No description available.

No description available.

No description available.

Multiple-Input Multiple-Output (MIMO) systems have gained an enormous amount of attention as one of the most promising research areas in wireless communications. However, while MIMO systems have been extensively explored over the past decade, few schemes acknowledge the nonlinearity caused by the use of high power amplifiers (HPAs) in the communication chain. When HPAs operate near their saturation points, nonlinear distortions are introduced in the transmitted signals, and the resulting MIMO channel will be nonlinear. The nonlinear distortion is further exacerbated by the fading caused by the propagation channel. The goal of this thesis is: 1) to use neural networks (NNs) to model and identify nonlinear MIMO channels; and 2) to employ the proposed NN model in designing efficient detection techniques for these types of MIMO channels. In the first part of the thesis, we follow a previous work on modeling and identification of nonlinear MIMO channels, where it has been shown that a proposed block-oriented NN scheme allows not only good identification of the overall MIMO input-output transfer function but also good characterization of each component of the system. The proposed scheme employs an ordinary gradient descent based algorithm to update the NN weights during the learning process and it assumes only real-valued inputs. In this thesis, natural gradient (NG) descent is used for training the NN. Moreover, we derive an improved variation of the previously proposed NN scheme to avoid the input type restriction and allow for complex modulated inputs as well. We also investigate the scheme tracking capabilities of time-varying nonlinear MIMO channels. Simulation results show that NG descent learning significantly outperforms the ordinary gradient descent in terms of convergence speed, mean squared error (MSE) performance, and nonlinearity approximation. Moreover, the NG descent based NN provides better tracking capabilities than the previously proposed NN. The second part of the thesis focuses on signal detection. We propose a receiver that employs the neural network channel estimator (NNCE) proposed in part one, and uses the Zero-Forcing Vertical Bell Laboratories Layered Space-Time (ZF V-BLAST) detection algorithm to retrieve the transmitted signals. Computer simulations show that in slow time-varying environments the performance of our receiver is close to the ideal V-BLAST receiver in which the channel is perfectly known. We also present a NN based linearization technique for HPAs, which takes advantage of the channel information provided by the NNCE. Such linearization technique can be used for adaptive data predistortion at the transmitter side or adaptive nonlinear equalization at the receiver side. Simulation results show that, when higher modulation schemes (>16-QAM) are used, the nonlinear distortion caused by the use of HPAs is greatly minimized by our proposed NN predistorter and the performance of the communication system is significantly improved. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2007-08-08 14:55:50.489

This work presents three techniques for parameter identification for nonlinear systems. The methods presented are expanded from those presented in Adetola and Guay [3, 4, 5] and are intended to improve the performance of existing adaptive control systems. The first two methods exactly recover open-loop system parameters once a defined convergence condition is met. In either case, the true parameters are identified when the regressor matrix is of full rank and can be inverted. The third case uses a novel method developed in Adetola and Guay [5] to define a parameter uncertainty set. The uncertainty set is periodically updated to shrink around the true value of the parameters. Each method is shown to be applicable to a large class of linearly parameterized nonlinear discrete-time system. In each case, parameter convergence is guaranteed subject to an appropriate convergence condition, which has been related to a classical persistence of excitation condition. The effectiveness of the methods is demonstrated using a simulation example. The application of the uncertainty set technique to nonlinearly parameterized systems constitutes the main contribution of the thesis. The parameter uncertainty set method is generalized to the problem of adaptive estimation in nonlinearly parameterized systems, for both continuous-time and discrete-time cases. The method is demonstrated to perform well in simulation for a simplified model of a bioreactor operating under Monod kinetics. / Thesis (Master, Chemical Engineering) -- Queen's University, 2010-10-19 10:58:24.888

Coherent anti-Stokes Raman scattering (CARS) microscopy has developed rapidly and is opening the door to new types of experiments. This work describes the development of new laser sources for CARS microscopy and their use for different applications. It is specifically focused on multimodal nonlinear optical microscopy—the simultaneous combination of different imaging techniques. This allows us to address a diverse range of applications, such as the study of biomaterials, fluid inclusions, atherosclerosis, hepatitis C infection in cells, and ice formation in cells. For these applications new laser sources are developed that allow for practical multimodal imaging. For example, it is shown that using a single Ti:sapphire oscillator with a photonic crystal fiber, it is possible to develop a versatile multimodal imaging system using optimally chirped laser pulses. This system can perform simultaneous two photon excited fluorescence, second harmonic generation, and CARS microscopy. The versatility of the system is further demonstrated by showing that it is possible to probe different Raman modes using CARS microscopy simply by changing a time delay between the excitation beams. Using optimally chirped pulses also enables further simplification of the laser system required by using a single fiber laser combined with nonlinear optical fibers to perform effective multimodal imaging. While these sources are useful for practical multimodal imaging, it is believed that for further improvements in CARS microscopy sensitivity, new excitation schemes are necessary. This has led to the design of a new, high power, extended cavity oscillator that should be capable of implementing new excitation schemes for CARS microscopy as well as other techniques. Our interest in multimodal imaging has led us to other areas of research as well. For example, a fiber-coupling scheme for signal collection in the forward direction is demonstrated that allows for fluorescence lifetime imaging without significant temporal distortion. Also highlighted is an imaging artifact that is unique to CARS microscopy that can alter image interpretation, especially when using multimodal imaging. By combining expertise in nonlinear optics, laser development, fiber optics, and microscopy, we have developed systems and techniques that will be of benefit for multimodal CARS microscopy. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2011-08-11 13:46:26.065

No description available.

A nonlinear wave equation invariant with respect to unitary representations of the Lorentz group is considered in an attempt to describe extended particles with spin and positive definite energy by means of a self-confined classical field. The wave function has an infinite number of components and, in the specific representations used, the corresponding internal degree of freedom is identified with the spin. A fractional power of the scalar bilinear invariant appears as an appropriate choice for the nonlinearity in order that all the stationary states be localized. Two approximation methods are proposed and both lead to results that bear a resemblance to the results of the MIT bag model.

Most real world phenomena is modeled by ordinary and/or partial differential equations. Most of these equations are highly nonlinear and exact solutions are not always possible. Exact solutions always give a good account of the physical nature of the phenomena modeled. However, existing analytical methods can only handle a limited range of these equations. Semi-numerical and numerical methods give approximate solutions where exact solutions are impossible to find. However, some common numerical methods give low accuracy and may lack stability. In general, the character and qualitative behaviour of the solutions may not always be fully revealed by numerical approximations, hence the need for improved semi-numerical methods that are accurate, computational efficient and robust. In this study we introduce innovative techniques for finding solutions of highly nonlinear coupled boundary value problems. These techniques aim to combine the strengths of both analytical and numerical methods to produce efficient hybrid algorithms. In this work, the homotopy analysis method is blended with spectral methods to improve its accuracy. Spectral methods are well known for their high levels of accuracy. The new spectral homotopy analysis method is further improved by using a more accurate initial approximation to accelerate convergence. Furthermore, a quasi-linearisation technique is introduced in which spectral methods are used to solve the linearised equations. The new techniques were used to solve mathematical models in fluid dynamics. The thesis comprises of an introductory Chapter that gives an overview of common numerical methods currently in use. In Chapter 2 we give an overview of the methods used in this work. The methods are used in Chapter 3 to solve the nonlinear equation governing two-dimensional squeezing flow of a viscous fluid between two approaching parallel plates and the steady laminar flow of a third grade fluid with heat transfer through a flat channel. In Chapter 4 the methods were used to find solutions of the laminar heat transfer problem in a rotating disk, the steady flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation and the classical von Kάrmάn equations for boundary layer flow induced by a rotating disk. In Chapter 5 solutions of steady two-dimensional flow of a viscous incompressible fluid in a rectangular domain bounded by two permeable surfaces and the MHD viscous flow problem due to a shrinking sheet with a chemical reaction, were solved using the new methods. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

The objective of this dissertation is to expand on the proofs and concepts of Degree Theory, dealt with in chapters 1 and 2 of Deimling [28], to make it more readable and accessible to anyone who is interested in the field. Chapter 1 is an introduction and contains the basic requirements for the subsequent chapters. The remaining chapters aim at defining a ll-valued map D (the degree) on the set M = {(F, Ω, y) / Ω C X open, F : Ὠ → X, y ɇ F(∂Ω)} (each time, the elements of M satisfying extra conditions) that satisfies : (D1) D(I, Ω, y) = 1 if y Є Ω. (D2) D(F, Ω, y) = D(F, Ω1 , y) + D(F, Ω2, y) if Ω1 and Ω2 are disjoint open subsets of Ω o such that y ɇ F(Ὠ \ Ω1 U Ω2 ). (D3) D(I - H(t, .), Ω, y(t)) is independent of t if H : J x Ὠ →X and y : J → X. An important property that follows from these three properties is (D4) F-1(y) ≠ Ø if D(F, Ω, y) ≠ 0. This property ensures that equations of the form Fx = y have solutions if D(F, Ω, y) ≠ 0. Another property that features in these chapters is the Borsuk property which gives us conditions under which the degree is odd and hence nonzero. / Thesis (M.Sc.)-University of Durban-Westville, 1989.