By nature discrete solitons represent self-trapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of self-localized states has been successfully observed in both one-and two-dimensional nonlinear waveguide arrays. In recent years such lattice structures have been implemented or induced in a variety of material systems including those with cubic (Kerr), quadratic, photorefractive, and liquid-crystal nonlinearities. In all cases the underlying periodicity or discreteness leads to new families of optical solitons that have no counterpart whatsoever in continuous systems. In the first part of this dissertation, a theoretical investigation of linear and nonlinear optical wave propagation in semi-infinite waveguide arrays is presented. In particular, the properties and the stability of surface solitons at the edge of Kerr (AlGaAs) and quadratic (LiNbO3) lattices are examined. Hetero-structures of two dissimilar semi-infinite arrays are also considered. The existence of hybrid solitons in these latter types of structures is demonstrated. Rabi-type optical transitions in z-modulated waveguide arrays are theoretically demonstrated. The corresponding coupled mode equations, that govern the energy oscillations between two different transmission bands, are derived. The results are compared with direct beam propagation simulations and are found to be in excellent agreement with coupled mode theory formulations. In the second part of this thesis, the concept of parity-time-symmetry is introduced in the context of optics. More specifically, periodic potentials associated with PT-symmetric Hamiltonians are numerically explored. These new optical structures are found to exhibit surprising characteristics. These include the possibility of abrupt phase transitions, band merging, non-orthogonality, non-reciprocity, double refraction, secondary emissions, as well as power oscillations. Even though gain/loss is present in this class of periodic potentials, the propagation eigenvalues are entirely real. This is a direct outcome of the PT-symmetry. Finally, discrete solitons in PT-symmetric optical lattices are examined in detail.

In this study, the properties of the reflected paths and scattering phenomena were investigated in the LMDS band (28 GHz). We used the newly developed sampling swept time delay short pulse (SSTDSP) sounder to collect field data in certain locations on the Virginia Tech campus. The sounder collected the channel impulse response analog waveform, sampled, digitized and reconstructed it. The stored data were used to produce the power delay profile and other channel parameters. In particular, we collected scattered and reflected data regarding the channel response with different incident angle and distance set-ups from brick and limestone walls. We used the reflected pulse width and maximum excess delay derived from each power delay profile to analyze the rough surface scattering phenomena. We found that limestone and brick walls exhibited some diffuse scattering. The reflected pulse of a limestone wall had more maximum excess delay spread than did a brick wall at -15dB power threshold. The mean maximum excess delay for the reflected pulse of the limestone wall measurement set-ups was more than two times that of the brick wall. With equal transmitter and receiver distances to the wall, we found that as the incident angle increased, the maximum excess delay decreased but the perpendicular reflection coefficient increased. It is recommended that for future study, a second generation SSTDSP sounder will replicate the measurement with larger distance and angle set-ups as well as in non-line-of-sight areas. / Master of Science

An investigation has been made of the propagation characteristics of magnetostatic waves with frequencies in the range 890-990 MHz in a crystal of Yttrium Iron Garnet. The sample was mounted in a two port strip line assembly and magnetised axially along the (100) direction. The experiments were performed at room temperature. Magnetostatic waves were observed in external magnetic fields in the neighbourhood of 500 Cersteds. and to explain the experimental results a non-uniform distribution of magnetisation along the axial direction is proposed for the unsaturated sample. Theoretical results for the demagnetising field and the time delay have been computed using this model to explain the excitation and transmission of the observed magnetostatic waves. / Thesis / Master of Engineering (ME)

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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.

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.

Land mobile satellite systems that are currently being designed for implementation in the next decade will need to operate in the presence of propagation effects such as vegetative shadowing and multipath that will cause signal fading. This paper discusses the statistical modeling and simulation of the land mobile satellite fading environment. Simple models are developed to approximate the complex analytical expressions for the fade distributions. The Average Path Model, which relates the physical parameters of the vegetation along the path to the propagation model parameters, is verified and shown as a useful model for estimating the propagation parameters. Discrepancies between the VT Propagation Simulator and the analytical models are resolved and results comparing secondary fading statistics from the simulator to measured data are given. Results of a study using the propagation simulator to simulate spatial diversity to combat vegetative fading are given. / Master of Science

This thesis describes the findings of research conducted as to the feasibility of using the U.S. Coast and Geodetic Survey (USCGS) digital topographic database for the automated prediction of radio transmitter coverage area. The objective was to assess the adequacy of the USCGS database to support radio-frequency path-loss and terrain clearance calculations. The assessment was made by investigating the basic features of the tapes and of the coverage calculation process. From this investigation, a prototype computer program was developed which calculated coverage areas from sample data tapes. The computer code for the program is included. / M.S.