We study the Korteweg-de Vries-Burgers equation. With a deep investigation into the spectral and smoothing properties of the linearized system, it is shown by applying Banach Contraction Principle and Gronwall's Inequality to the integral equation based on the variation of parameters formula and explicit representation of the operator semigroup associated with the linearized equation that, under appropriate assumption appropriate assumption on initial states w(x, 0), the nonlinear system is well-posed and its solutions decay exponentially to the mean value of the initial state in H1(O, 1) as t -> +". / Ph. D.

In this work, we introduce the Sensitivity Equation Method (SEM) as a method for approximately solving infinite dimensional optimal design problems. The SEM couples a trust-region/quasi-Newton optimization algorithm with gradient information provided by apprOXimately solving the sensitivity equation for (design) sensitivities. The sensitivity equation is (in the problems considered here) a partial differential equation (POE) which describes the influence of a design parameter on the state of the system. It is shown that obtaining design sensitivities from the sensitivity equation has advantages over finite difference and semi-analytical methods in that there is no need to remesh or compute mesh sensitivities (even if the domain is parameter dependent), the sensitivity equation is a linear POE for the sensitivities and can be approximated in an efficient manner using the same approximation scheme used to approximate the states. The applicability of the SEM to shape optimization problems, where the state is described by the Euler equations, is studied in detail. In particular, we prove convergence of the method for a one dimensional test problem. These results are used to speculate on the applicability of the method for more complex problems. Finally. we solve a two dimensional forebody simulator design problem (for use in wind tunnel experiments) using the SEM, which is shown to be a very efficient method for this problem. / Ph. D.

This dissertation consists of five chapters on the informational contents of strategies and the role of the perfect recall condition for information partitions in extensive games. The first, introductory, chapter gives basic definitions of extensive games and some results known in the game theory literature. The questions that will be investigated in the remaining chapters and their significance in the literature are also described. In the second chapter it is shown that strategies defined as contingent plans may contain some information that is additional to what the information partition describes. Two types of additional information that strategies may contain when perfect recall is violated are considered. Both behavior and mixed strategies contain the first type of information, but only mixed strategies contain the second type. Addition of either type of information, however, leads to a refinement of the information partition that satisfies perfect recall. The perfect recall condition is found to be significant in demarcating the roles of strategies and information partitions in extensive games. In the third chapter the full informational contents of mixed strategy spaces is explored. The informational content of mixed strategy spaces is found to be invariant over a range of information partitions. A weakening of the perfect recall condition called A-loss is obtained and found to be necessary and sufficient for the information contained in mixed strategies to be equivalent to that of a game with perfect recall. An implication of this result is that a player whose information partition satisfies A-loss can play "as-if" he has perfect recall and a player without A-loss can't. In other words, if an information partition satisfies A-loss, every mixed strategy makes up for any lack of perfect recall described by the information partition. For behavior strategies, we never obtain informational equivalence between distinct information partitions. A-loss turns out to also be a necessary condition for a game without chance moves to have a Nash equilibrium in pure strategies for all payoff assignments. In the fourth chapter the role of the perfect recall condition in preserving some information in the transformation from an extensive game to its agent normal form is discussed. If we interpret a player as a team of agents (one at each information set) then the essential difference between an extensive game and the associated agent normal form game is that in the former the agents act cooperatively while in the latter they act independently. The perfect recall condition is shown to be necessary and sufficient for the perfect equilibria of an extensive game to coincide with those of the associated agent normal form game for all payoff assignments. The contribution of this result is necessity; sufficiency is already known. Since this is proved using pure strategies for the player with imperfect recall in question, one subtle implication is obtained: a perfect equilibrium of the agent normal form game where each agent effectively knows the actions taken and information acquired by his preceding agents, may not be a perfect equilibrium in the original extensive game. This means that perfect recall implies more than just effective knowledge of what happened previously. Chapter 5 concludes. / Ph. D.

CO₂ CH₄, and N₂ are key volatile constituents of the earth; therefore, thermochemical data on these gas species and their mixtures find application in geochemical modeling of crustal fluids in a wide variety of geologic environments. However, volumetric data for gaseous mixtures are scarce, particularly at high pressures and temperatures. In this study, the volumetric properties of binary and ternary mixtures in the system CO₂-CH₄-N₂ were measured at 100-1000 bars, 50-300°C, using a vibrating-tube densimeter constructed at the Oak Ridge National Laboratory. An isobaric, isothermal flow-through method was employed to obtain a statistically significant number of measurements for the period of vibration at each set of P-T-X conditions. During each experimental session, three well Characterized standard gases (He, N₂ and Ar) were used to calibrate the response of the instrument. Precisions achieved in experimentation were: P, ±0.1 bar; and T, ±0.01 °C. Conservative estimates of accuracy are: P, ±0.2 bar; and T, ±0.05 °C. The uncertainties associated with volumetric determinations derive from counting statistics and vary as a function of the density and composition of the gas mixture. Generally, the uncertainty in volume ranges from ±0.1 to ±0.3 %. / Ph. D.

Various media (text, audio, graphics, and animation) were examined in the context of a multimedia environment. These media were used to test predictions based on a model of dual-coding theory (DCT) and on an engineering design principle named visual momentum. DCT is a general cognitive information processing theory. Under DCT, external stimuli are represented in either the verbal or nonverbal symbolic systems. The verbal system is specialized to handle language or abstract information. The nonverbal system is specialized to handle more concrete information such as images, environmental sounds, and writing patterns. Visual momentum is a general design principle used to demonstrate relationships between successively viewed computer screens. This study applied visual momentum through the use of animation to explicitly demonstrate the relationships between information represented in one format to that represented in another format both within and between computer screens. Subjects were required to complete a multimedia program explaining material about total quality management. A 3 x 3 between subjects design was modeled after DCT and visual momentum. Ninety subjects were exposed to various media conditions and were subsequently tested for retention and problem solving as well as several other measures. Generally, the results do not support DCT. However, some findings do support DCT. Dual—coded groups spent less time answering retention questions while performing better than single—coded groups. However, subjects spent more time on the material in these conditions. Subjects only receiving a single medium reviewed the material more often than those subjects receiving dual media except when presented with audio. This difference between text and audio does not support DCT. Those subjects in dual-coded graphic conditions reported more referential and associative processing than those subjects receiving dual-coded animation conditions. Generally, the results support visual momentum. Visual momentum reduce the time needed to answer retention questions as will as improved test performance beyond results predicted by DCT. Visual momentum also reduce the amount of cognitive processing needed to correctly answer the retention and problem solving questions. / Ph. D.

Injection Molding The effects of partial miscibility on the mechanical properties and morphology of thermotropic liquid crystalline polymer blends were investigated in this part of the work. Blends of an immiscible (Vectra A900) and partially miscible (HX1000) thermotropic liquid crystalline polymer (TLCP) with a polyetherimide (PEI) were used in the investigations. The blends were injection molded into mini-tensile bars and rectangular plaques, and their mechanical properties were evaluated. Interfacial, rheological, and morphological properties along with molecular orientation analysis were carried out in order to explain the mechanical properties of the blends. Mechanical tests showed that both the tensile and flexural modulus deviate positively from the law of mixtures. However, for the PEI/HX1000 system the deviation from the law of mixtures appeared at lower TLCP concentrations compared to the PEI/Vectra A900 system. It was found that the tensile modulus correlated well with the structure developed during injection molding. Morphological tests show that finer higher aspect ratio TLCP fibers developed in the PEI/HX1000 system relative to the PEI/Vectra A system. In addition, both blends showed a maximum in the tensile modulus at 90 wt% TLCP. Rheological tests indicated that for TLCP-rich compositions, a higher viscosity was observed for the blends in comparison to the neat TLCPs. Therefore, due to a greater viscosity, higher magnitudes of stresses, consequently inducing a higher degree of molecular orientation, were experienced by the blends relative to the neat TLCPs. Although partial miscibility seemed to affect more strongly the stiffness of the in situ composite, the ultimate properties of the TLCP strongly dominated the ultimate properties of the PEI/TLCP composite. Mechanical tests showed that the ultimate properties of Vectra A were at least twice those of HX1000. Consequently, for TLCP-rich compositions, higher values of toughness, elongation at break and tensile strength were observed for PEI/Vectra A blends compared to PEI/HX1000 blends. The study presented here seems to suggest that the selection of a TLCP to reinforce a polymeric matrix is not only dependent upon whether partial miscibility or compatibility between the TLCP and matrix polymer exist, but also on the mechanical properties of the TLCP. Shearfree Elongational Deformation The effects of uniaxial, planar and biaxial deformations on the morphology and mechanical properties of bends of a polyetherimide with thermotropic liquid crystalline polymers were investigated in this part of the work. Extruded sheets and molded plaques of PEI/Vectra A and PEI/HX1000 blends were used in the studies. In the case of injection molded plaques, in which the initial morphology was that of fibers and droplets, the direction of the applied deformation relative to the initial direction of the TLCP fibrils was an important factor in affecting the resultant morphology and corresponding mechanical properties of the blends. If the direction of the applied uniaxial deformation was parallel to the initial fiber direction, the deformation tended to increase the average aspect ratio of the TLCP fibers and mechanical properties were enhanced along the direction of deformation. However, if the deformation was applied transverse to the initial fiber direction, the fibers tended to follow the deformation and a 90° rotation was observed. In terms of mechanical properties, an increase in the transverse direction properties accompanied by a reduction in the flow direction properties followed the realignment of the fibers. In addition, equal flow and transverse mechanical properties appeared at 0.5 units of transverse uniaxial strain. Planar deformation led to the spreading of the fibers in the plane of deformation and a ribbon-like morphological structure developed. However, at comparative magnitudes of planar strains, transverse planar compression tends to promote a greater spreading of the fibers relative to planar compression applied parallel to the initial direction of the fibers. In addition, planar stretching applied in a direction perpendicular to the initial direction of the TLCP fibers was effective in reducing the mechanical anisotropy of the molded plaques. Samples showing equal flow and transverse properties were obtained when planar strains greater than 0.5 units were applied in a direction perpendicular to the initial direction of the fibers. In the case of extruded sheets, in which the initial morphology was that of drops, it appeared that partial miscibility was an important factor in affecting the final morphology of the sheet. For the immiscible PEI/Vectra A system, longer and more stable TLCP fibrils were found compared to PEI/HX1000 system. It is believed that, due to lower interfacial tension, stress induced fiber breakup occurred during stretching of the PEI/HX1000 blend. Thermoforming of In Situ Composites The use of in situ thermoplastic composites based on blends of a polyetherimide with an amorphous and a semicrystalline liquid crystalline polymer in the thermoforming process was explored in this part of the work. Injection molded and extruded samples, in which the initial morphology of the dispersed TLCP phase was either in the form of fibers or droplets, were subjected to thermoforming. It was found that in the case where the initial morphology of the dispersed TLCP phase was that of droplets, the elongational stresses generated during forming were capable of deforming the TLCP phase into fibers, and the aspect ratio of the fibers was increased with depth of draw. However, when the initial morphology of the the TLCP phase was in the form of fibers, then the relative alignment of the fibers with respect to the forming direction was an important factor in affecting the final structure of the TLCP phase in the formed tray. When the fibers were aligned parallel to the forming direction, the elongational strains generated during forming tended to further increase the aspect ratio of the fibers. In the case where the initial TLCP fibers were aligned transversely to the forming direction, the fibers tended to spread into a ribbon-like structure after forming. Pre-stretching of the samples prior to thermoforming tended to contribute to an increase in the aspect ratio of the TLCP fibers. As a result, an enhancement in the deflection resistance of the prestretched/formed samples was observed. In situ thermoplastic composites seemed to be advantageous compared to glass reinforced thermoplastics in thermoforming applications. The elongational stresses generated during forming tended to deform the TLCP phase into a specific morphology. Depending on the relative direction of the deformation, either fibers or a ribbon-like structure may be developed. This is in contrast to glass reinforced PEI, in where breakage of the glass fibers occurred upon forming, which may contribute to a reduction in the mechanical performance of glass reinforced materials. / Ph. D.

Laboratory and field studies of Hydrotaea aenescens were undertaken to provide information on this predator's biology and ecology under differing conditions, and to promote its use as a biocontrol agent for controlling house flies in poultry houses. Taxonomic diversity of arthropods in a new high-rise cage layer poultry house was determined from manure samples collected from different manure moisture categories. Stabilization of taxonomic diversity and taxonomic evenness of manure-inhabiting arthropods occurred after the house had been operating for eight months. In contrast, overall diversity in high-rise poultry houses at a well managed, longer established farm was significantly higher than that observed at the new farm, even after 1 1/2 years of operation. When the densities of selected manure-inhabiting predatory arthropods collected from the manure samples (including Carcinops pumilio, pseudoscorpions, a dermapteran species, an anthocorid species, and H. aenescens) were correlated with percent manure moisture, the results showed that, of these predators, only H. aenescens was positively correlated with both manure moisture and with densities of house fly larvae. This information emphasized that although predators such as C. pumilio may exhibit high predation rates on house fly eggs and first instars, their effectiveness 1s reduced by their spatial separation from their supposed prey. This contrasts greatly with H. aenescens performance. Decreases in survival of house fly larvae occurred when the larvae were exposed to H. aenescens of higher larval stadia. This was dramatically demonstrated when 100 first instar house flies were exposed to 100 second instar H. aenescens. No house fly larvae survived. Developmental times were determined at constant temperatures for egg, and larval H. aenescens. Developmental times decreased as temperature increased. Median time for egg and larval development ranged from 1.3 and 14.6 days at 22.2°C to 0.5 and 8.3 days at 35.0°C, for the respective stages. All of this information, together with developmental times and mortality of H. aenescens immatures gathered in a study of temperature dependent development has enhanced understanding of the biotic interactions in accumulated poultry manure. These data will be invaluable in designing integrated pest management programs especially in the area of computer-aided decision making. / Ph. D.

In this dissertation, we first present a unified treatment of compact moment problems, both the truncated and full moment cases. Second, we define the lower and upper functions V±(ð₁,... ð _n) on the convex hull of the curve Γ_n = {(t,.·.,tⁿ): t ∈ [0,1] } for each positive integer n. Explicit formulas of these functions are derived and applied to the study of the subnormal completion problem in operator theory. Last, we show that certain power functions are the building blocks of completely positive functions; by our definition, these functions are the continuous functions on the interval [0, 1] that map each Hausdorff moment sequence of a probability measure into another one. / Ph. D.

For perturbations of the Callias and Anghel type the L2-index of the perturbed Dirac operator on a Spin c -manifold is realized as the result of pairing an element in K -homology with an element of compactly supported K -cohomology. This is achieved by putting the problem of calculating the Fredholm index of the perturbed Dirac operator in the framework of KK-theory and using the identification of K-groups with KK-groups. The formula for the Fredholm index is given in terms of topological data of the Spin c-manifold and the structure of the perturbation. / Ph. D.

The traditional product development process has been sequential in nature, with the product going through design, process planning, manufacturing and assembly. This sequential decision making results in increased costs and higher product development times. With the trend towards better product quality, product customization, shorter product life cycle, and international competition, manufacturers are faced with the challenge of improving product quality while reducing product development time, manufacturing lead-time, and product cost. To cope with these challenges, the product development process has to be made more efficient by integrating manufacturing and assembly considerations in the design phase itself, through the use of techniques such as Design For Manufacturability (DFM) and Design For Assembly (DFA). DFM techniques have to be automated to take advantage of the vast advances in CAD and CAM systems. However, the automation of DFM has been constrained, especially for machined components, by the lack of methodologies which are dependent on the process of manufacture, and the incomplete part data representation in CAD systems. This research created a DFM methodology for machined components, along with an appropriate data representation scheme. Also, a software prototype was developed to demonstrate and validate both the methodology and the data structure. The DFM methodology consists of three modules: DFM feasibility, process plan generation, and DFM analysis. The DFM feasibility module performs an initial feasibility check on the material, dimensions, tolerances, and configuration of the part. It also generates the spatial relationships between features. The process plan generation module uses a sequence identifier algorithm to generate the manufacturing sequence. The DFM analysis module evaluates tolerances relative to their stacking effects and manufacturability. It then analyzes the part configuration for possible design and process plan improvements. A software prototype was developed using C++. It addresses the dimension checking, tolerance checking, configuration checking and spatial relationships generation in the DFM feasibility module. In the process plan generation module, the sequence of surfaces/features to be generated has been automated. This sequence is one of the major inputs to a computer-aided process planning module. Other methodologies for non-machined components can be easily integrated into the DFM framework for complete automation of DFM analysis. / Ph. D.