Thesis (Ph. D.)--University of California, Los Angeles, 1963. / Photocopy of typescript. Ann Arbor, Mich., University Microfilms, 1967. 22 cm. Vita. Bibliography: leaves 170-171.

Thesis (M.S.)--University of Wisconsin--Madison, 1984. Includes tables. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 150-152).

Thesis (Ph.D.)--Tennessee Technological University, 2006. / Bibliography: leaves 47-50.

This thesis examines buoyancy driven steady flows in mouths of sea straits and around coastal protrusions. At high latitudes, the Coriolis force keeps these currents banked against the coast even around relatively sharp re-entrant (convex) corners with radii of curvature that are comparable to the width of the current. On the other hand, if the radius of curvature of the corner is much smaller than the width of the current, the current may leave the coast at the apex of the corner. A central part of the thesis is the solution of the nonlinear problem of a steady inviscid reduced gravity flow in a wedge, 0<θ<π/a (with a>l/2), around a sharp corner on an f-plane. An exponential upper layer upstream depth profile, h=Hexp(-x/X) (where x and X are the offshore distance and the current width scale, respectively), is combined with conservation of potential vorticity, Bernoulli and transport equations. The resulting nonlinear equations are expanded in a Rossby number ∈=V/fX (where f is the Coriolis parameter and V is the upstream boundary value of velocity). The 0(1) and 0(∈) equations are solved. First, they are simplified via transformations of the transport streamfunction variables: ⍦₀=p⁴ʹ³ and ⍦₁=2p¹ʹ³q. By modifying the results of Bromwich's (1915) and Whipple's (1916) diffraction theory, the 0(1) solution is expressed in a compact integral form, [formula omitted] The 0(∈) contribution q is calculated using an approximate Green's function method. The wedge of an angle 3π/2 (a=2/3) is used as an example to show details of the solution. The results exhibit the relative importance of the centrifugal, Coriolis and pressure gradient forces. Centrifugal upwelling (surfacing) of the interface occurs very close to the apex. For a rounded re-entrant corner, the upwelling is important only if the radius of curvature is much smaller than the lateral scale X. liorever, for re-entrant corners, the flow is supercritical within an arc, whose size depends upon the Rossby number and the angle of the wedge. Using two or more corner solutions, plausible flow streamlines can be generated in more complicated domains, as long as no two corners are closer than the Rossby radius of deformation. This procedure is illustrated with two examples: (a) circulation in a channel mouth and (b) flow around a square bump in a coastline. Finally, baroclinic circulation is modeled for boundaries that approximate coastlines near the mouth of Hudson Strait. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

This thesis consists of two essays. Each essay addresses a research problem involving some aspects of uncertainty and financial economics. Essay 1 deals with the general question of whether classical results in risk aversion and portfolio choice based on expected utility hypothesis are robust with respect to recent works in nonlinear utility theories generalizing expected utility. We investigate the implications of an axiomatic generalization called weighted utility theory along with the weaker, but unaxiomatized linear Gateaux utility. We establish the equivalence among three definitions of individual global risk aversion, i.e., in terms of conditional certainty equivalent, mean preserving spread, and conditional risky-asset demand, without any differentiability assumptions about the preference functional. The only requirement is that the preference ordering be complete, transitive, consistent with first-degree stochastic dominance, and continuous in distribution. The equivalence between the first two definitions is also extended to a comparative context. We also identify the necessary and sufficient condition for the single risky asset to be a normal good to a weighted utility maximizer with concave lottery-specific utility functions. Unlike its expected utility counterpart, which depends only on the agent's initial wealth and preferences, this condition also depends on the characteristics of the risky asset. The second essay examines the role of a sequential competitive bidding process in the endogenous determination of interest rates and the corresponding allocation of loans and savings in a widely observed class of informal financial markets called the 'rotating credit association'. Optimal bidding strategies are obtained for individual agents with concave and time-additive utility functions. After deriving some comparative statics and efficiency implications of the individual optimal bidding strategy, we impose further restrictions, including risk neutrality, to obtain a tractable form of a Nash equilibrium bidding strategy. This yields, for each agent, an ex post borrowing, as well as lending, interest rate depending on the history of the realized winning bids, including the one for the period in which he won the auction. Weighted by the Nash equilibrium-induced probability of winning in each period, ex ante borrowing and lending interest rates result. / Business, Sauder School of / Graduate

A new "circuit" model is developed to study non-linear effects in holography. The model links classical signal detection theory to holography, for it clearly shows that the reconstructed images in a thin hologram can be computed from mathematical formulas obtained for the output of non-linear detectors. In preparation for hologram analysis, the results for the (time-) autocorrelation of electrical ʋth-law devices in response to signal plus noise are extended to memoryless non-linear detectors with arbitrary characteristics. Mathematical parallels are next established between holography and the non-linear detection of signals, and these are incorporated in the model. The ready-made formulas for electrical detectors apply directly to give formulas for the (space-)autocorrelation of holograms of diffuse objects. The autocorrelation function predicts distorted multi-pie images, their relative positions, orientations, widths, and strengths. The multiplicity of images is due to the generation of harmonics; the background halo-like noise components added to the faithful images are mainly due to the multiplicity of the first harmonic itself. The analysis is further expanded to include a still more general case in which the reflected light from the object is depolarized. A decrease in signal-to-noise ratio (decrease in fringe visibility); a loss of information, and an augmentation of non-linear distortion could be expected. A simple way of reducing these effects is suggested. Finally, holography with more than one reference beam is studied. An exact formulation is given for double-reference-beam holograms. For multiple-reference-beam holograms, only approximate closed forms are presented. It is shown that the addition of extra reference beams during the recording step of the hologram may amplify the faithful images without increasing their background noise significantly. Experiments confirm the theoretical expectations. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

No description available.

No description available.

The use of counter-rotating propellers is often desirable for aerospace and ocean engineering applications. Counter-rotating propellers offer higher peak efficiencies, better off-design performance, and roll control capabilities. But counter-rotating propeller matching is a difficult and complex procedure. Although much research has been done on the design of optimal counter-rotating propeller sets, there has been less focus on predicting the performance of unmatched counter-rotating sets. In this study, it was desired to use off-the-shelf marine propellers to make a counter-rotating pair for a high speed autonomous underwater vehicle (AUV). Counter-rotating propellers were needed to provide roll control for the AUV. Pre-existing counter-rotating propeller design methods were not applicable because they all require inputs of complex propeller blade geometries. These geometries are rarely known for off-the-shelf propellers. This study proposes a new method for predicting the counter-rotating performance of unmatched propeller sets. It is suggested here that propeller performance curves can be used to predict counter-rotating thrust and torque performance. Propeller performance tests were run in the Virginia Tech Water Tunnel for a variety of small, off-the shelf propellers. The collected data was used to generate the propeller performance curves. The propellers were then paired up and tested as counter-rotating sets. A momentum theory based model was formulated that predicted counter-rotating performance using the propeller performance data. The counter-rotating data was used to determine the effectiveness of the method. A solution was found that successfully predicted the counter-rotating performance of all of the tested propeller sets using six interaction coefficients. The optimal values of these coefficients were used to write two counter-rotating performance prediction programs. The first program takes the forward and aft RPMs and the flow speed as inputs, and predicts the generated thrust and torque. The second program takes the flow speed and the desired thrust as inputs and calculates the forward and aft RPM values that will generate the desired thrust while producing zero torque. The second program was used to determine the optimal counter-rotating set for the HSAUV. / Master of Science

In this work, rotating beams which are isospectral to non-rotating beams are studied. A rotating beam is isospectral to a non-rotating beam if both the beams have the same spectral properties i.e; both the beams have the same set of natural frequencies under a given boundary condition. The Barcilon-Gottlieb transformation is extended, so that it converts the fourth order governing equation of a rotating beam (uniform or non-uniform), to a canonical fourth order eigenvalue equation. If the coefficients in this canonical equation match with the coefficients of the non-rotating beam (non-uniform or uniform) equation, then the rotating and non-rotating beams are isospectral to each other. The conditions on matching the coefficients lead to a pair of coupled differential equations. We solve these coupled differential equations for a particular case, and thereby obtain a class of isospectral rotating and non-rotating beams. However, to obtain isospectral beams, the transformation must leave the boundary conditions invariant. We show that the clamped end boundary condition is always invariant, and for the free end boundary condition to be invariant, we impose certain conditions on the beam characteristics. The mass and stiffness functions for the isospectral rotating and non-rotating beams are obtained. We use these mass and stiffness functions in a finite element analysis to verify numerically the isospectral property of the rotating and non-rotating beams. Finally, the example of beams having a rectangular cross section is presented to show the application of our analysis. Since experimental determination of rotating beam frequencies is a difficult task, experiments can be easily conducted on these rectangular non-rotating beams, to calculate the frequencies of the isospectral rotating beams.