The problem of rough surface scattering and propagation over rough terrain in ducting environments has been receiving considerable attention in the literature. One popular method of modeling this problem is the parabolic wave equation (PWE) method. In this method, the Helmholtz wave equation is replaced by a PWE under the assumption of predominant forward propagation and scattering. The resulting PWE subjected to the appropriate boundary condition(s) is then solved, given an initial field distribution, using marching techniques such as the split-step Fourier algorithm. As is obvious from the assumption on which it is based, the accuracy of the PWE approximation deteriorates in situations involving appreciable scattering away from the near-forward direction, i.e. when the terrain under consideration is considerably rough. The backscattered field is neglected in all PWE-based models. An alternative and more rigorous method for modeling the problem under consideration is the boundary integral equation (BIE) method, which is formulated in two steps. The first step involves setting up an integral equation (the magnetic field integral equation, MFIE, or the electric field integral equation EFIE) governing currents induced on the rough surface by the incident field and solving for these currents numerically. The resulting currents are then used in the appropriate radiation integrals to calculate the field scattered by the surface everywhere in space. The BIE method accounts for all orders of multiple scattering on the rough surface and predicts the scattered field in all directions in space (including the backscattering direction) in an exact manner. In homogeneous media, the implementation of the BIE approach is straightforward since the kernel (Green's function or its normal derivative) which appears in the integral equation and the radiation integrals is well known. This is not the case, however, in inhomogeneous media (ducting environments) where the Green's function is not readily known. Due to this fact, there has been no attempt, up to our knowledge, at using the BIE (except under the parabolic approximation) to model the problem under consideration prior to the work presented in this thesis. In this thesis, a closed-form approximation of the Green's function for a two-dimensional ducting environment formed by the presence of a linear-square refractivity profile is derived using the asymptotic methods of stationary phase and steepest descents. This Green's function is then modified to more closely model the one associated with a physical ducting medium, in which the refractivity profile decreases up to a certain height, beyond which it becomes constant. This modified Green's function is then used in the BIE approach to study low grazing angle (LGA) propagation over rough surfaces in the aforementioned ducting environment. The numerical method used to solve the MFIE governing the surface currents is MOMI, which is a very robust and efficient method that does not require matrix storage or inversion. The proposed method is meant as a benchmark for people studying forward propagation over rough surfaces using the parabolic wave equation (PWE). Rough surface scattering results obtained via the PWE/split-step approach are compared to those obtained via the BIE/MOMI approach in ducting environments. These comparisons clearly show the shortcomings of the PWE/split-step approach. / Ph. D.

With the recent resurgence of interest in double negative (DNG) materials and the reported construction of a metamaterial with DNG characteristics, applications of these materials become feasible and examination of the behavior of systems and devices a potentially fruitful topic. The most promising area of research, upon inquiry into past work related to DNG materials, proves to be dielectric waveguides. The present investigation, then, focuses on the inclusion of DNG materials in various planar dielectric waveguide configurations. These waveguides involve a core region surrounded by various numbers of symmetrically-placed cladding layers. The present investigation involves the review of the electromagnetic properties of DNG materials by a thorough analysis based on Maxwell's equations. The use of a negative index of refraction for these materials is justified. These results are then used to perform a frequency domain analysis of an N-layer formulation for dielectric waveguides which is general for any combination of DNG and double positive (DPS) materials. This N-layer formulation allows for the derivation of the characteristic equation, which relates the operating frequency and the propagation constant solutions, along with the cutoff conditions and field distributions. A causal material model which obeys the Kramers-Kronig relations and which is based on measurements of a realized metamaterial is studied and used in the investigation in order to produce realistic results. The N-layer formulation is then applied to the three-layer (slab) waveguide and known results are reviewed. A new interpretation of intramodal degeneracy is given, whereby degenerate modes are split into two separate modes, one with positive phase velocity and one with negative phase velocity but both with a causal positive group (energy) velocity. Next, the formulation is applied to the five-layer waveguide. New behaviors are observed in this case which are not seen for the three-layer waveguide, including the return of the fundamental mode in some cases, whereas it is never present for the three-layer guide, the absence of certain higher-order modes in some situations and the appearance of new modes. Additionally, for some configurations the order of the even and odd modes in the DNG frequency range is found to be reversed from that of conventional waveguides. The photonic crystal waveguide, which involves an infinite number of periodically placed cladding layers, is next studied using ray analysis, and a slight variation of the N-layer formulation is used to compare these results with those of the pseudo-photonic crystal waveguide. The pseudo-photonic crystal waveguide is identical to the photonic crystal waveguide with the exception that it has only large but finite number of layers. It is seen that the results of these two cases are similar for conventional modes, but the photonic crystal waveguide allows for new modes called photonic crystal modes which are inaccessible through conventional waveguides. Interesting phenomena such as mode crossings among the photonic crystal modes are observed and discussed. Using the results from the frequency domain analysis of the five-layer waveguide, a Fourier transform technique is used to study pulse propagation in a waveguide containing DNG materials. A Gaussian pulse is launched in the waveguide over the frequency range covering a portion of the positive- and negative-phase-velocity fundamental transverse electric (TE) modes. Splitting of the input pulse into two separate pulses is observed, where both of these new pulses have a causal, positive energy velocity. The interpretation of intramodal degeneracy given in previous discussions is buttressed with evidence from this portion of the investigation, thus completing the analysis and bringing the present study to its conclusion. / Ph. D.

This dissertation presents a new framework for the development and analysis of blind adaptive algorithms. An adaptive algorithm is said to be 'blind' if it does not require a known training sequence. The main focus is on application of these algorithms to adaptive antenna arrays in mobile radio communications. Adaptive antenna arrays can reduce the effects of cochannel interference, multipath fading, and background noise as compared to more conventional antenna systems. For these reasons, the use of adaptive antennas in wireless communication has received a great deal of attention in the literature. There are several reasons why the study of blind adaptive algorithms is important. First, it is common practice to switch to a blind mode once the training sequence has been processed in order to track a changing environment. Furthermore, the use of a blind algorithm can completely eliminate the need for a training sequence. This is desirable since the use of a training sequence reduces the number of bits available for transmitting information. The analysis framework introduced here is shown to include the well-known Constant Modulus Algorithm (CMA) and decision directed algorithm (DDA). New results on the behavior of the CMA and DDA are presented here, including analytic results on the convergence rate. Previous results have relied on Monte Carlo simulation. This framework is also used to propose a new class of blind adaptive algorithms that offer the potential for improved convergence rate. / Ph. D.

The behavior of large and tightly interconnected power systems resembles, in certain circumstances, the behavior of a continuously distributed system. This resemblance motivated the derivation of continuum models, which were used to explain and predict disturbance propagation, un-damped power oscillations, and the stability of power systems. In this dissertation, we propose a one-dimensional continuum representation suitable for meshed power systems. Previous continuous representations of meshed power systems used two-dimensional spatial domains. Thus our approach has the potential to provide better resolution for comparable computational burden. It is important to note that, the computational burden required to obtain solutions for PDEs involved in the continuum representation varies notably with the solver implementation. The contributions of this dissertation are: a) Reviewing a previous continuum model and providing a detailed derivation for the one-dimensional version of it. b) Providing and describing in detail a parameter distribution technique adequate for the continuum approach. c) Identifying and documenting limitations on the continuum model voltage calculation. e) Providing a procedure to simulate the behavior of meshed power systems using the one dimensional continuum model. And f) Identifying and applying a numerical PDE solver for the continuum approach. / Ph. D.

With the rise of the Internet of Things (IoT) and smart buildings, new algorithms are being developed to understand how occupants are interacting with buildings via structural vibration measurements. These vibration-based occupant inference algorithms (VBOI) have been developed to localize footsteps within a building, to classify occupants, and to monitor occupant health. This dissertation will present a three-stage journey proposing a path forward for VBOI research based on physically informed data-driven models of structural dynamical systems. The first part of this dissertation presents a method for extracting temporal gait parameters via underfloor accelerometers. The time between an occupant's consecutive steps can be measured with only structural vibration measurements with a similar accuracy to current gait analysis tools such as force plates and in-shoe pressure sensors. The benefit of this, and other VBOI gait analysis algorithms, is in their ease of use. Gait analysis is currently limited to a clinical setting with specialized measurement systems, however VBOI gait analysis provides the ability to bring gait analysis to any building. VBOI algorithms often make some simplifying assumptions about the dynamics of the building in which they operate. Through a calibration procedure, many VBOI algorithms can learn some system parameters. However, as demonstrated in the second part of this dissertation, some commonly made assumptions oversimplify phenomena present in civil structures such as: attenuation, reflections, and dispersion. A series of experimental and theoretical investigations show that three common assumptions made in VBOI algorithms are unable to account for at least one of these phenomena, leading to algorithms which are more accurate under certain conditions. The final part of this dissertation introduces a physically informed data-driven modelling technique which could be used in VBOI to create a more complete model of a building. Continuous residue interpolation (CRI) takes FRF measurements at a discrete number of testing locations, and creates a predictive model with continuous spatial resolution. The fitted CRI model can be used to simulate the response at any location to an input at any other location. An example of using CRI for VBOI localization is shown. / Doctor of Philosophy / Vibration-based occupant inference (VBOI) algorithms are an emerging area of research in smart buildings instrumented with vibration sensors. These algorithms use vibration measurements of the building's structure to learn something about the occupants inside the building. For example the vibration of a floor in response to a person's footstep could be used to estimate where that person is without the need for any line-of-sight sensors like cameras or motion sensors. The storyline of this dissertation will make three stops: The first is the demonstration of a VBOI algorithm for monitoring occupant health. The second is an investigation of some assumptions commonly made while developing VBOI algorithms, seeking to shed light on when they lead to accurate results and when they should be used with caution. The third, and final, is the development of a data-driven modelling method which uses knowledge about how systems vibrate to build as detailed a model of the system as possible. Current VBOI algorithms have demonstrated the ability to accurately infer a range of information about occupants through vibration measurements. This is shown with a varied literature of localization algorithms, as well as a growing number of algorithms for performing gait analysis. Gait analysis is the study of how people walk, and its correlation to their health. The vibration-based gait analysis procedure in this work demonstrates extracting distributions of temporal gait parameters, like the time between steps. However, many current VBOI algorithms make significant simplifying assumptions about the dynamics of civil structures. Experimental and theoretical investigations of some of these assumptions show that while all assumptions are accurate in certain situations, the dynamics of civil structures are too complex to be completely captured by these simplified models. The proposed path forward for VBOI algorithms is to employ more sophisticated data-drive modelling techniques. Data-driven models use measurements from the system to build a model of how the system would respond to new inputs. The final part of this dissertation is the development of a novel data-driven modelling technique that could be useful for VBOI. The new method, continuous residue interpolation (CRI) uses knowledge of how systems vibrate to build a model of a vibrating system, not only at the locations which were measured, but over the whole system. This allows a relatively small amount of testing to be used to create a model of the entire system, which can in turn be used for VBOI algorithms.

The complex molecular machinery of the cell controls its response to various signals and environmental conditions. A natural approach to study these molecular mechanisms and cellular processes is with protein interaction networks. Due to the complexity of these networks, sophisticated computational techniques are required to extract biological insights from them. In this thesis, I develop and apply network-based algorithms for three different challenges. 1. I develop a novel, highly-scalable algorithm for network-based label prediction methods that enables the integration of functional annotations and interaction networks across many species in order to predict the functions of genes in newly-sequenced bacteria. 2. To overcome the limitations of experimental approaches to find human proteins and processes that are hijacked by SARS-CoV-2, I adapt network propagation approaches for predicting human interactors of the virus. 3. Large-scale experimental techniques to screen chemicals for toxicity have tested their effects on many individual proteins. I integrate human protein-protein interactions with this data to gain insights into the molecular networks those chemicals affect. For each of these research problems, I perform comprehensive evaluations and downstream analyses to demonstrate both the accuracy of our approaches and their utility in obtaining a broader understanding of the molecular systems in question. / Doctor of Philosophy / The functions of all living cells are governed by complex networks of molecular interactions. A major goal of systems biology is to understand the components of this machinery and how they regulate each other to control the cell's response to various conditions and signals. Advances in experimental techniques to understand these systems over the past couple of decades have led to an explosion of data that probe various aspects of a cell such as genome sequencing, which reads the DNA blueprint, gene expression, which measures the amount of each gene's products in the cell, and the interactions between those products (i.e., proteins). To extract biological insights from these datasets, increasingly sophisticated computational methods are required. A powerful approach is to model the datasets as networks where the individual molecules are the nodes and the interactions between them are the edges. In this thesis, I develop and apply network-based algorithms to utilize molecular systems data for three related problems: (i) predicting the functions of genes in bacterial species, (ii) predicting human proteins and processes that are hijacked by the SARS-CoV-2 virus, and (iii) suggesting cellular signaling pathways affected by exposure to a chemical. Developments such as those presented in these three projects are critical to obtaining a broader understanding of the functions of genes in the cell. Therefore, I make the methods and results for each project easily accessible to aid other researchers in their efforts.

A new method of numerical integration is presented here, the variable-step Stormer-Cowell method. The method uses error control to regulate the step size, so larger step sizes can be taken when possible, and is double-integration, so only one evaluation per step is necessary when integrating second-order differential equations. The method is not variable-order, because variable-order algorithms require a second evaluation. The variable-step Stormer-Cowell method is designed for space surveillance applications,which require numerical integration methods to track orbiting objects accurately. Because of the large number of objects being processed, methods that can integrate the equations of motion as fast as possible while maintaining accuracy requirements are desired. The force model used for earth-orbiting objects is quite complex and computationally expensive, so methods that minimize the force model evaluations are needed. The new method is compared to the fixed-step Gauss-Jackson method, as well as a method of analytic step regulation (s-integration), and the variable-step variable-order Shampine-Gordon integrator. Speed and accuracy tests of these methods indicate that the new method is comparable in speed and accuracy to s-integration in most cases, though the variable-step Stormer-Cowell method has an advantage over s-integration when drag is a significant factor. The new method is faster than the Shampine-Gordon integrator, because the Shampine-Gordon integrator uses two evaluations per step, and is biased toward keeping the step size constant. Tests indicate that both the new variable-step Stormer-Cowell method and s-integration have an advantage over the fixed-step Gauss-Jackson method for orbits with eccentricities greater than 0.15. / Ph. D.

In a large and dense power network, the transmission lines, the generators and the loads are considered to be continuous functions of space. The continuum technique provides a macro-scale analytical tool to gain an insight into the mechanisms by which the disturbances initiated by faults and other random events propagate in the continuum. This dissertation presents one-dimensional and two-dimensional discrete models to illustrate the propagation of electromechanical waves in a continuum system. The more realistic simulations of the non-uniform distribution of generators and boundary conditions are also studied. Numerical simulations, based on the swing equation, demonstrate electromechanical wave propagation with some interesting properties. The coefficients of reflection, reflection-free termination, and velocity of propagation are investigated from the numerical results. Discussions related to the effects of electromechanical wave propagation on protection systems are given. In addition, the simulation results are compared with field data collected by phasor measurement units, and show that the continuum technique provides a valuable tool in reproducing electromechanical transients on modern power systems. Discussions of new protection and control functions are included. A clear understanding of these and related phenomena will lead to innovative and effective countermeasures against unwanted trips by the protection systems, which can lead to system blackouts. / Ph. D.

The decline of many freshwater mussel populations in the United States has brought about the need for facilities in which mussels can be held for purposes of relocation, research, and propagation. The Aquatic Wildlife Conservation Center (AWCC) of the Virginia Department of Game and Inland Fisheries (VDGIF) serves as a freshwater mussel conservation facility in southwest Virginia. The goals of this study were: (1) to determine whether adult freshwater mussels could maintain energy reserves at AWCC (2) to determine whether adults could produce mature gametes at AWCC and (3) to establish suitable rearing conditions for juvenile mussels at the AWCC. In fall 2002, four species of mussels, Villosa iris, V. vanuxemensis, Amblema plicata, and Pleurobema oviforme, served as surrogates for endangered species and were relocated to the AWCC. Three energy reserves (glycogen, protein, and lipid) were measured seasonally (fall 2002 to summer 2004) from mantle tissue and compared between AWCC specimens and those from their wild source populations. The gametogenic stage of each species was also compared to determine whether gametogenesis was occurring in captivity. In summer 2003, the first of two juvenile experiments tested the effects of three rates of water flow (1 L/min, 3 L/min, and 7 L/min) on the survival and growth of V. iris and Epioblasma capsaeformis reared in flow-through troughs. In summer 2004, round flow-through tanks were used to assess the effects of three sizes of substrate (fine sediment, fine sand, and coarse sand) and sampling frequency on the survival and growth of V. iris. Gut content analyses also were conducted at the end of each experiment to determine which algal species were being consumed. Overall survival rates were as follows: A. plicata, 100 %; V. vanuxemensis, 86 %; V. iris, 79 %; P. oviforme (2002 collection), 53 %; and P. oviforme (2003 collection), 50 %. All energy reserves varied among seasons, but every species except P. oviforme (2003 collection) had levels higher than those in source populations at the end of this experiment. Glycogen appeared to be the best indicator of condition in these species, with protein also being important in the 2003 collection of P. oviforme. Mature gametes were found in all four captive species in 2003 and 2004, with lipids appearing to fuel gametogenesis. Additionally, gametogenesis was occurring earlier in captive long-term brooders than in the wild, possibly due to warmer water temperatures at AWCC. The first juvenile experiment resulted in 15 % overall survival, with 1 L/min having the greatest survival (18 %), and the 3 L/min having the greatest growth (656 μm). In the second experiment, dishes left unsampled had significantly greater survival (40 %) (P<0.05) of juveniles than those which were sampled (27 %). The unsampled fine sand treatment had significantly greater survival than the other two unsampled treatments (52 %) (P<0.001). Sampled juveniles in fine sediment had the greatest growth (887 μm). Also, juveniles from Experiment 1 were consuming primarily Navicula, with Coelastrum and Chlorella consumed in greatest abundance in Experiment 2. Results indicate that most adult mussels maintained energy reserves and produced mature gametes, and that juveniles of V. iris had good survival and growth. Only P. oviforme had survival rates lower than expected and did not appear to maintain condition at AWCC. Based on results of the species tested, environmental conditions at AWCC appear suitable for the survival of most adult and juvenile freshwater mussels. / Master of Science

The Super Dual Auroral Radar Network (SuperDARN) is an international network of high frequency (HF) coherent scatter radars, employed to detect backscatter from magnetic field aligned plasma irregularities in the ionosphere and to study the near- Earth space weather. Space weather impacts many technological systems including HF communications, Global Positioning System (GPS), and surveillance radars. Variations in the pattern of the backscatter from the ground ("ground scatter") observed by the SuperDARN radars give information regarding the state of the ionosphere. In this thesis, ray tracing simulation of the observed ground scatter pattern for the mid-latitude SuperDARN radar at Blackstone, Virginia is implemented. An existing ray tracing code was modified, to incorporate the IRI-2007 model for electron density. This ray tracing code was used to simulate the ground scatter pattern observed at Blackstone in the year 2009. Simulations were compared with the observed ground scatter to assess our understanding of the ionospheric conditions. The IRI-2007 model is found to be adequate to predict the average ground scatter pattern observed through the year, including the winter anomaly. However, one deficiency with the IRI-2007 model is its inability to predict the sporadic E layer formation in summer and an anomalous evening enhancement in backscatter power observed in some months of the year, described here for the first time. Finally some suggestions are presented for the further improvement of the simulation methods for backscatter prediction. / Master of Science