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In this thesis a study is made of the damage layer (as defined by its solubility in a HF-H2o2, or concentrated HF solution) produced by ion bombardment of Si. This thesis is concerned with not only the layer but also its usefulness in the study of radiation damage itself. The layer is examined with respect to the adverse effects it has upon the anodic oxidation and stripping technique, to the dose of incident ions required to produce it (ie the threshold dose), and to its relationship to the amorphous layer which has been observed with ion bombardment of Si. Annealing of the damage has been approached from two points of view. First the temperature dependence of the threshold dose is used to obtain information about the annealing of the damage that occurs between the formation of a discrete damage zone and the formation of a layer. Secondly using gas release of the radioactive Kr85 the annealing of the fully formed amorphous damage layer is followed. The solubility of the damage layer in a HF-H2o2 solution is shown to be a very useful tool in the study of radiation damage. Firstly it provides a convenient means of obtaining the mean range of the damage distribution as a function of incident ion energy. Secondly it is used to obtain the threshold dose for the formation of the damage layer, and thirdly it is used in the gas release experiments to give more detailed information about the Kr85 motion. / Thesis / Master of Science (MS)

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Several aspects of the subharmonic instability of boundary layers are studied. First, the subharmonic instability of incompressible flows over a flat plate is investigated using the resonant triad model and the Floquet model. The primary wave is taken in the form of a two-dimensional (2-0) Tollmien-Schlichting (T-S) wave. The subharmonic wave is taken in the form of a three-dimensional (3-D) wave. Results from both models are presented and compared with the experimental data and numerical simulation. It is found that the results of the Floquet model are in good agreement with the experimental data and numerical simulation, whereas the results of the resonant triad model agree only qualitatively with the experimental data. Second, the subharmonic instability of incompressible flows over a 2-0 hump is studied using the Floquet model. The mean flow over the hump is calculated by using interacting boundary layers, thereby accounting for viscid/inviscid interactions. The results show that increasing the hump height results in an increase in the amplification factors of the primary and subharmonic waves. When the hump causes separation, the growth rates of both the primary and subharmonic waves are considerably larger than those obtained in the case of no separation. Third, the subharmonic instability of compressible boundary layers over a flat plate is studied using the Floquet model. Results are presented for adiabatic wall boundary conditions and subsonic, transonic, and supersonic flows. For supersonic flows results are presented for first- and second-mode primary waves. The effect of Mach number, spanwise wavenumber, primary-wave amplitude, Reynolds number, and frequency are studied. Fourth, results for the effect of heat transfer on the subharmonic instability of a two-dimensional compressible boundary layer over a flat plate are presented for different Mach numbers. For supersonic flows results are presented for first- and second-mode waves. The effect of different levels of heat transfer on changing the features of the subharmonic compressible instability is evaluated. Fifth, results for the effect of suction on the subharmonic instability of a two-dimensional compressible boundary layer over a flat plate are presented. It is found that when the primary wave is a first-mode merging with a second-mode, the subharmonic wave is strongly destabilized by suction. Sixth, the effect of a bulge on the subharmonic instability of compressible boundary layers is studied. It is found that the effect of compressibility on reducing the growth rate of the disturbances weakens as the hump height increases. / Ph. D.

Recently, many new types of wireless networks have emerged for both civil and military applications, such as wireless sensor networks, ad hoc networks, among others. To improve the performance of these wireless networks, many advanced communication techniques have been developed at the physical layer. For both theoretical and practical purposes, it is important for a network researcher to understand the performance limits of these new wireless networks. Such performance limits are important not only for theoretical understanding, but also in that they can be used as benchmarks for the design of distributed algorithms and protocols. However, due to some unique characteristics associated with these networks, existing analytical technologies may not be applied directly. As a result, new theoretical results, along with new mathematical techniques, need to be developed. In this dissertation, we focus on the design of new algorithms and optimization techniques to study theoretical performance limits associated with these new wireless networks. In this dissertation, we mainly focus on sensor networks and ad hoc networks. Wireless sensor networks consist of battery-powered nodes that are endowed with a multitude of sensing modalities. A wireless sensor network can provide in-situ, unattended, high-precision, and real-time observation over a vast area. Wireless ad hoc networks are characterized by the absence of infrastructure support. Nodes in an ad hoc network are able to organize themselves into a multi-hop network. An ad hoc network can operate in a stand-alone fashion or could possibly be connected to a larger network such as the Internet (also known as mesh networks). For these new wireless networks, a number of advanced physical layer techniques, e.g., ultra wideband (UWB), multiple-input and multiple-output (MIMO), and cognitive radio (CR), have been employed. These new physical layer technologies have the potential to improve network performance. However, they also introduce some unique design challenges. For example, CR is capable of reconfiguring RF (on the fly) and switching to newly-selected frequency bands. It is much more advanced than the current multi-channel multi-radio (MC-MR) technology. MC-MR remains hardware-based radio technology: each radio can only operate on a single channel at a time and the number of concurrent channels that can be used at a wireless node is limited by the number of radio interfaces. While a CR can use multiple bands at the same time. In addition, an MC-MR based wireless network typically assumes there is a set of "common channels" available for all nodes in the network. While for CR networks, each node may have a different set of frequency bands based on its particular location. These important differences between MC-MR and CR warrant that the algorithmic design for a CR network is substantially more complex than that under MC-MR. Due to the unique characteristics of these new wireless networks, it is necessary to consider models and constraints at multiple layers (e.g., physical, link, and network) when we explore network performance limits. The formulations of these cross-layer problems are usually in very complex forms and are mathematically challenging. We aim to develop some novel algorithmic design and optimization techniques that provide optimal or near-optimal solutions. The main contributions of this dissertation are summarized as follows. 1. Node lifetime and rate allocation We study the sensor node lifetime problem by considering not only maximizing the time until the first node fails, but also maximizing the lifetimes for all the nodes in the network. For fairness, we maximize node lifetimes under the lexicographic max-min (LMM) criteria. Our contributions are two-fold. First, we develop a polynomial-time algorithm based on a parametric analysis (PA) technique, which has a much lower computational complexity than an existing state-of-the-art approach. We also present a polynomial-time algorithm to calculate the flow routing schedule such that the LMM-optimal node lifetime vector can be achieved. Second, we show that the same approach can be employed to address a different but related problem, called LMM rate allocation problem. More important, we discover an elegant duality relationship between the LMM node lifetime problem and the LMM rate allocation problem. We show that it is sufficient to solve only one of the two problems and that important insights can be obtained by inferring the duality results. 2. Base station placement Base station location has a significant impact on sensor network lifetime. We aim to determine the best location for the base station so as to maximize the network lifetime. For a multi-hop sensor network, this problem is particularly challenging as data routing strategies also affect the network lifetime performance. We present an approximation algorithm that can guarantee (1- ε)-optimal network lifetime performance with any desired error bound ε > 0. The key step is to divide the continuous search space into a finite number of subareas and represent each subarea with a "fictitious cost point" (FCP). We prove that the largest network lifetime achieved by one of these FCPs is (1- ε)-optimal. This approximation algorithm offers a significant reduction in complexity when compared to a state-of-the-art algorithm, and represents the best known result to this problem. 3. Mobile base station The benefits of using a mobile base station to prolong sensor network lifetime have been well recognized. However, due to the complexity of the problem (time-dependent network topology and traffic routing), theoretical performance limits and provably optimal algorithms remain difficult to develop. Our main result hinges upon a novel transformation of the joint base station movement and flow routing problem from the time domain to the space domain. Based on this transformation, we first show that if the base station is allowed to be present only on a set of pre-defined points, then we can find the optimal sojourn time for the base station on each of these points so that the overall network lifetime is maximized. Based on this finding, we show that when the location of the base station is un-constrained (i.e., can move to any point in the two-dimensional plane), we can develop an approximation algorithm for the joint mobile base station and flow routing problem such that the network lifetime is guaranteed to be at least (1- ε) of the maximum network lifetime, where ε can be made arbitrarily small. This is the first theoretical result with performance guarantee on this problem. 4. Spectrum sharing in CR networks Cognitive radio is a revolution in radio technology that promises unprecedented flexibility in radio communications and is viewed as an enabling technology for dynamic spectrum access. We consider a cross-layer design of scheduling and routing with the objective of minimizing the required network-wide radio spectrum usage to support a set of user sessions. Here, scheduling considers how to use a pool of unequal size frequency bands for concurrent transmissions and routing considers how to transmit data for each user session. We develop a near-optimal algorithm based on a sequential fixing (SF) technique, where the determination of scheduling variables is performed iteratively through a sequence of linear programs (LPs). Upon completing the fixing of these scheduling variables, the value of the other variables in the optimization problem can be obtained by solving an LP. 5. Power control in CR networks We further consider the case of variable transmission power in CR networks. Now, our objective is minimizing the total required bandwidth footprint product (BFP) to support a set of user sessions. As a basis, we first develop an interference model for scheduling when power control is performed at each node. This model extends existing so-called protocol models for wireless networks where transmission power is deterministic. As a result, this model can be used for a broad range of problems where power control is part of the optimization space. An efficient solution procedure based on the branch-and-bound framework and convex hull relaxations is proposed to provide (1- ε)-optimal solutions. This is the first theoretical result on this important problem. / Ph. D.

An experiment has been conducted to examine the generation and subsequent evolution of boundary-layer disturbances on a two-dimensional airfoil up through transition to turbulent flow. The experiment was conducted at the NASA Langley Research Center "2 ft by 3 ft Low Speed Wind Tunnel Facility." The primary objective of the experiment was to generate a comprehensive database that includes the effect of the external disturbance environment on the transition process and can be used as a benchmark for future transition prediction tools. The airfoil used for this experiment was custom designed. The model was a 6% thick, 4-ft chord unswept symmetric wing. A description of the design procedure, along with the theoretical stability characteristics of the airfoil will be presented in this paper. The experiment consisted of establishing the mean flow conditions, forcing two-dimensional Tollmien-Schlichting (T-S) waves in the boundary layer using modulated acoustic bursts in the free-stream, and acquiring the mean boundary-layer data and fluctuating disturbance data using hot-wire probes. The acoustic receptivity due to surface roughness near Branch I has been examined. The surface roughness consisted of two-dimensional strips of tape applied at and symmetrically spaced about Branch I. Repeated roughness elements were spaced one wavelength apart based upon the wavelength of the primary forcing frequency as determined by linear-stability theory. The test conditions consisted of mean flow velocities of 15 and 20 m/s, which correspond to chord Reynolds numbers of 1.25 and 1.68 million, respectively. Boundary-layer disturbance profiles and constant boundary-layer height chordwise traverses were acquired and examined at individual frequencies and in total energy amplitude / broadband forms. The experimental results match well with linear stability theory and linear parabolized stability equations, indicating breakdown of disturbances between N-factors of 7 and 11 with surface roughness on the model. It was observed that when the flow physics change, differences between linear-stability theory and experiment are strongly apparent. An amplitude-based breakdown criterion was defined for the developing boundary-layer responses, which were burst-type packets like the acoustic forcing signal. A criterion was defined for the breakdown of both maxima of the T-S-like disturbance profile. Overall, the effects of surface roughness and free-stream acoustic forcing on boundary-layer receptivity and stability were examined in a well-documented disturbance environment. These results will be used to validate and refine non-linear flow theories as well as help to provide an improved understanding and improved methods to control flow transition. / Ph. D.

The Session Initiation Protocol (SIP) was first published in 1999, by the Internet Engineering Task Force (IETF), to be the standard for multimedia transfers. SIP is a peer-to-peer signaling protocol that is capable of initiating, modifying, and terminating media sessions. SIP utilizes existing Internet Protocols (IP) such as Domain Name Service (DNS) and the Session Description Protocol (SDP), allowing it to seamlessly integrate into existing IP networks. As SIP has matured and gained acceptance, its deficiencies when functioning as a multipoint communications protocol have become apparent. SIP currently supports two modes of operation referred to as conferencing and multicasting. Conferencing is the unicast transmission of session information between conference members. Multicasting uses IP multicast to distribute session information. This thesis proposes an extension for the Session Initiation Protocol that improves functionality for multipoint communications. When using conferencing, a SIP user-agent has limited information about the conference it is taking part in. This extension increases the awareness of a SIP node by providing it with complete conference membership information, the ability to detect neighboring node failures, and the ability to automatically repair conference partitions. Signaling for conferencing was defined and integrated into a standard SIP implementation where it was used to demonstrate the above capabilities. Using a prototype implementation, the additional functionality was shown to come at the cost of a modest increase in transaction message size and processing complexity. IP multicast has limited deployment in today's networks reducing the usability of this useful feature. Since IP multicast support is not guaranteed, the use of application layer multicast protocols is proposed to replace the use of IP multicast. An efficient means of negotiating an application layer protocol is proposed as well as the ability to provide the protocol with session information to begin operation. A ring protocol was defined and implemented using the proposed extension. Performance testing revealed that the application layer protocol had slightly higher processing complexity than conferencing, but on average had a smaller transaction message size. / Master of Science