This investigation consisted of a study of the kinetics of propylene disproportionation over a tungsten oxide on silica catalyst. A catalyst of ten percent WO₃ on silica gel (223 square meters per gram B.E.T. surface area) was used in a microcatalytic reactor. Electron probe scans of the commercially prepared catalyst showed that the standard liquid impregnation technique used in preparation of this catalyst can result in large radial variations in the distribution of the promoter within the pellet. Both flow and pulse reactor techniques were used. It had been reported that external mass transfer effects could not be eliminated in this system. Here linear velocities in excess of those used previously were investigated, and it has been found that both external and intraparticle mass transfer effects can be eliminated, though exceptionally high linear velocities are required to eliminate the external mass transfer effects. Initial rate data were obtained for the disproportionation of propylene by this catalyst. Temperatures of 399° to 454° Centigrade and pressures from one to nine atmospheres were used. The experimental data were well correlated by assuming that a Langmuir-Hinshelwood, dual-site surface reaction was the rate controlling step in the reaction mechanism. The mechanism parameters and their temperature dependence were extracted from the experimental data using a linear least squares technique. An apparent activation energy of 24.73 Kcal per mole was found for this catalytic system. During the initial contacting of freshly activated samples of this catalyst with propylene, significant increases in disproportionation activity were observed for periods up to twenty four hours. The rate of catalyst break-in was found to depend on both the temperature and pressure with an activation energy of 47.17 Kcal/mole and a first order propylene partial pressure dependency. Data are presented to establish that both a reduction of the catalyst to WO₂.₉ and the strong adsorption of an olefin are responsible for this period of transient activity. Prior reduction to the normally thermodynamically unfavorable oxidation state of WO₂ was found to give a thirty percent increase in the steady-state activity of this catalyst. The strong adsorption of an olefin was found to be at least partly reversible in an inert atmosphere. / Doctor of Philosophy

A search has been performed for the reaction µ⁻ + Cu ⟶ e⁺ + Co, which is allowed by the lepton conservation scheme that assigns the same lepton number to the µ⁻, e⁺, v_µ , and vₑ. Momentum analysis of particles emitted following muon capture was performed using a magnetic spectrometer with magnetostrictive readout wire spark chambers. The time of flight through the spectrometer and energy loss in a scintillation counter were measured for each event. One event was observed, at momentum 89.9 ± 3.5 MeV/c, which is consistent with the above process. Background from radiative muon capture was expected to produce ~ 0.01 events that could simulate the searched for reaction. However, there exists uncertainty in the relative yield and cutoff for high energy photons from radiative muon capture. Although we cannot be certain whether or not the reaction µ⁻ + Cu ⟶ e⁺ + Co has been detected, we can set an upper limit on the branching ratio relative to ordinary muon capture of R < 2.6 x 10⁻⁸ (90% confidence level). According to a calculation by Kisslinger, this can be related to an upper limit on the coupling constant of this type of interaction relative to the vector coupling constant of (G_Δ I Gᵥ) ≤ 0.10^+0.05_-0.03. / Ph. D.

A novel circulator design method is presented. It utilizes H. Bosma’s suggested electrical model, a program written for a digital computer representing this model, Fay & Comstock’s design method to calculate electrical and physical properties of applied ferrite cylindrical resonators and measured impedance values of those, for computation of designed circulator performance. The main results are summarized as follows: (i) The method described eliminates the use of the trial and error method in the laboratory. (ii) It permits the prediction of performance accurate within a few dB-s in the 20-30 dB range. Earlier design methods and proposed solutions are each illustrated by a numerical example. (i) Fay & Comstock’s method (ii) H. Bosma’s method (iii) Proposed solution The first example exhibits considerable discrepancy between specifications and measured performance of the realized circulator. The second method is an analysis. Here again predicted performance is quite different from measured performance on the realized device, the parameters of which were used as data for the analysis. The third method shows good agreement of measured performance and specifications. Further research possibilities include a refinement of H. Bosma’s boundary value solution and the establishment of an electrical model exhibiting measured puck impedance values for easy matching network synthesis. / Ph. D.

The method of invariant estimation proposed in this dissertation relies on defining a group of transformations on the sample space such that i) the group structure is isomorphic to the parameter space and"carries" the estimation problem in a natural manner (thus defining an “carries” the estimation problem), and ii) the group structure generates orbits on the parameter space and the problem is to estimate the orbit in which the parameter lies (thus defining an invariant estimation problem). If the group of transformations can be expressed as the semi-direct product of two subgroups, one a"nuisance" group which is a normal subgroup, then an estimator of orbits under the nuisance group in the invariant estimation problem can be naturally obtained from the best estimator in the equivariant estimation problem. The primary application is to the invariant estimation of the parameters in the general linear model under the (nuisance) group of scale changes on the dependent and independent variables. The invariant estimator of the regression coefficient is found to be a"standardized regression coefficient,'' but this standardized regression coefficient is not the same as the typical one ("beta coefficient") found in elementary statistics texts and social science research. Comparison of the proposed estimator to the usual estimator, in the case in which the input matrix is nonstochastic, shows the proposed estimator to be superior to the usual estimator in terms of such criteria as consistency, unbiasedness, and simplicity of distribution. In the case in which the input matrix is stochastic, some justification can be found for the use of the usual estimator. Application of the proposed method of invariant estimation to the problem of obtaining estimators invariant under nonsingular transformations is straightforward, although the estimator obtained is difficult to interpret. / Ph. D.

An approach to the design of suboptimal linear regulators is developed. Two techniques are proposed for obtaining a reduced order aggregated model for a constant coefficient dynamic system. This model is then used to determine a suboptimal control law to solve an output regulator problem. The research is developed by first examining the problems involved when the design and implementation of the optimal regulator is attempted. The idea of using a reduced order model to overcome some of these problems is discussed and a set of criteria that the reduced model must satisfy is presented. Two methods for determining a reduced order model that satisfies the criteria are then developed and used to design controllers for two example systems. The methods are based on using gradient descent to minimize the error between the exact system output and the output of an observer dependent aggregated model. The use of a stochastic input to serve as the test function for this minimization is proposed and shown to be quite useful. The procedure developed is applicable to multi-input systems and to systems with unstable modes. In addition, there is no requirement that the exact model be in any special form. / Ph. D.

An experimental and theoretical investigation has been undertaken to study the trajectory and growth of thermal effluents having a range of discharge velocities and temperatures. The discharge of a turbulent effluent into a waterway was mathematically modeled as a submerged jet injection process by using an integral method which accounts for natural fluid mechanisms such as turbulence, entrainment, buoyancy, and heat transfer. The analytical results are supported by experimental data and demonstrate the usefulness of the theory for estimating the location and size of the effluent with respect to the discharge point. The capability of predicting jet flow properties, as well as two- and three-dimensional jet paths, was enhanced by obtaining the jet cross sectional area during the solution of the conservation equations (a number of previous studies assume a specific growth for the area). Realistic estimates of temperature in the effluent were acquired by accounting for heat losses in the jet flow due to forced convection and to entrainment of free-stream fluid into the jet. / Ph. D.

A theoretical analysis of large deflections and large strains in a circular plate with varying thickness and a circular membrane is considered. The exact tensor first approximation equilibrium equations, converted into physical equations for a rotationally symmetric thin plate are used with the Alexander constitutive relations for a rubber-like material to analyze the deflections, stress resultants and change in the thickness for a plate clamped along the outer edge and deflected by a uniform pressure applied normal to the deformed surface. The equations are quasilinearized and solved numerically with the aid of a digital computer. The thickness is allowed to vary in the radial direction but is held constant in the circumferential direction. Several variations in thickness were considered. The solutions found by using the Alexander constitutive relations were compared with the solutions using the Rivlin and Saunders constitutive relations and the Hart-Smith constitutive relations. Numerical results from the solution of a plate with uniform thickness were compared with those for a similar plate given by J. T. Oden. / Ph. D.

Given is an investigation of experimental plans that require a minimum number of assemblies, minimal multidimensional designs (MMD's) and minimal augmented multidimensional designs (MAMD's). Such designs are incomplete factorials which allow for only some two-factor interactions. An analysis of incomplete factorials with and without interactions is developed from a reduced form of the normal equations. C_ip_i = Q_i where p_i is a vector of estimates of factor i effects and C_i is the coefficient matrix for pi and Qi is a vector of transformed observations. The general forms for C_i and Q_i are presented. The construction of MMD's and MAMD's is made possible from results obtained on connected designs. A definition of a connected design where two-factor interactions are assumed leads to a procedure for"connecting" experimental plans. This procedure provides a way of adding assemblies to a design in order to estimate contrasts not originally estimable in the design. Using this augmentation procedure and the minimum number of assemblies to be added, MAMD's may be constructed. MMD's follow by sequentially augmenting with the minimum number of assemblies, m-factor designs, m = 1,2,...,m*, whose total number of factor level combinations are a minimum. A method for finding MMD's and MAMD's which are optimal for one factor or for a set of two-factors is then presented as well as some examples of MMD's and MAMD's with and without two-factor interactions. Data is generated and analyzed for a particular design which is both a MAMD and a MMD, and a discussion of this design's optimality is also given. / Ph. D.

Populations of the wax scales, Ceroplastes ceriferus (Fabricius) and Ceroplastes sinensis Del Guercio, have become established in Virginia. A third species, Ceroplastes floridensis Comstock, is periodically brought into the state but is apparently unable to overwinter. Ceroplastes ceriferus the primary species in Virginia, was originally found in Norfolk in 1942. In the past 30 years C. ceriferus has spread into 40 counties, All infestations are east of the Blue Ridge Mountains, the majority of which are in the Piedmont area from Charlottesville, Richmond and Danville eastward. Its host range encompasses 122 species of plants in 46 families, primarily ornamentals, some shade trees, and several weeds. Ceroplastes sinensis, a minor species in Virginia, was originally found in Norfolk in 1938. It has been recorded in three southeastern counties from four species of Ilex. Each instar of the three species of Ceroplastes found in Virginia is characterized in this study including measurements and illustrations. Of these, C. ceriferus and C. floridensis are completely described for the first time. Keys are provided for separation of the instars for each species. Mounting techniques are given. The biologies of the established species were recorded from oviposition to development of the adult stage. Both species have three instars, overwinter in the adult stage and produce one generation a year. Males of the Japanese wax scale were collected for the first time in the United States from greenhouse colonies in Virginia and Maryland. C. ceriferus oviposits in April and May; hatching begins in June and in dense populations may occur as late as July; settling occurs primarily on the stems of the host. The time required for seasonal development of populations varies with the location of the infestation. In rural and suburban areas infestations required approximately 72 days to complete development from egg to adult while infestations in urban areas required only 52 days. C. sinensis begins oviposition in May; hatching begins in late June. The first and second instars settle and develop on the leaves in July and the third nymphal instar migrates back-to the stems in late August to complete development. This species requires 75 days for development from egg to adult in a suburban area. Laetilia coccidivora (Comstock) and Coacophagus fraternus Howard are the primary predator and parasite, respectively, of Ceroplastes in Virginia. Laetilia coccidivora and Anicetus towneyeUae Milliron, a parasite of adult C. sinensis, are here recorded on Ceroplastes for the first time. Carbaryl, carbofuran, Imidan®, malathion, diazinon, ethion, carbophenothion, monitor, Supracide®, Orthene®, dimethoate and oxydementonmethyl, sprays and phorate, disulfoton arid aldicarb granules were the materials tested for control of C. ceriferus. The additive Nufilm-17® was tested with malathion, diazinon, and carbophenothion,' Results showed that applications of insecticides at hatching produced the best results. Carbaryl, Imidan® and carbofuran showed the most consistent and effective control of the wax scales. / Ph. D.

Two releases of 50 birds each were made on the Virginia Polytechnic Institute and State University Farm. One release was made in the fall, the other release was made in the spring. The birds were a cross between Western Iranian black-necked (Phasianus colchicus talischensis) and Chinese ring-necked pheasants (P. c. torquatus). Ten of the pheasants released in the fall and five of the pheasants released in the spring were instrumented with transmitters. Equipment difficulties with both releases reduced the ability to monitor the birds. As a result of these difficulties, field observations were resorted to for the bulk of the data. Known mortality amounted to 26% of the total number of birds released. Seven cases of dispersal off the study area were recorded. The dispersal ranged from l~ to 4 miles from the release sites. The pheasants were most frequently observed in, or adjacent to, woodlots. The spring-released pheasants exhibited a more gradual decline in numbers observed on the study area than the fall released birds. Breeding activity was thought to be partly responsible for the increase in spring observations. Three hens which were thought to be nesting were killed by mowing operations in hayfields. Several broods were observed during the summer. / Master of Science