Over the past decade there has been a great deal of interest in graphene, a 2-dimensional allotrope of carbon with exceptional mechanical and electrical properties. Its outstanding mobility, minimal size, and mechanical stability make it an appealing material for use in next generation electronic devices. Epitaxial graphene growth on silicon carbide is a reliable, scalable method for the production of high quality graphene films. Recent work has shown that the SiC can be patterned prior to graphitization, in order to selectively grow graphene nanostructures. Graphene nanoribbons grown using this technique do not suffer from the rough edges caused by lithographic patterning, and recent measurements have revealed extraordinary transport properties. In this thesis the magnetic properties of these nanoribbons are investigated through spin polarized current injection. The sensitivity of these nanoribbons to spin polarized current is interesting from a fundamental physics standpoint, and may find applications in future spintronic devices.

The postulated characteristics of double-negative (DNG) materials--i.e., materials with simultaneously negative permittivity and negative permeability (ε < 0, μ < 0)--and recent attempts to realize those characteristics with synthetic metamaterials are briefly reviewed. Investigations into the causality of signal propagation in a DNG medium are then presented. Previous research in this topic is examined, and it is verified that a DNG medium must be dispersive in order to be causal. An accurate time-domain description of propagation in a DNG medium is shown to be elusive due to the presence of dispersion, though approximate solutions and recommendations for future analytical research are provided. The results of numerical investigations into this topic are then discussed, and the anticipated combination of causal signal transmission and a negative phase shift are observed in the numerical data. Potential applications of DNG metamaterials to antenna systems are then presented. A DNG shell is observed to reduce the intrinsic reactance sensed by an infinitesimal electric dipole, thereby increasing the dipole's radiated power. Analytical expressions for the fields in the dipole--DNG shell system are derived, and numerical results for a variety of DNG shell configurations are discussed. The presence of a DNG shell is shown to increase the dipole's radiated power by orders of magnitude in some cases. A circuit model of the dipole--DNG shell system is additionally presented and used to interpret the system's physical behavior. The scattering properties of nested metamaterial shells are then analyzed. Various layering combinations of DNG, double-positive (DPS) and single-negative (SNG) shells are observed to produce resonant scattering of an incident, fundamental radial transverse-magnetic (TMᵣ) wave. Reciprocity between the metamaterial configurations that exhibit TMᵣ scattering resonances and those shown to maximize the power radiated by the infinitesimal electric dipole is demonstrated. Several additional metamaterial configurations are shown to produce both resonant TMᵣ scattering and resonant dipole radiation. A resonant configuration with one epsilon-negative (ENG) shell is especially appealing due to its manufacturability. The effects of a DNG layer on the creeping waves scattered by a small metal sphere are also discussed as a minor yet curious offshoot to the scattering analyses.

Modeling and evaluation of communication and computing systems is an important undertaking. In many cases, large-scale systems are designed in an ad-hoc manner, with validation (or disappointment regarding) system performance coming only after an implementation is made. This does not need to be the case. Modern modeling tools and techniques can yield accurate performance predictions that can be used in the design process. Stochastic activity networks (SANs), stochastic Petri nets (SPNs) and analytic solution methods permit specification and fast solution of many complex system models. To enhance the modeling power of SANs (SPNs), new steady-state analysis methods have been proposed for SAN (SPN) models that include non-exponential activities (transitions). The underlying stochastic process is a Markov regenerative process (MRP) when at most one non-exponential activity (transition) is enabled in each marking. Time-efficient algorithms for constructing the Markov regenerative process have been developed. However, the space required to solve such models is often extremely large. This largeness is due to the large number of transitions in the MRP. Traditional analysis methods require all these transitions be stored in memory for efficient computation. If the size of available memory is smaller than that needed to store these transitions, a time-efficient computation is impossible using these methods. To use this class of SANs to model real systems, the space complexity of MRP analysis algorithms must be reduced. In this thesis, we propose a new steady-state analysis method that is time and space efficient. The new method takes advantage of the structure of the underlying process to reduce both computation time and required memory. The performance of the proposed method is compared to existing methods using several SAN examples. In addition, the ability to model real systems using SANs that include exponential and deterministic activities is demonstrated by modeling and evaluating the performability of a group communication protocol, called Psync. In particular, we study message stabilization time (the time required for messages to arrive at all hosts) under a wide variety of workload and message loss probabilities. We then use this information to suggest a modification to Psync to reduce message stabilizing time. Another important issue we consider is the dependability modeling and evaluation of fault-tolerant parallel and distributed systems. Because of the inherent component redundancy in such systems, the state space size of the underlying stochastic process is often very large. Reduced base model construction techniques that take advantage of symmetries in the structure of such systems have the potential to avoid this state space growth. We investigate this claim, by considering the application of SANs together with reduced base model construction for the dependability modeling and evaluation of three different systems: a fault-tolerant parallel computing system, a distributed database architecture, and a multiprocessor shared-memory system.

A two-step methodology for predicting the radiated fields from lines radiating in the presence of conductor-backed substrates is presented. The method employs the use of transmission line theory to find the current distributions on the lines forming the interconnects of a circuit. These currents are used to evaluate the far-fields of the circuit through the use of dipole theory and superposition. The method was tested and validated by comparison to full-wave models. Investigations established that radiation from common-mode currents, which are not accounted for by the circuit analysis, are found to be dominated by the radiation due to differential mode currents, and thus EMI prediction based on the two-step methodology is found to have good engineering accuracy. A full-wave method based on the Finite-Difference Time-Domain (FDTD) is presented for the evaluation of radiation from structures of such geometrical complexity that the transmission line model is not applicable. The Perfectly Matched Layer truncation scheme is implemented in the FDTD and investigated for radiating structures found in printed circuit boards (PCBs). Proximity effects of the PML dictate careful attention to the proper implementation of this absorbing boundary condition. Also, the FDTD subcell model for thin wires is investigated for modelling thin microstrip interconnect lines. To evaluate the far-fields from radiating structures found in multilayer electronic packages, a novel near-to-far field transform at a single frequency is developed and implemented for sources in stratified medium. This transform is validated and investigated with regard to PML and structure proximity. The near-to-far field transform is also implemented in a methodology for obtaining the radiated emissions from a radiating structure. This methodology is used to address important concerns regarding the grounding of heat sinks, "floating" conducting planes, and the electromagnetic behavior of split ground planes.

In many applications it is necessary to determine coupling from a line current source to a nearby wire. Applications include current coupling in high-speed interconnects and wire interaction with a charged particle beam. A common physical configuration occurs when the source and wire are perpendicular to each other. In this dissertation, we investigate the scattered field and coupled current that result from such a configuration. We solve the problem for three different sources: a dipole, an array of dipoles, and a continuous line current. We detail the solution for the line current source where we obtain the scattered field by numerical integration, the far-zone approximation using steepest descents, and the excited current by numerical integration. We also show that the solution of an infinite number of phased dipoles approaches the continuous line source excitation. For the continuous line source case, we assume an infinite traveling wave line current. We also assume that the current magnitude and phase are not affected by the existence of the nearby wire. The current travels with a speed less than the speed of light in the surrounding medium. The wire is infinitely long and infinitesimally thin, and is located a distance d from the line source. We solve for the scattered field both numerically and approximately using steepest descents. We then add corrections to the saddle point approximation through two different approaches. We also solve numerically for the coupled current on the wire. Finally, we produce plots that allow us to compare the levels of the field with and without the wire present. Our problem could serve as a prelude to investigation of a traveling wave of current and an array of parallel wires. However, such a problem is quite different since the physical configuration would then allow the presence of guided waves.

The formation and propagation of hotspots in a cylindrical medium that is undergoing microwave heating is studied in detail. A mathematical model developed by Garcia-Reimbert, C., Minzoni, A. A. and Smyth, N. in Hotspot formation and propagation in Microwave Heating, IMA, Journal of Applied Mathematics (1996), 37, p. 165-179 is used. The model consists of Maxwell's wave equation coupled to a temperature diffusion equation containing a bistable nonlinear term. When the thermal diffusivity is sufficiently small the leading order temperature solution of a singular perturbation analysis is used to reduce the system to a free boundary problem. This approximation accurately predicts the steady-state solutions for the temperature and electric fields in closed form. These solutions are valid for arbitrary values of the electric conductivity, and thus extend the previous (small conductivity) results of Garcia-Reimbert et.al. A time-dependent approximate profile for the electric field is used to obtain an ordinary differential equation for its relaxation to the steady-state. This equation appears to accurately describe the time scale of the electric field's evolution even in the absence of a temperature front (with zero coupling to the temperature), and can be of wider interest than the model for microwave heating studied here. With sufficiently small thermal diffusivity and strong coupling, the differential equation also accurately describes the time evolution of the temperature front's location. A closed form expression for the time scale of the formation of the hotspot is derived for the first time in the literature of hotspot modeling. Finally, a rigorous proof of the existence of steady-state solutions of the free boundary problem is given by a contraction mapping argument.

Six thunderstorms that occurred at the NASA Kennedy Space Center, Florida, have been studied in an attempt to characterize their electrical structure and electrification. Ground-based measurements of the cloud electric fields, the locations of lightning VHF radio sources, cloud-to-ground lightning strike points, and dual-polarization radar data were used in this study. Changes in the electric field due to lightning were used to determine the locations and magnitudes of changes in cloud charge. The fields themselves were used to compute displacement current densities following lightning flashes. The altitudes of negative charge regions were between 6.5 and 8.5 km and were almost constant. The altitude of upper positive charge exhibited more variability, and usually increased as cells developed. Amounts of charge removed by lightning increased during each cell in large storms but were nearly constant during the early part of small storms. A lower positive charge center (LPCC) usually appeared in the fields before any other charge regions could be detected at the ground. A LPCC appeared to be involved in the initiation of the majority of CG flashes. During periods of lightning, a LPCC was sometimes created by a flash, but more typically, LPCCs were produced by a cloud charge separation process. Displacement current densities were used to estimate charge accumulation rates in the cloud. The rates derived for the main negative and upper positive charge regions were compared to the average rate of charge removal by lightning. The generation rates and average lightning currents each had values ranging from 0.2 to 1.5 A and were approximately equal within expected errors in single-cell storms. Once the storm was multicellular, however, the lightning current was larger than the cloud charging rate, possibly because lightning was removing residual charge from older cells. The cloud charging rates and average lightning currents were compared with the currents computed using a non-inductive ice-graupel charging mechanism and radar-derived cloud microphysical data. This mechanism provided currents that were comparable to the observed charging rates and lightning currents and appeared to be capable of producing the LPCC.

Heterogeneous ferromagnetic-superconducting systems such as a regular array of ferromagnetic nano dots deposited on the top of a superconducting thin film have attracted many research teams both experimental and theoretical. The interest in these systems does not only stem from being good candidates for technological applications, but also because they represent a new class of physical systems where two competing order parameters can coexist. This work focuses on the theoretica laspects of these systems by studying the static and dynamics of few model systems. In the first part, the static properties of a superconducting thin film interacting with a ferromagnetic texture are considered within the London approximation. In particular, the ferromagnetic textures considered here are a circular dot of submicrometer size with in-plane magnetization, an elliptical dot magnetized in the direction perpendicular to the superconductor, and a ferromagnetic dot magnetized in the direction normal to the superconducting film and containing non magnetic cavities. I also consider the interaction of vortices in the superconductor with a ferromagnetic columnar defect which penetrates the supercondcting film. In each case the vector potential and magnetic field of the ferromagnet in the presence of the superconductor are calculated. Afterward the presence of vortices in the superconductor is assumed and the energy of vortex-texture system is found. The pinning potential and force supplied by the texture are then derived from the energy of interaction between the ferromagnet and superconductor. I show that if the magnetization of the ferromagnet exceeds a critical value then vortices are spontaneously created in the ground state of the system. Such spontaneous creation of vortices is possible mostly in a close vicinity of the superconducting transition temperature Ts. For every case, the threshold value of the magnetization at which vortices start to be spontaneously created in the SC is calculated as a function of the parameters of the texture geometry. The phase diagrams for transitions from vortexless regime to regimes with one or more vortices are determined for all cases. In the second problem, the transport properties of a ferromagnetic superconducting bilayer with alternating magnetization and vortex density are studied within a phenomenological model. I show that pinning forces do not appear for continuous distribution of vortices, so a discrete model for the bilayer system is constructed. Afterward, I calculate the pinning forces acting on vortices and antivortices resulting from highly inhomogeneous distribution of flux lines and prove that this system has strong transport anisotropy. In the absence of random pinning, the system displays a finite resistance for the current in the direction perpendicular to the domains while its resistance vanishes for the parallel current. The transport anisotropy strongly depends on temperature. I study this dependence and show that the ratio of parallel to perpendicular critical current is largest close to the superconducting transition temperature Ts and the vortex disappearance temperature Tv while it has a minimum in between them.

In this work we solve two new matrix models, using standard and new techniques. The two models are based on matrix ensembles not previously considered. They are represented by special forms of antisymmetric matrices and are classified in the DIII generator ensemble. It is shown that, in the double scaling limit, their free energy has the same behavior as previous models describing oriented and unoriented surfaces. We also found an additional solution for the chapter 3 model.

<p> Edge magnetoplasmons (EMPs) and pinning mode resonances in two dimensional electron systems (2DESs) can both be thought of as lower hybrid modes of cyclotron and plasma resonances. This dissertation describes low temperature microwave spectroscopy of both of these modes. EMPs have oscillating charge confined at the 2DES edge by the combination of the perpendicular magnetic field and the electrostatic potential that produces the edge. Pinning mode resonances are from electron solids oscillating against confinement provided by disorder in the bulk of the 2DES. </p><p> The first part of this dissertation concerns the search for a mode similar to an EMP but confined solely by a linear magnetic inhomogeneity in the perpendicular magnetic field (<i>B_z</i>). While we do not observe such an excitation, we do observe a marked reduction in the velocity of an EMP in the presence of a <i>B_z</i>-inhomogeneity. </p><p> In the second part of this dissertation, we investigate pinning modes in &ldquo;wide'' quantum well samples, for which the effective electron-electron interaction is softened at short range due to the vertical extent of the wavefunction. We observe a pinning mode resonance whose peak frequency (<i>f_pk</i>) vs Landau level filling (&nu;) shows an anomalous increase as &nu; moves away from &nu; = 1 under roughly the same conditions as anomalous quantum Hall effects observed previously in DC transport. A region of &nu; with enhanced <i>f_pk</i> is interpreted as evidence for a new electron solid phase.</p>