Digitized by Kansas Correctional Industries

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Physics. / M̲i̲c̲ṟo̲f̲i̲c̲ẖe̲ c̲o̲p̲y̲ a̲v̲a̲i̲ḻa̲ḇḻe̲ i̲ṉ A̲ṟc̲ẖi̲v̲e̲s̲ a̲ṉḏ S̲c̲i̲e̲ṉc̲e̲. / Includes bibliographical references. / Ph.D.

Predicting the temperature-strain phase diagram of VO$_2$, including the various structural allotropes, from first principles is a grand challenge of materials physics, and even the phase diagram remains unclear at T = 0K. The coexistence of Peierls and Mott physics suggests that a theory which can capture strong electronic correlations will be necessary to compute the total energies. In order to understand the complex nature of the first-order transition of VO$_2$, we build a minimal model of the structural energetics using the Peirels-Hubbard model and solve it exactly using the Density Matrix Renormalization Group (DMRG) methods demonstrating that the on-site interaction $U$ has a minimal effect on the structural energetics for physical parameters. These results explain the qualitative failures of Density Functional Theory (DFT) and DFT+$U$ for the structural energetics, in addition to the partial success of the unorthodox DFT+$U$ results (i.e. non-spin-polarized and small $U$). It also guides the creation of empirical corrections to the DFT+$U$ functional which allow us to semi-quantitatively capture the phase stability of the rutile and monoclinic phases as a function of temperature and strain. Our work demonstrates that VO$_2$ is better described as a Mott assisted Peierls transition.

The present thesis is examining the forced vibrations of a circular cylinder in the low Reynolds number flow of 200. A numerical study is performed that employs an already existing algorithm developed by (Breuer 1998) and enhanced with the characteristic of the cylinder's motion by (MadaniKermani 2014) who employed the moving frame of reference method of (L. Li, Sherwin et al. 2002). The algorithm was extensively assessed for the benchmark studies of flow around a stationary circular cylinder. A new observation was made on the effect of the aspect ratio of the computational cells in the mid region of the wake. The studies so far are emphasizing on the characteristic of a dense mesh, with a small aspect ratio, in the high divergence areas in the near region of the cylinder surface, neglecting the effect of the regions away from the surface. The present study on a stationary circular cylinder flow, proved that the aspect ratio of the distant cells has a significant effect on the St number and the force coefficients. The main study of the thesis emphasizes on the lock-in region where the wake oscillates in unison with the harmonic motion of the cylinder. The study makes a new observation on the qualitative and quantitative description of the lock-in conditions. In particular, it reveals two regions of resonance and non-resonance lock-in. Despite the fact that the lock-in is achieved, when the frequency ratio is in the first part of the region away from the unity ratio, the forces are not greatly magnified. As the ratio approaches the unity the forces experience a resonance that reaches the highest value after the unity. Furthermore, the adaptation time of the flow to the motion of the cylinder is examined and extends the results of (Anagnostopoulos 2000) to the full extent of the lock-in and the non-lock-in regions. More precisely the flow strives to reach a steady state when it is in the lock-in region rather in the non-lock in cases it reaches the steady state faster. It is postulated that the adaptation time depends on both the numerical and the physical adaptation. Moreover, the force coefficients characteristic of sinusoidal behaviour in the lock-in region is attempted to be approximated by a Newton polynomial that is built by making use of the divided differences method. The amplitude of the forces is approximated by a third degree Netwon polynomial built from the results of the present thesis simulations. The use of an approximation is providing faster results ignoring the need for a full resolution of the Navier-Stokes equation.

Fan, Sin Tsun Edward. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 85-87). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Motivation --- p.5 / Chapter 1.2 --- Main results --- p.10 / Chapter 2 --- Preliminaries --- p.14 / Chapter 2.1 --- Z-gradations of Semisimple Lie Algebras --- p.14 / Chapter 2.2 --- Basic Facts about Algebraic Groups --- p.15 / Chapter 3 --- Weight Multiplicity Free Representations and Pre- homogeneous Vector Spaces --- p.18 / Chapter 3.1 --- Weight Multiplicity Free Representations --- p.18 / Chapter 3.2 --- Prehomogeneous Vector Spaces --- p.22 / Chapter 4 --- Augmentations of Dynkin Diagrams --- p.25 / Chapter 5 --- Orbit Finiteness and Prehomogeneity --- p.32 / Chapter 6 --- Termination of Z-grading --- p.36 / Chapter 7 --- Explicit Construction of Generic Elements in Simply- laced Cases --- p.42 / Chapter 8 --- The Ambient Lie Algebras of Parabolic PVS's --- p.47 / Chapter 9 --- PVS's of Twisted Affine Type --- p.52 / Chapter 10 --- "Orbit Structure of (GL2 x SL2m+1,C2 x A2C2m+1)" --- p.55 / Chapter 11 --- Nilvarieties and Generalisation of Open Orbits --- p.59 / Chapter 11.1 --- Nilvarieties and Visible Representations --- p.59 / Chapter 11.2 --- Augmeantations of Affine Dynkin Diagrams --- p.62 / Chapter 11.3 --- Classification of Irreducible Visible Representations --- p.67 / Chapter 12 --- Real Forms of PVS of Parabolic Type --- p.70 / Chapter 12.1 --- Representations of Real Reductive Lie Algebras and Satake Diagrams --- p.70 / Chapter 12.2 --- Real Forms of PVS of Parabolic Type --- p.77 / Chapter 13 --- Tables --- p.81 / Bibliography --- p.85

Starting from a mathematical basis where one analyses and developing different techniques in how to solve and represent different kinds of integrals with diagrams. Representing the integrals as n-valent vertices and introducing propagators is a great tool that helps with the book-keeping of the solutions and will sometimes do the calculations redundant. The symmetries of diagrams are analysed and how one extracts the symmetry factors from looking at a diagram by using some fairly simple combinatorics and cleverness. Introducing the probability amplitude and do some analysis of the path integral formulation is the step into physics. Discussing experiments as the double-slit experiment and deriving the Schrödinger equation from the generating functional. Looking at diagrams in Quantum Mechanics and Quantum Field Theory will explore the use of the crucial understanding of our generators for the diagrams. This thesis makes use of the so called generating functional almost throughout and to connect the first discussed mathematics to real physical theories is the aim.

Metals in industrial settings such as power plants are often subjected to high temperature and pressure aqueous environments, where failure to control corrosion compromises worker and environment safety. For instance, zircaloy (1.2-1.7 wt.% Sn) fuel rods are exposed to aqueous 250-310 oC coolant in CANDU reactors. The Pourbaix (EH-pH) diagram is a plot of electrochemical potential versus pH, which shows the domains of various metal species and by inference, corrosion susceptibility. Elevated temperature data for tin +II and tin +IV species were obtained using solid-aqueous phase equilibria with the respective oxides, in a batch vessel with in-situ pH measurement. Solubilities, determined via spectroscopic techniques, were used to calculate equilibrium constants and the Gibbs energies of Sn complexes for E-pH diagram construction. The SnOH3+ and Sn(OH) species were incorporated, for the first time, into the 298.15 K and 358.15 K diagrams, with novel G ͦ values determined at 358.15 K. / UOIT

Control charts are designed to monitor population parameters. Selection of a control chart sampling plan involves determination of the frequency of samples, size of each sample, and critical values to determine when the system is sending an out-of-control signal. Since the main use of control charts is in industry, a widely accepted measure of a good sampling plan is one that minimizes the total cost of operating the system per unit time. Methods for selection of control chart sampling plans for economically optimal X charts are well established. These plans focus on single stage sampling at each sampling period. However, some populations naturally call for two stage sampling. Here, the cost of operating a system per unit time is redefined in terms of two stage sampling plans, and computer search techniques are developed to determine the control chart parameters. First the sample sizes and critical values are fixed, and Newton's method is used to determine the optimal time between samples. Then, a Hooke - Jeeves search is used to simultaneously determine the optimal critical value, sample sizes and time between samples. Adjustment to the latter is required whenever any of the other three parameters change. Alternative methods are also discussed. Information from a single sample is usually used to control shifts in both the process mean and variance. With two stage sampling, this means two additional control charts are used, one for each variance component. The computer algorithm developed for selection of parameters for X charts is adapted by expanding the Hooke Jeeves search region to a six dimensional space, now over three critical values, sample sizes for both stages of sampling, and the time between samples. These methods are applied to a real data set that requires two stage sampling. A representative analysis of the sensitivity of the optimal sampling scheme to the input parameters completes the paper. / Graduation date: 1990

Modern seismic imaging tools for oil and gas exploration and production (E&P) assume that seismic data contain responses only of waves that bounce (e.g., reflect, diffract) only once at each interface in the subsurface. This type of response is called a primary. Unfortunately, actual seismic data also contain responses of waves that bounce at several interfaces in the subsurface. This type of response is called a multiple. In general, multiples in seismic data fall into two categories: (1) events that bounce at least once at the free surface in addition to any other bounce in the sub- surface and (2) events that do not bounce at the free surface but instead inside the subsurface, at two or more interfaces. The first category has the greater amount of energy; therefore most of the research and development efforts in E&P have so far focused on attenuating this category of multiples accurately. At present, more knowledge of the subsurface is expected from seismic imaging. To avoid any misinterpretation of these details, there is a growing need in the E&P industry to also attenuate the second category of multiples, known as internal multiples. In this work I describe a new method of attenuation of internal multiples. The method consists of predicting the internal multiples and then subtracting them from the data. The prediction of internal multiples from seismic data is made possible by the discovery of a new type of seismic scattering event known as a virtual event. Seismic virtual events constitute a calculational device, which is becoming an important part of seismic data processing. Virtual events combine forward and back- ward wave propagation in such a way that their convolution with real events allows us to predict internal multiples. In addition to showing how virtual events can be constructed from real seismic events, I also show that virtual events obey physical laws, despite their counterintuitive wavepath. I have illustrated the findings in this thesis with synthetic examples. In particu- lar, I have shown the effectiveness of my internal-multiple-attenuation method for a 1D data set, which includes several primaries and internal multiple interferences.

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