Consider a Markov jump process, X(t), with a nonnegative state space as a model for a queueing system. The motivation of this study is about useful estimates of system performance. For example, in a system with finite queues, the probability of the system of queues going from an empty state to a state in which the population of at least one queue reaches a large number before becoming empty again is one and the typical sample trajectory of this event is another. To answer these questions, we establish the large deviation principle (LDP) for an appropriate class of queueing processes. The model of our concern is the Jackson network which has a tree-type topological structure. Under carefully designed conditions, the LDP for a time homogeneous Markov process has been well established by Wentzel. However, mainly due to the nonnegativity constraint, the queue length process, X(t), of our model does not satisfy the assumed conditions. As a detour, we define the “potential process”, Y(t), which allows the negativity in state space in the way that even if a queue is empty, the server in the empty queue is working with a same rate as if the queue is not empty. Therefore, each Y_i(t) can be expressed as the difference of the accumulated number of customers who came to station i and the accumulated number of services, done in station, i, up to time t. Then the scaled processes, Y^∊(t) = ∊Y(t/∊), obeys LDP with a certain rate function, I_[0,T](x,Φ), i.e. P(Y^∊(.)∈ B|Y^∊(0) = x| ≈ exp[-1/∊ inf_Φ∊B I_[0,T](x,Φ)], (UTLE) for some B ⊂ D^r[0,T] = { right continuous R^r — valued function which has a left limit at every point on [0,T]}. UTLE stands for ‘up to logarithmic equivalence’. By defining an appropriate Skorohod problem, we obtain a continuous mapping θ from D^r to D^r₍₊₎,) such that θ(Y)(t) is a version of X(t). Then we “push the LDP of potential process through” θ so that LDP of the queue length process can be achieved. The procedure of ‘pushing through’ is another principle of the large deviation theory. It is called “contraction principle” [3]. The contraction principle provides the rate function J_[0,T] of the LDP for the queue length process and J_[0,T](Φ) = inf_ψ|θ(ψ)=Φ J_[0,T](ψ). That is, when X^∊ ≡ ∊X(t/∊), for an appropriate set B ⊂ D^r₍₊₎, P(X^∊(.)∈ B|X^∊(0) = x| ≈ exp[-1/∊ inf_Φ∊B I_[0,T](x,Φ)], (UTLE) The rate function, J_[0,T], is expressed in a closed form. / Ph. D.

This dissertation describes the analysis of the carbohydrate portion of glycosphingolipids from colorectal carcinoma cells, SW1116, by metabolically labelling the cells with radioactive monosaccharide precursors. SW1116 cells (1 x 10⁶) metabolically labelled with 222 μCi/ml of either 6-[³H]-D-galactose (25 Ci/mMol) or 6-[³H]-D-glucosamine (38 Ci/mMol) for 30 hours, incorporated 1%-3% of the radioactivity into their glycoconjugates. Approximately 63% of the radioactivity recovered in the glycoconjugates corresponded to glycolipids when cells were labelled with 6-[³H]-D-galactose, and about 12% when cells were radiolabelled with 6- [³H]-D-glucosamine. Metabolically radiolabelled glycolipids were separated into neutral (88-91% of the radioactivity recovered in glycolipids) and acidic (9-12% of the radioactivity in glycolipids) fractions by ion exchange chromatography. Glycolipids in these fractions were subjected to ozonolysis and alkali fragmentation to release the oligosaccharide chains from the ceramide portion. Oligosaccharides obtained from the neutral glycolipids were separated into single components by a combination of high performance liquid chromatography (HPLC) and Ricinus communis agglutinin I (RCA-I)-agarose affinity chromatography. Oligosaccharides were identified based on the monosaccharide composition, methylation analysis, and exoglycosidase digestions. Major glycolipid components present in the neutral fraction were, glucosylceramide (Glc-Cer), galactosylceramide(Gal-Cer), galabiosylceramide (Galαl-4Gal-Cer), lacto-N-tetraosylceramide (Galβ1-3GIcNAcβ1-3Galβ1-4Glc-Cer), Le^a- pentaglycosylceramide (Galβ1-3[Fucal-4]GlcNAcβ1-3Galβ1-4Glc-Cer), HIpentaglycosylceramide (Fucal-2Galβ1-3GlcNAcβ1-3Galβ1-4Glc-Cer), a difucosylated lacto-N-tetraosylceramide, and a fucosylated lacto-Nnorhexaglycosylceramide. Minor components detected in this fraction corresponded to lactosylceramide (Galfp1-4Glc-Cer), lacto-Nneotetraosylceramide (Galβ1-4GlcNAcβ1-3Galβ1-4Glc-Cer), and fucosylated and difucosylated lacto-N-neotetraosylceramides. The acidic fraction was separated into monosialylgangliosides and _ disialylgangliosides by ion exchange chromatography. Monosialyloligosaccharides were further purified on HPLC, and biochemically characterized by methylation analysis, exoglycosidase digestions, and monosaccharide composition. The major component of this fraction corresponded to the sialyl-Le^a glycolipid (NeuAcα2-3Galβ1-3[Fucαl-4]GlcNAcβ1-3Galβ1-4Glc-Cer) as previously reported by Magnani et al. [183]. GM3 (NeuAcα2-3Galβ1-4Glc-Cer) (0.42% of radioactivity recovered in glycolipids), sialyltetraosylceramide a (NeuAcα2-3Galβ1-3GlcNAcβ1-3Galβ1-4Glc-Cer) (0.46% of radioactivity in glycolipids), sialyltetraosylceramide b (Galβ1-3[NeuAcα2-6]GIcNAcβ1-3Galβ1- 4Glc-Cer) (0.21% of radioactivity in glycolipids), and sialyllated fucosylhexaglycosylceramide, were present in minor quantities. Results from this study demonstrate that metabolic radiolabelling provides a method for the structural analysis of glycolipids, as sensitive as the immunostaining procedures, as unmistakable as physical techniques (Mass Spectrometry, and Nuclear Magnetic Resonance), and that permits the identification of the majority of glycolipids expressed by a cell line, using relatively small number of cells in culture (6 x 10⁶). Application of this method could be extended to the study of changes in glycolipid accompanying oncogenic transformation and differentiation, glycolipid biosynthesis, intracellular sorting of glycolipids, recycling and turnover. / Ph. D.

Spectral wind wave models seek to solve a four-dimensional energy (or action) balance equation for values of the spectrum discretized in frequency and direction of propagation at fixed positions in space. When modeling an ocean area of any appreciable size, computational time and storage capacity limit resolution to relatively coarse grids in all four dimensions. Propagation schemes used in these models, typically the 1st order upwind scheme, encounter difficulty arising from the poor directional resolution (typically 30 degrees) in regions of varying depth and current where wave energy is refracted and concentrated into a small number of directional bins. Since the widely used 1st order upwind scheme is not appropriate for such a rapid bin to bin variation, higher order numerical schemes are investigated to identify one which will produce better results for this wind wave propagation problem. After evaluating the characteristics and performance of the 2nd-order upwind scheme, Lax-Wendroff scheme, and modified Lax-Wendroff scheme suggested by Gadd, for both steady and transient cases, a new propagation scheme is proposed using a time-splitting method and a limiter which combines the modified Lax-Wendroff scheme with the 1st order upwind scheme. For varying depth and current fields, it is shown that the new scheme gives results superior to the ordinary 1st order upwind scheme without any increase of storage capacity at an increased cost in computing time which is minor to the overall wind wave model. / Ph. D.

This dissertation is concerned with the metabolic bioactivation of several amines which are either known or suspected to be neurotoxic and with the exploration of bioactivation processes in order to generate metabolites with therapeutic potential. The following three programs were pursued in this work: (1) Theoretical considerations and recent experimental data have prompted an investigation of the neurotoxicological properties of the 6-hydroxydopamine analog 2-methylamino-1-(2,4,5-trihydroxyphenyl) propane and its possible precursor intermediate 1-(2-hydroxy-4,5-methylenedioxyphenyl)-2-methylaminopropane, potential metabolites of the serotonergic neurotoxin 2-methylamino- 1-(4,5-methylenedioxyphenyl)propane, (Methylenedioxymethamphetamine, MDMA). The syntheses and serotonergic neurotoxic properties of the potential metabolites are discussed. (2) The further biotransformation of the 1-(1-phenylcyclohexy!)- 3,4,5,6-tetrahydropyridinium metabolite derived from_ the psychosis inducing agent phencyclidine [1-(1-phenylcyclohexy]l)- piperidine, PCP] has been examined in rat liver and brain subcellular fractions. In the presence of brain mitochondria this tetrahydropyridinium compound was converted to 1-(phenylcyclohexyl)- 1,2,3,4-tetrahydropyridine-5-carboxaldehyde. The same product was identified in the corresponding liver mitochondrial and microsomal incubation mixtures and in liver microsomal incubations of phencyclidine. The chemical conversion of the synthetic tetra hydropyridinium perchlorate to this product by N⁵-formyltetrahydrofolic acid (folinic acid) suggests that the metabolic reaction is mediated by a transformylation process involving this or the corresponding N¹⁰-formyltetrahydrofolic acid. (3) Extensive substrate-activity studies have established that only those 1,2,3,6-tetrahydropyridine derivatives bearing a lipophilic C-4 substituent and an N-methyl group are likely to be good monoamine oxidase B substrates. The design and synthesis of potential prodrugs based on this enzyme-substrate selectivity has been pursued with model compounds. / Ph. D.

The objectives of this dissertation are: (1) to examine the relationship between the accuracy and reliability of methods of estimating settlements of footings on sand and gravel, (2) to develop a procedure for estimating horizontal movements and rotations of footings without the need of determining soil modulus values, and (3) to develop a simple procedure for calculating movements of retaining walls due to the weight of backfill. The accuracy and reliability of twelve methods of estimating settlements of footings on sand and gravels were examined by comparing calculated settlements with the measured values. Eleven of the methods are based on Standard Penetration Test Results, while Schmertmann’s method is based on Cone Penetration Test Results. The study showed that methods which are more accurate tend to underestimate settlements about half of the time; while those which are more reliable (in the sense that they infrequently underestimate settlements) tend to be less accurate. The study also indicated that these methods of estimating settlements of footings on sands and gravels involve approximately the same relationship between accuracy and reliability, regardless of the approach that they use to calculate settlement. The results demonstrate that there is a tradeoff between accuracy and reliability. Any of the methods can be adjusted to achieve approximately the same combination of accuracy and reliability as other method. A simple procedure is presented to relate horizontal movements and rotations of footings to settlements. The procedure does not require the determination of soil modulus, and its accuracy and reliability can be assessed qualitatively by association with the method used to calculate the settlement. A simple procedure based on elastic theory was also developed to estimate movements of abutments and retaining walls due to the weight of backfill placed behind them. To avoid the inherent difficulty in determining the soil modulus, a procedure for relating these movements to the settlement of the wall was also developed. The new procedure was applied to a case history, and the calculated movements agree quite well with those calculated using the finite element method, and with field observations. / Ph. D.

Brittle materials are characterized by a wide scatter in their strength data and by size effects. In this work, size effects in brittle composite structures such as beams and plates with and without stress raisers are investigated experimentally and analytically. For structures with geometrical irregularities such as notches, holes or cut-outs, no analytical solutions exist and approximate numerical schemes have to be employed. For this purpose, the finite element method is extensively used. For stress analysis of isotropic beams under four point bending and composite plates under in-plane loading, a finite element analysis program F2DELAST based on two-dimensional elasticity theory was developed and verified with existing literature and also by a commercial finite element code ABAQUS. For composite beams under four-point bending, ABAQUS is used. For stress and failure analysis of laminated composite plates under transverse loading, a nonlinear finite element analysis program ENCOMPLIT which accounts for the geometrical nonlinearity in von Karman sense and transverse shear deformation was developed. Both the finite element programs written by the author and the ABAQUS were used for stress analysis as convenience dictates. For post-processing purposes, PATRAN and I-DEAS are used. Linear and nonlinear stress analyses were performed for the case of composite plates under transverse loading. A methodology for reliability analysis is developed for composite beams and plates with and without stress concentration under various loading conditions and various finite element reliability analysis programs were written. The materials used for the analysis are mainly carbon-carbon composites, however, where validation of finite element codes or comparison of the proposed failure criteria with other criteria are needed, graphite-epoxy composites, which are extensively used in the literature, are also used. The model is based on Weibull statistics. The Weibull model was extended to account for the three-dimensional stress field including interlaminar stresses. The effect of interlaminar stresses on the total reliability is investigated. Various failure theories for composite materials are reviewed. New failure criteria for bi-directional orthotropic lamina are developed and proposed. Failure analysis in the non-probabilistic sense (i.e. First-ply-failure analysis) is performed on carbon-carbon composite beams under 4-point bending and carbon-carbon composite plates under transverse loading using the existing failure criteria and the failure criteria proposed in this work. Comparisons are made with the existing failure criteria and also with experiments. An attempt was made to relate the (probabilistic) reliability analysis with (non-probabilistic) first-ply-failure analysis in terms of failure loads for composite beams under 4-point bending and square and rectangular composite plates under transverse loading. / Ph. D.

An A-B monomer containing an ether group, 4(4-acetoxyphenoxy) benzoic acid (PAPBA) was successfully synthesized via a new route using 4-methoxyphenol and 4-chlorobenzonitrile as starting materials. Another ether containing monomer, 4(2-acetoxy-6-naphthoxy) benzoic acid (PANBA), which appears to be a novel monomer, was also prepared in high yields from 6-methoxy-2-bromonaphthalene and ethyl-4-hydroxybenzoate via the Ullmann condensation reaction. These monomers were found to be useful for synthesizing LCP copolymers and segmented copolymers. A variety of polyarylates based on 5-tertiary butylisophthalic acid were synthesized via melt acidolysis techniques. The resulting high molecular weight polyarylates were amorphous polymers and the t-butyl groups along the polymer backbones were found to be thermoxidatively stable. Thermotropic liquid crystalline polyesters (LCPs) are well known for their thermoxidative stability, ductility, solvent resistance and the potential of generating extremely strong, stiff molecular chains. In this dissertation research, several novel liquid crystalline aromatic polyether-ester copolymers were synthesized by the incorporation of an A-B monomer, either PAPBA or PANBA, into the polymer main chain. The corresponding copolymers were thermoxidatively stable and melt processable over a wide compositional range. Novel carboxyl terminated oligomers of an amorphous engineering polymer, poly(arylene ether ketone)(PEK) were successfully synthesized. The synthetic method was somewhat similar to that of carboxyl terminated poly(arylene ether sulfone) oligomers. The PEKCOOH oligomers were quantitatively endcapped and their molecular weights could be controlled. Thermogravimetric analysis revealed that the PEKCOOH oligomers were thermoxidatively stable and therefore suitable for high temperature post-reactions. In general, thermotropic liquid crystalline polymers show excellent properties in the longitudinal direction. Nevertheless, to improve the transverse mechanical properties of liquid crystalline polymers, novel poly(arylene ether ketone)-LCP segmented copolymers were synthesized via melt acidolysis techniques. Chemically bonding an isotropic engineering thermoplastic into a potentially liquid crystalline anisotropic polyester affords segmented copolymers which may possess a balance of mechanical properties in both the longitudinal and transverse directions. In the case of PEK-poly(oxybenzoate)(PEK-POB), a limited amount of POB (~25 wt %) could be incorporated so as to produce segmented copolymers which would yield coherent films. On the other hand, when PEK-POB was modified by adding PAPBA to form PEK-POB-POPB segmented copolymers, a series of the segmented copolymers with various compositions was realized. The liquid crystalline behavior was found to be retained in the segmented copolymers, depending on the degree of the LCP content. The structural analysis of the A-B monomers mentioned earlier was performed by elemental analysis, mass spectroscopy, proton NMR and FT-IR. All the polymers synthesized were characterized by thermal analysis (DSC and TGA). The molecular weight of the carboxyl terminated PEK oligomers was determined by an automatic titration method, and indirectly, by intrinsic viscosity measurements. The latter method was also used to assess the molecular weight of the amorphous polyarylates. For liquid crystalline polyether-ester copolymers and PEK-LCP segmented copolymers, DSC and hot stage optical microscopy were utilized to investigate their thermotropic liquid crystalline behavior. DMTA was used to determine the high temperature properties of the polymers and tensile tests, i.e. stress-strain data, were employed to obtain information on their mechanical properties. / Ph. D.

This dissertation reflects the results of probably the very first attempt to cure sol gel ceramers using microwaves. These materials were first prepared in 1985, but were found to take almost two to six days to cure, when stored under ambient conditions. Microwaves have been found to provide a method for circumventing this problem under certain conditions. It was discovered that the more highly phase separated ceramer systems can be cured in twenty minutes when subjected to heating in a microwave field. Curing in a conventional oven, has on the other hand been found to hinder the extent of reaction because the slow initial rate of heating (which allows for evaporation of some of the compatibilizing solvent media) is believed to leave the reactants in a somewhat diffusion limited state. Dielectric investigations on the ceramer films show the existance of Maxwell Wagner Sillars intefacial polarization which results from charge migration in the ceramer system and also show the possibility of PTMO chain expansion at higher metal alkoxide contents in these ceramers when cast onto a substrate onto which the film adheres. Finally, structural investigations into the ceramers using SAXS, gives an idea of the fractal dimensions of the scattering phases. These investigations have also proved quite conclusively that there exists a contribution to scattering from the porosity present in the inorganic phase at metal alkoxide contents as low as 40 wt%. / Ph. D.

Recently, a new class of sensors has emerged which have scalar outputs derived from distributed measurements over a significant gauge length; these sensors are known as distributed-effect sensors. The most familiar example of a distributed-effect sensor is the piezoelectric laminate PVDF film; other examples include holographic sensors and modal domain optical fiber sensors. Optical fiber sensors are particularly attractive for smart structure and materials applications because they have low mass, are flexible, and can be easily embedded in a variety of materials. Distributed-effect sensors can be fabricated with spatially varying sensitivity to the distributed measurand and act as spatial filters. The spatial variation in the sensor sensitivity, known as the sensor's weighting function, determines the measurement provided by the spatial filter. Spatial filters can be configured to measure a variety of structural parameters, such as modal amplitudes and traveling waves, that can not be measured directly using point sensors. The mathematical model of the sensor is described and incorporated into a state-space model of a flexible structure. Several criteria are described in this dissertation for selecting the weighting functions of distributed-effect sensors for structural control laws. The weighting function realized in the fabrication of a distributed-effect sensor may differ from the desired weighting function, causing the output of the manufactured sensor to differ from the desired measurement. In order to design reliable structural control laws, the nature and effects of errors in the implemented weighting functions of distributed-effect sensors must be understood. This dissertation describes several causes of errors in distributed-effect sensor weighting functions. Errors in the weighting functions of distributed-effect sensors are integrated into the mathematical models of the sensors, and the effects of these errors on the sensor outputs are examined. / Ph. D.

A novel bidirectional decomposition of exact solutions to the scalar wave equation has been shown to form a natural basis for synthesizing localized wave (LW) solutions that describe localized, slowly decaying transmission of energy in free space. In this work, we demonstrate the existence of LW solutions in optical fiber waveguides operated in the linear regime. In this sense, these solutions are fundamentally different from the non-linear, soliton-based communication systems. Despite the dielectric waveguiding constraints introduced by the fiber, solutions that resemble the free-space solutions can be obtained with broad bandwidth source spectra. As with the free-space case, these optical waveguide LW solutions propagate over very long distances, undergoing only local variations. Four different source modulation spectra that give rise to solutions similar to Focus Wave Modes (FWM’s), splash pulses, the scalar equivalent of Hillion’s spinor modes and the Modified Power Spectrum (MPS) pulses are considered. A detailed study of the MPS pulse is performed, practical issues regarding source spectra are addressed, and distances over which such LW solutions maintain their non-decaying nature are quantified. Present day state-of-the-art technology is not capable of meeting requirements that will make practical implementation of LW solution-based fiber optic systems a reality. We address futuristic technology issues and briefly describe efforts that could lead to efficient LW solution-based fiber optic systems. / Ph. D.