This dissertation is devoted to investigating the time dependent neutron transport equations with reflecting boundary conditions. Two typical geometries --- slab geometry and spherical geometry --- are considered in the setting of <I>L^p</I> including <I>L^1</I>. Some aspects of the spectral properties of the transport operator <I>A</I> and the strongly continuous semigroup <I>T(t)</I> generated by <I>A</I> are studied. It is shown under fairly general assumptions that the accumulation points of { m Pas}(A):=sigma (A) cap { lambda :{ m Re}lambda > -lambda^{ast} }, if they exist, could only appear on the line { m Re}lambda =-lambda^{ast}, where lambda^{ast} is the essential infimum of the total collision frequency. The spectrum of <I>T(t)</I> outside the disk {lambda : |lambda| leq exp (-lambda^{ast} t)} consists of isolated eigenvalues of <I>T(t)</I> with finite algebraic multiplicity, and the accumulation points of sigma (T(t)) igcap{ lambda : |lambda| > exp (-lambda^{ast} t)}, if they exist, could only appear on the circle {lambda :|lambda| =exp (-lambda^{ast} t)}. Consequently, the asymptotic behavior of the time dependent solution is obtained. / Ph. D.

Bulimia is often viewed as an extreme expression of eating concerns and body image disturbances that afflicts many adolescent and adult women. The cognitive strategies employed by individuals to inhibit eating and facilitate bingeing and purging are thought to include disattending internal sensations of hunger and satiety while sustaining attention on food, distorted beliefs, and interoceptive experiences (e.g., Heatherton & Baumeister, 1991). To the extent that these attentional and perceptual shifts mediate bulimic symptomatology, individuals with bulimic tendencies should exhibit certain cognitive attributes. Because hypnotizability, dissociation, and absorption have each been invoked (either directly or indirectly) as explanatory constructs for clinical and subclinical bulimia, the present study evaluated the absolute and relative effects of these factors on bulimic symptomatology in a large sample of undergraduate women (N = 309) using structural equation modeling. Following 2 assessments of hypnotic susceptibility (Harvard Group Scale of Hypnotic Susceptibility, Form A [Shor & Orne, 1962] & Group Stanford Hypnotic Susceptibility Scale, Form C [Crawford & Allen, 1982]), participants completed measures of eating disorder symptomatology (Eating Disorders Inventory-2 [Garner, 1991]; Three Factor Eating Questionnaire [Stunkard & Messick, 1985]), dissociation (Dissociative Experiences Scale [Carlson & Putnam, 1986]; Dissociation Questionnaire [Vanderlinden et al., 1993]), and absorption (Tellegen Absorption Scale [Tellegen & Atkinson, 1974]; Differential Attentional Processes Inventory [Crawford, Brown, & Moon, 1993; Grumbles & Crawford, 1981]). A final model including the latent constructs Hypnotizability, Dissociation, Absorption, and Bulimic Symptomatology provided a very good fit to the data (X 2 (58, N = 309) = 31.09, NFI = .932, CFI = .967, & RMSEA = .053). As hypothesized, dissociation was found to a have moderate effect (Standardized coefficient = .32, p < .01) on Bulimic Symptomatology when controlling for Hypnotizability and Absorption. Moreover, contrary to past research, the path between Hypnotizability and Bulimic Symptomatology and the path between Absorption and Bulimic Symptomatology were not significant. Based on these finding, we can now speak with increased confidence of a meaningful link between dissociation and the continuum of bulimic symptomatology. A pathological dissociative style appears to contribute to the development of bulimia. / Ph. D.

Burgers' equation is a one-dimensional simple model for convection-diffusion phenomena such as shock waves, supersonic flow about airfoils, traffic flows, acoustic transmission, etc. For high Reynolds number, the open-loop system (no control) produces steep gradients due to the nonlinear nature of the convection. The steep gradients are stabilized by feedback control laws. In this phase, sufficient conditions for the control input functions and the location of sensors are obtained. Also, explicit exponential decay rates for open-loop and closed-loop systems are obtained. Numerical experiments are given to illustrate some of typical results on convergence and stability. / Ph. D.

Three discrete dynamical models are used to solve the Chandrasekhar H-equation with a positive or negative characteristic function. Two of them produce series of continuous functions which converge to the solution of the H-equation. An iteration model of the nth approximation for the H-equation is discussed. This is a nonlinear n-dimensional dynamical system. We study not only the solutions of the nth approximation for the H-equation but also the mathematical structure and behavior of the orbits with respect to the parameter function, i.e. characteristic function. The dynamical system is controlled by a manifold. For n=2, stability of the fixed points is studied. The stable and unstable manifolds passing through the hyperbolically fixed point are obtained. Globally, the bounded orbits region is given. For parameter c in some region a periodic orbit of one dimension will cause periodic orbits in the higher dimensional system. For changing parameter c, the bifurcation points are discussed. For c ∈ (-5.6049, 1] the system has a series of double bifurcation points. For c ∈ (-8, -5.6049] chaos appears. For c in a window contained the chaos region, a new bifurcation phenomenon is found. For c ≤ -7 any periodic orbits appear. For c in the chaos region the behavior of attractor is discussed. Chaos occurs in the n-dimensional dynamical system. / Ph. D.

This thesis is a numerical study of the coupled Burgers equation. The coupled Burgers equation is motivated by the Boussinesq equations that are often used to model the thermal-fluid dynamics of air in buildings. We apply Finite Element Methods to the coupled Burgers equation and conduct several numerical experiments. Based on these results, the Group Finite Element method (GFE) appears to be more stable than the standard Finite Element Method. The design and implementation of controllers heavily relies on rapid solutions to complex models such as the Boussinesq equations. Thus, we further examine the feasibility and efficiency of the Proper Orthogonal Decomposition (POD) for the coupled Burgers equation. Using POD, we reduce the system to a "minimal" number of ODE's and conduct numerous numerical studies comparing the POD and GFE method. Further numerical experiments consider an application where the dynamics are projected on a POD basis and then the governing parameters of the system are varied. / Master of Science

In fiber optic communication systems, the main linear phenomenon that causes optical pulse broadening is called dispersion, which limits the transmission data rate and distance. The principle nonlinear effect, called self-phase modulation, can also limit the system performance by causing spectral broadening. Hence, to achieve the optimal system performance, high data rate and low bandwidth occupancy, those effects must be overcome or compensated. In a nonlinear dispersive fiber, properties of a transmitting pulse: width, chirp, and spectra, are changed along the way and are complicated to predict. Although there is a well-known differential equation, called the Nonlinear Schrodinger Equation, which describes the complex envelope of the optical pulse subject to the nonlinear and dispersion effects, the equation cannot generally be solved in closed form. Although, the split-step Fourier method can be used to numerically determine pulse properties from this nonlinear equation, numerical results are time consuming to obtain and provide limited insight into functional relationships and how to design input pulses. One technique, called the Variational Method, is an approximate but accurate way to solve the nonlinear Schrodinger equation in closed form. This method is exploited throughout this thesis to study the pulse properties in a nonlinear dispersive fiber, and to explore ways to compensate dispersion for both single link and concatenated link systems. In a single link system, dispersion compensation can be achieved by appropriately pre-chirping the input pulse. In this thesis, the variational method is then used to calculate the optimal values of pre-chirping, in which: (i) the initial pulse and spectral width are restored at the output, (ii) output pulse width is minimized, (iii) the output pulse is transform limited, and (iv) the output time-bandwidth product is minimized. For a concatenated link system, the variational calculation is used to (i) show the symmetry of pulse width around the chirp-free point in the plot of pulse width versus distance, (ii) find the optimal dispersion constant of the dispersion compensation fiber in the nonlinear dispersive regime, and (iii) suggest the dispersion maps for two and four link systems in which initial conditions (or parameters) are restored at the output end. The accuracy of the variational approximation is confirmed by split-step Fourier simulation throughout this thesis. In addition, the comparisons show that the accuracy of the variational method improves as the nonlinear effects become small. / Master of Science

The goal of this project was improve the fundamental understanding of the wood-resin interaction, by looking at the relationship between the resin wetting onto wood and the resulting penetration into wood lumens. Wetting was analyzed with the sessile drop method, which observed the initial contact angle and change in contact angle over 35s. Penetration was measured within each individual tracheid. The Lucas-Washburn equation analyzed the wetting and penetration by calculating the penetration and comparing it to the measured penetration. Wetting of four resins was compared on 3 species, to improve the understanding of adhesive wetting behavior. This study agreed with previous research, that the non-aqueous resin exhibited favorable wetting and presumably better penetration than aqueous resins, with exception of urea-formaldehyde. Wetting and penetration of pMDI was studied on 5 wood species using the Lucas-Washburn equation. The wetting behaviors exhibited grain and species effects, which had implications on the resin availability for flake/strand-based composite products. The greater surface energy of loblolly pine most likely accounted for the significantly greater penetration of loblolly pine compared to Douglas-fir. The calculated penetration, via the Lucas-Washburn equation, exceeded the measured penetration, but it was concluded that the Lucas-Washburn equation predicted penetration reasonably well. Wetting and penetration of phenol-formaldehyde and subsequent adhesives was compared on 3 wood species using the Lucas-Washburn equation. All contact angles were unfavorable due to a skin formation. The Lucas-Washburn equation did not predict any penetration; however, penetration was observed with all systems. The findings suggest that the system was too complex for the Lucas-Washburn equation to be able to predict accurately. / Master of Science / Although the wood-based composites industry has been in operation for over a century, fundamental aspects of the wood/resin interaction- what happens when the liquid resin touches wood- remain poorly understood. An important aspect of this wood/resin interaction is penetration, which is critical to the strength and durability of wood-based composites. The two types of resins used, oil-based and water-based, were observed on a variety of wood species, Douglas-fir, loblolly pine, spotted gum, European beech and yellow-poplar. When using the oil-based resin, penetration measurements were in reasonable agreement with theoretical predictions. However, when using the water-based resins, the theory predicted no penetration which contradicted measurements- a shallow penetration was clearly observed. This means that parameters modeled by theory were in error, and this is sensible because we expect water to transfer from resin into the dry wood. Consequently, controlling parameters such as resin viscosity, resin surface tension, and wood surface energy were changing. This contributes fundamental knowledge, providing a better understanding of a critical step in the manufacture of wood-based composites, the materials most North Americans use to build their homes.

An optimization algorithm has been developed to study the effectiveness of substituting time tested ODEs with FDEs as applied to ship motions, specifically with an eye toward modeling different forms of roll damping. Relations between the order of differentiation a and damping coefficient b in the FDEs have been drawn for changing damping, added moment of inertia, and initial roll angle. A pitch model has also been studied and compared to the roll model. The error at each of these a and b pairs has also been calculated using an L2-norm. An initial effort was made to correlate the FDE coefficients to differing mechanisms of roll damping as characterized by Himeno. / Master of Science

No / High temperature reversion tests have revealed a state of pre-existing molecular orientation in extruded polyethylene sheet. This state is related to differences in stress-deformation behaviour when specimens of the sheet are stretched along different angles with respect to the extrusion direction. An established large deformation, rate-dependent constitutive equation has been developed to model this material, by incorporating the pre-orientation by the addition of a strained Gaussian network. The level of pre-orientation is deduced from the dimensional changes on shrinkage. The constitutive equation is incorporated into the finite element package , and the shapes and drawing forces of tensile specimens extended at various angles to the extrusion direction are modelled.

Yes / Given a prescribed boundary of a Bezier surface we compare the Bezier surfaces generated by two different methods, i.e. the Bezier surface minimising the Biharmonic functional and the unique Bezier surface solution of the Biharmonic equation with prescribed boundary. Although often the two types of surfaces look visually the same, we show that they are indeed different. In this paper we provide a theoretical argument showing why the two types of surfaces are not always the same.