It is well known that ultrashort, high intensity pulses with peak powers exceedinga certain critical value (Pcr) undergo self-focusingleading to collapse and filamentation. During the initial stagesof propagation at low intensities the beamdynamics are dominated by diffraction and dispersion. During filamentation, self-focusing resulting from the nonlinear Kerr effect is balanced by higher order nonlinearities such as plasma induced defocusing and absorption.This work examines the role that linear processes combined with initial spatial and temporal conditioningplay in the generation and subsequent evolution of filaments within nonlinearbeams. It is demonstrated that, because of linear diffraction, initial spatial beam shaping can have a dramatic effect on the filament pattern, the number of filaments and the energy contained in each filament. These ideas are applicable to cases that arequite common, such as circularly apodized beams, and help to explain interestingbehavior observed in these types of beams. Finally, it is demonstrated thatwith appropriate preconditioning of multiple subcritical pulses, linear effects can be employed to accurately control when and where filamentation occurs during long distance propagation through conditional collapse of overlapping pulses.

<p>As research in electromagnetics has expanded, it has given rise to the examination of metamaterials, which possess nontrivial electromagnetic material properties such as engineered permittivity and permeability. Aside from their application in the microwave industry, metamaterials have been associated with novel phenomena since their invention, including sub-wavelength focusing in negative refractive index slabs, evanescent wave amplification in negative index media, and invisibility cloaking and its demonstration at microwave frequency with controlled material properties in space.</p><p>Effective medium theory plays a key role in the development and application of metamaterials, simplifying the electromagnetic analysis of complex engineered metamaterial composites. Any metamaterial composite can be treated as a homogeneous or inhomogeneous medium, while every unit structure in the composite is represented by its permittivity and permeability tensor. Hence, studying an electromagnetic wave's interaction with complex composites is equivalent to studying the interaction between the wave and an artificial material.</p><p>This dissertation first examines the application of a magnetic metamaterial lens in wireless power transfer (WPT) technology, which is proposed to enhance the mutual coupling between two magnetic dipoles in the system. I examine and investigate the boundary effect in the finite sized magnetic metamaterial lens using a numerical simulator. I propose to implement an anisotropic and indefinite lens in a WPT system to simplify the lens design and relax the lens dimension requirements. The numerical results agree with the analytical model proposed by Smith et al. in 2011, where lenses are assumed to be infinitely large.</p><p>By manipulating the microwave properties of a magnetic metamaterial, the nonlinear properties come into the scope of this research. I chose split-ring resonators (SRR) loaded with varactors to develop nonlinear metamaterials. Analogous to linear metamaterials, I developed a nonlinear effective medium model to characterize nonlinear processes in microwave nonlinear metamaterials. I proposed both experimental and numerical methods here for the first time to quantify nonlinear metamaterials' effective properties. I experimentally studied three nonlinear processes: power-dependent frequency tuning, second harmonic generation, and three-wave mixing. Analytical results based on the effective medium model agree with the experimental results under the low power excitation assumption and non-depleted pump approximation. To overcome the low power assumption in the effective medium model for nonlinear metamaterials, I introduced general circuit oscillation models for varactor/diode-loaded microwave metamaterial structures, which provides a qualitative prediction of microwave nonlinear metamaterials' responses at relatively high power levels when the effective medium model no longer fits.</p><p>In addition to 1D nonlinear processes, this dissertation also introduces the first 2D microwave nonlinear field mapping apparatus, which is capable of simultaneously capturing both the magnitude and phase of generated harmonic signals from nonlinear metamaterial mediums. I designed a C-band varactor loaded SRR that is matched to the frequency and space limitation of the 2D mapper. The nonlinear field generation and scattering properties from both a single nonlinear element and a nonlinear metamaterial medium composite are experimentally captured in this 2D mapper, and the results qualitatively agree with numerical results based on the effective medium model.</p> / Dissertation

This dissertation deals with smooth feedback stabilization of control-affine systems via Interconnection and Damping Assignment - Passivity-Based Control (IDA-PBC). The IDA-PBC methodology is a feedback control design technique that aims to establish or manipulate a port-Hamiltonian structure of the closed-loop system. For a mechanical control system, a port-Hamiltonian system is a natural description of the dynamics, and several effective controller designs have been presented for this class of systems. In other fields of engineering, the development of such controller design is an active area of research. In particular, applications of IDA-PBC techniques prove to be difficult in practice for process control applications where the concept of energy is usually ill-defined. This thesis seeks to extend the application of the IDA-PBC methodology beyond mechanical control systems. This is achieved by following three directions of research. First, we establish conditions under which a port-Hamiltonian system can be written as a feedback interconnection of two port-Hamiltonian system. We identify such an interconnection structure for linear control systems based on their intrinsic properties. Second, as observed in application of IDA-PBC to non-mechanical systems, several additional assumptions on the structure of the desired port-Hamiltonian system can effectively reduce the complexity of the matching problem. We establish a unified approach that considers these additional assumptions. Third, we connect the matching problem to the classical feedback equivalence approach. We show that feedback equivalence between control-affine systems can be employed to construct some feasible interconnection and damping structures. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2011-01-31 12:59:56.828

Thesis (Master)--İzmir Institute of Technology, İzmir, 2005 / Keywords: Nonlinear differential equations, finite difference method, numeric simulation. Includes bibliographical references (leaves. 55-57).

Thesis (Ph. D.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (M.S.)--Rochester Institute of Technology, 1994. / Typescript. Includes bibliographical references (leaves 103-104).

Thesis (M.S.)--Rochester Institute of Technology, 2005. / Typescript. Includes bibliographical references (leaves 144-146).

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (leaves 94-98).

Master of Science / Department of Electrical and Computer Engineering / Alexei Nikitin / Balasubramaniam Natarajan / It has been shown that the performance of communications systems can be severely limited by non-Gaussian and impulsive interference from a variety of sources. The non-Gaussian nature of this interference provides an opportunity for its effective mitigation by nonlinear filtering. In this thesis, we describe blind adaptive analog nonlinear filters, referred to as Adaptive Nonlinear Differential Limiters (ANDLs), that are characterized by several methodological distinctions from the existing digital solutions. When ANDLs are incorporated into a communications receiver, these methodological differences can translate into significant practical advantages, improving the receiver performance in the presence of non-Gaussian interference. A Nonlinear Differential Limiter (NDL) is obtained from a linear analog filter by introducing an appropriately chosen feedback-based nonlinearity into the response of the filter, and the degree of nonlinearity is controlled by a single parameter. ANDLs are similarly controlled by a single parameter, and are suitable for improving quality of non-stationary signals under time-varying noise conditions. ANDLs are designed to be fully compatible with existing linear devices and systems (i.e., ANDLs’ behavior is linear in the absence of impulsive interference), and to be used as an enhancement, or as a simple low-cost alternative, to state-of-the-art interference mitigation methods. We provide an introduction to the NDLs and illustrate their potential use for noise mitigation in communications systems. We also develop a digital implementation of an ANDL. This allows for rapid prototyping and performance analysis of various ANDL configurations and use cases.

In this thesis, we examine a family of vectorial boolean functions on F22m inspired by Kim function, in order to find new APN permutations on F22m for m > 2. The functions of this family are defined as F(X) = X3 + bX3q + cX2q+1 + dXq+2 , where parameters b, c and d are from F2m . Necessary and sufficient conditions for this functions to be APN or equivalent to a permutation are presented in this thesis. To find conditions for being APN, Trace-0/Trace-1 decomposition method is used. A method using exponential sums is used to deduce which functions of this family is CCZ-equivalent to a certain type of permutation. These results were then used to search for APN permutations on F26 and F210 . 1