do ímã (estrutura), provocam uma deformação no GMM, que é detectada com extensômetros do tipo Strain Gauge ou Redes de Bragg. Neste trabalho apresenta-se a caracterização da deformação de GMM em relação a um campo constante aplicado, e análises do seu comportamento para diferentes geometrias. Efeitos de pressão, polarização com um segundo ímã, e diferentes gradientes de campo magnético são também estudados. É observado um comportamento local para a deformação quando a medida é realizada em diferentes regiões do GMM. Os resultados obtidos permitiram a medição de deslocamentos de alguns micra estando o elemento sensor a até 10 mm de distância do elemento cursor. / [en] Magnetostriction is a property of ferromagnetic materials to deform in the presence of a magnetic field. Magnetostriction is an inherent property of magnetic materials, which is unchangeable with time. Materials exhibiting strains in the order of 10-3 are known as giant magnetostrictive materials (GMM).In this dissertation we study the application of these materials in displacement sensors where there is not contact between the cursor element (magnet) and sensor element (GMM). Its principle of operation consists of applying a magnetic field gradient to a GMM located at a fixed position. The magnetic field gradient is produced by a magnet attached to the component or structure in which the displacement will be measured.The variation on the magnetic field in the GMM position originated from the displacement of the magnet, results in a strain in the GMM that can be detected with a Strain Gauge or Bragg Grating extensometers. In this work is presented the characterization of the strain on GMM cuboids against a constant magnetic field and the analysis of its behavior for different geometries. Effects of pressure, polarization with a second magnet, and different gradients of magnetic field are also studied. It is observed a local behavior for strains when it is measured in different regions of GMM cuboid. The results obtained allow us to measure displacements of about few micra when the sensor is at a distance of 10 mm from the cursor element.