The bending of thin flat plates has occupied the interests of mechanicians and applied mathematicians since J. L. Lagrange discovered the differential equation characterizing the behavior of such structural members. One particular phase of investigation in this field concerns itself with the solution of the differential equation subject to given boundary conditions. Indeed, it may be safely stated that the bulk of the literature on the subject of flat plates is concerned with the solution of problems involving the specification of the transverse loading on the plate and the conditions at the boundary of the plate. Various mathematical techniques are available for the solution of such problems. Among these, the most prominent are, a.) the method of series, b) the method of singularities, and c) the complex variable techniques. A survey of the literature in this area has revealed a paucity of solutions of certain types of problems; notably, those problems in which boundary conditions are mixed a.long a portion of the edge of the plate which ha.s a continuously turning tangent. By mixed boundary conditions, we mean a. change in condition from prescription of bending moment and vertical shear to assignment of slope and deflection along a portion of the edge which has a continuously turning tangent. In the first section of this thesis, a number of problems are considered for the half-plane. The attendant boundary conditions considered a.re combinations of clamping and simple support. The second portion consists of a number of problems associated with the quarter-plane. Solutions for these problems are obtained by utilizing the method of images in conjunction with the solutions presented in the first section. After this, we examine some problems connected with the circular plate. In particular, a numerical solution is given for a uniformly loaded circular plate simply-supported over half of its boundary and clamped over the remaining portion. The last chapter is a brief discussion of plates in the form of rectangles. Here, a closed solution is presented for the bending moments in terms of Weierstrassian elliptic functions. Another numerical example is included for a uniformly loaded plate clamped over a portion of one edge and simply- supported over the remainder of its boundary. / Doctor of Philosophy

Urban landscapes homogenize our world at global scales. This sameness contributes to "extinction of experience", where people feel increasingly disconnected from native ecosystems and the services they provide. Numerous approaches have been proposed for combatting extinction of experience, all of which require community support to be successful. Because comparative assessments are relatively rare, however, it is difficult to say which options are most supported. We addresses this knowledge gap using human subject surveys and multi-criteria decision analysis to evaluate landscape preferences and their implications for three approaches recommended to combat extinction of experience: ecosystem conservation, turf replacement and nature-based solutions. Our study focuses on universities in Southern California, where native ecosystem remnants, nature-based solutions, lawns, and ornamental gardens co-exist, which is necessary to compare community support for transitions among them. Our results suggest that conservation of native ecosystems, particularly sage scrub (top ranked landscape overall), is well supported by campus communities, as are turf replacement programs (lawns ranked lowest overall). Support for nature-based solutions was more intermediate (and variable), which may reflect their relative newness, both on university campuses and in urban spaces more generally. Not all university populations preferred the same landscapes; preferences differed with degree of pro-environmentalism and university status (undergrad, graduate student, staff). Even so, all groups exhibited landscape preferences consistent with at least one approach for combatting extinction of experience. This suggests we have a viable set of tools for increasing native ecosystem exposure on university campuses, and ultimately, in the next generation of urban homeowners. / Master of Science / Urban areas around the world are more like one another than the natural landscapes they replace. This can make people feel more at home in a city far away than they do in the landscapes that belong in their home state. Changing urban areas to reconnect people with nature requires community support to be successful. Whether this support is available, however, is not well understood. This study focuses on evaluating community support for three actions intended to bring people closer to nature. These include 1) protection of natural landscapes, 2) replacing lawns with natural plants, and 3) using nature instead of pipes and channels to manage the water that runs off paved surfaces during storms in urban areas. The community we focus on is university students and staff because they have access to all the different landscape types involved in the three actions described above. Our approach was to survey people on four campuses in Southern California and rank their landscape preferences to determine if they are likely to support these actions. We found that people tend to be supportive of protecting native landscapes and replacing turf grass with native plants. Support for nature-based alternatives to pipes and channels was more variable. This may be because they are presently uncommon, and people don't know how they feel about them yet. Not everyone on campus preferred the same landscapes, but most people's preferences were consistent with at least one approach for connecting people with nature. This suggests that there may be strong support for changing campus landscapes in ways that bring people closer to nature.

The Cauchy problem associated with the scalar wave equation in free space is used as a vehicle for a critical examination and assessment of the bidirectional and unidirectional spectral representations. These two novel methods for synthesizing wave signals are distinct from the superposition principle underlying the conventional Fourier method and they can effectively be used to derive a large class of localized solutions to the scalar wave equation. The bidirectional spectral representation is presented as an extension of Brittingham's ansatz and Ziolkowski's Focus Wave Mode spectral representations. On the other hand, the unidirectional spectral representation is motivated through a group-theoretic similarity reduction of the scalar wave equation. / Master of Science

M.S.

Dynamic spectrum access (DSA) is a promising approach to alleviate spectrum scarcity and improve spectrum utilization. Our work aims to enhance the utilization of the available white spaces in the licensed spectrum by enabling cooperative communication in the secondary networks. We investigate the ability of a two-hop cooperative transmission to reduce the effect of primary user interruption on secondary transmissions. We analyze the performance of a cooperative secondary transmission by modeling the interaction between primary user and secondary user transmissions using a discrete time Markov chain (DTMC). The analysis shows a significant enhancement in the secondary transmission efficiency and throughput when cooperative transmission is utilized compared to that of direct transmission, especially at high levels of primary user activity. We extend our study to model secondary cooperative transmission in realistic scenarios. We evaluate the throughput performance enhancement in the secondary infrastructure network analytical and by simulation. A simple scenario is modeled analytically by a DTMC that captures the probability of finding intermediate relays according to nodes' density and by discrete event simulation where both results confined each other. We introduce a dedicated cooperative and cognitive Media Access Control (MAC) protocol named CO2MAC to facilitate secondary users transmissions in infrastructure-based secondary networks. The proposed MAC enables utilizing cooperative Multi-Input-Multi-Output (MIMO) transmission techniques to further enhance the throughput performance. By using the proposed MAC, we quantify the enhancement in the throughput of secondary infrastructure networks via simulation for complex scenarios. The results show an enhancement in cooperative transmission throughput compared to that of direct transmission, especially at crowded spectrum due to the ability of cooperative transmissions to reduce the negative effect of primary user interruptions by buffering the data at intermediate relays. Also, the cooperative throughput performance enhances compared to that of direct transmission as the nodes' density increases due to the increase in the probability of finding intermediate relays. After that, we answer two questions. The first question is about the way a secondary user pays the cooperation price to its relay and what are the conditions under which the cooperation is beneficial for both of them. The second question is about how to pair the cooperating nodes and allocate channels in an infrastructure based secondary network. To answer the first question, we model the cooperation between the secondary user and its relay as a resource exchange process, where the secondary user vacates part of its dedicated free spectrum access time to the relay as a price for the energy consumed by the relay in forwarding the secondary user's packets. We define a suitable utility function that combines the throughput and the energy then we apply axiomatic bargaining solutions, namely Nash bargaining solution (NBS) and egalitarian bargaining solution (EBS) to find the new free spectrum access shares for the secondary user and the relay based on the defined utility in the cooperation mode. We show that under certain conditions, the cooperation is beneficial for both the secondary user and the relay where both achieve a higher utility and throughput compared to the non-cooperative mode. Finally, based on the bargaining based shares of the cooperating nodes, the node pairing and channel allocation are optimized for different objectives, namely maximizing the total network throughput or minimizing the maximum unsatisfied demand. Our bargaining based framework shows a comparable performance with the case when the nodes' free spectrum access time shares are jointly optimized with the pairing and allocation process, at the same time, our cooperation framework provides an incentive reward for the secondary users and the relays to involve in cooperation by giving every node a share of the free spectrum that proportional to its utility. We also study the case of using multiple secondary access points which gives more flexibility in node pairing and channel allocation and achieves a better performance in terms of the two defined objectives. / Ph. D.

This thesis studies equational theories incorporated into unification and describes STAR, a stratified term rewriting system that achieves a full integration. STAR is an advance over existing systems because it integrates an equational theory with unification at a lower, more fundamental level. Certain properties of STAR are proven including termination and confluence. We also discuss the algorithmic complexity of the reduction algorithm, a vital component of STAR. We compare our system with narrowing and discuss the merits and drawbacks of each technique. Since our system is an experimental integration of equation solving and unification, we are not concerned with the efficiency of the implementation. We do propose, however, some future improvements. / Master of Science

An accuracy study is made of central finite difference methods for solving boundary value problems which are governed by second order differential equations with variable coefficients leading to odd order derivatives. Three methods are studied through applications to selected problems. Definitive expressions for the error in each method are obtained by using Taylor series to derive the differential equations which exactly represent the finite difference approximations. The resulting differential equations are accurately solved by a perturbation technique which yields the error directly. A half station method, which corresponds to making finite difference approximations before expanding derivatives of function products in the differential equations, was found superior to two whole station methods which correspond to expanding such products first. / M.S.

Calculation of propagation constants in particulate matter is an important aspect of wave propagation analysis in engineering disciplines such as satellite comnnication, geophysical exploration, radio astronomy and material science. It is important to understand why different propagation constants produced by different theories are not applicable to a particular problem. Homogenization of the random media using effective medium theories yields the effective propagation constants by effacing the particulate, microscopic nature of the medium. The Maxwell-Gamet and Bruggeman effective medium theories are widely used but their limitations are not always well understood. In this thesis, some of the more complex homogenization theories will only be partially derived or heuristically constructed in order to avoid unnecessary mathematical complexity which does not yield additional physical insight. The intent of this thesis is to elucidate the nature of effective medium theories, discuss the theories' approximations and gain a better global understanding of wave propagation equations. The focus will be on the Maxwell-Garnet and Bruggeman theories because they yield simple relationships and therefore serve as anchors in a sea of myriad approximations. / Master of Science

The motivation for the determination of the viscosity of polymer solutions in dense fluids at the critical polymer concentration stems from the need to understand the factors that influence the time scale of phase separation in systems that undergo spinodal decomposition upon a pressure quench. In a recent investigation of PDMS + CO₂ and PE + n-pentane where molecular weights of the polymers and the critical polymer concentrations were comparable, significant differences were observed in the time evolution of new phase growth. Among the reasons that contribute to the difference in phase separation kinetics is the viscosity of the solutions. This thesis has been carried out to experimentally demonstrate the differences in viscosities of solutions at their critical polymer concentration. Specifically, the thesis focused on the high-pressure density and viscosity of solutions of poly(dimethylsiloxane) (Mw = 93,700, Mw/Mn = 2.99) in supercritical carbon dioxide and of polyethylene (Mw = 121,000, Mw/Mn = 4.3) in near-critical n-pentane. The measurements have been carried out at the critical polymer concentrations, which is 5.5 wt % for solution of PDMS in CO2 and 5.75 wt % for solution of PE in n-pentane. For PDMS + CO₂ system, the measurements were conducted at 55, 70, 85 and 100 oC and pressures up to 50 MPa. For PE + n-pentane system, the measurements were conducted at 140 and 150 °C and again up to 50 MPa. All measurements were conducted in the one-phase homogenous regions. At these temperatures and pressures, the viscosities were observed to be in the range from 0.14 mPa.s to 0.22 mPa.s for PDMS + CO₂, and from 2.3 mPa.s to 4.6 mPa.s for PE + n-pentane systems. In both systems the viscosities increase with pressure and decrease with temperature. The temperature and pressure dependence could be described by Arrhenius type relationships in terms of flow activation energy (E#) and flow activation volume (V#) parameters. The flow activation energies in PDMS + CO₂ system were about 7 kJ/mol compared to about 18 kJ/mol for the PE + n-pentane system. The activation volumes were in the range 40-64 cm3/mol for PDMS + CO₂ system and 65-75 cm3/mol for the PE + n-pentane solution. The higher values of E# and V# represent the higher sensitivity of viscosity to temperature and pressure changes in the PE + n-pentane system. The viscosity data could also be correlated in terms of density using free-volume based Doolittle type equations. Density is shown to be an effective scaling parameter to describe T/P dependency of viscosity. The closed packed volumes suggested from density correlations were found to be around 0.33 cm³/g for the PDMS and 0.48 cm3/g for the PE systems. Comparison of the viscosity data in these systems with the data on the kinetics of pressure-induced phase separation confirms that the slower kinetics in the PE + n-pentane stems from the higher viscosity in this solution compared to the PDMS + CO₂ system, despite the similarity in the molecular weight of the polymer and the critical polymer concentrations. These viscosity and density measurements were conducted in a special falling-body type viscometer. In the course of this thesis a more reliable procedure for determining the terminal velocity of the falling sinker was implemented. This is based on the precise and more complete description of the position of the sinker with time with the aid of a set of linear variable differential transformers (LVDTs). The design of the new arrangement and procedure for terminal velocity determination and calibration procedures for the viscometer are also presented. The densities and viscosities are determined with an accuracy of ± 1 % and ± 5 % or better, respectively. / Master of Science

The blending or mixing is extensively utilized in diverse processes of polymers to bring about advantageous properties, but the behavior becomes intriguing when associations are involved and multi-solvents are used. Explanations based on chemistry-specific arguments are less than satisfactory in abstracting essential features, and lack the general applicability across various systems. So, this work focuses on capturing the physical force governing the phenomenon of interest by using a generic model. Highly non-trivial behaviors of polymers are often observed in multi-solvent solutions. It is known that polymers swell and dissolve in good solvents, while they tend to collapse and aggregate in poor solvents. But for some specific systems, polymers that collapse in two different poor solvents become soluble in their mixtures, corresponding to cosolvency, and conversely, polymers that swell in two different good solvents become insoluble in their mixtures, pertaining to cononsolvency. The finding suggests that cononsolvency effect relies on the interplay between polymer-cosolvent preferential adsorptions and solvent-cosolvent attractions, which are typically investigated individually. The utilization of cononsolvency effect can either modify or induce micellization, leading to significant differences in morphology and thermodynamic properties compared to conventional micelles driven solely by hydrophobic interactions. The cosolvency project reveals that it arises from the cross competitions of Van der Waals-type interactions and the associative interaction (e.g., hydrogen bonding). The molecular association has long been a classical problem in physical chemistry, as it often gives rise to ”abnormal” phenomena, such as the elevation of boiling points due to hydrogen bonding. But the understanding of its effect on polymer system still remains rudimentary. So, this work tries to answer three fundamental questions by choosing three representative systems: 1. How will supramolecular complexations change the thermodynamics equilibrium morphology; 2. What is the impact of supramolecular bonds on the free energy landscape during the transition process; 3. How will association influence the single chain coil-globule conformational transition. It is found that the association not only results in versatile morphology, but also brings about distinct transition pathways. Besides, the conformational transition shows the dependence on the association pattern, which is actually decided by the statistical nature.