A dielectric filled cavity structure is currently being used to estimate the dielectric constant and loss factor over a wide range of frequencies of a dielectric material which fills the cavity structure [Saed, 1987]. A full field analysis is used to compute the effective complex permittivity of the sample material based on reflection coefficient measurements of the cavity structure and associated geometrical dimensions. The method has previously been used successfully to determine the dielectric constant of materials, but limitations in the Inethod have created difficulties in accurate determination of the dielectric loss factor. The effective loss in this method yields an estimate of the total cavity loss, including both the dielectric loss and that of the cavity conductor walls. In this dissertation a perturbation approach is used to separate the conductor loss from the total loss. The loss-free full-field analysis is used to determine the electric current at the conductor boundaries. This current is used to evaluate the perturbed power dissipated in the cavity walls based on known conductor properties. By subtracting the loss due to the conductor walls from the total loss measured in the structure, the dielectric loss and the resultant dielectric loss factor may be estimated. Measurements are presented for sample dielectric materials. The dielectric loss tangents computed by this new technique improve the unperturbed estimates in the microwave frequency range. / Ph. D.

An open loop control law is applied to a flexible spacecraft that admits translational, as well as rotational and flexural motion. The translational degrees of freedom are coupled to the rotation and deformation through the active controls applied to the structure. The objective of any maneuver is to control the attitude of the craft as well as to dissipate any vibrations of the structure. Depending on the type of maneuver specified, the equations of motion may be divided into two distinct optimal control problems. Single-axis rotational maneuvers (with small flexural deformations) constitute a strictly linear problem. The solution of the resulting two Q point boundary value problem is accomplished through the use of matrix exponential functions. Maneuvers which involve the translational degrees of freedom, are described by nonlinear equations. The solution method presented is a algorithm that generates successive approximations similar to quasi-linearization. A perturbed linear optimal control problem is solved for each approximation. Examples are presented which illustrate the effectiveness of the solution methods for both types of maneuvers. / Master of Science

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This work employs perturbation techniques to price and hedge financial derivatives in a stochastic volatility framework. Fouque et al. [44] model volatility as a function of two processes operating on different time-scales. One process is responsible for the fast-fluctuating feature of volatility and corresponds to the slow time-scale and the second is for slowfluctuations or fast time-scale. The former is an Ergodic Markov process and the latter is a strong solution to a Lipschitz stochastic differential equation. This work mainly involves modelling, analysis and estimation techniques, exploiting the concept of mean reversion of volatility. The approach used is robust in the sense that it does not assume a specific volatility model. Using singular and regular perturbation techniques on the resulting PDE a first-order price correction to Black-Scholes option pricing model is derived. Vital groupings of market parameters are identified and their estimation from market data is extremely efficient and stable. The implied volatility is expressed as a linear (affine) function of log-moneyness-tomaturity ratio, and can be easily calibrated by estimating the grouped market parameters from the observed implied volatility surface. Importantly, the same grouped parameters can be used to price other complex derivatives beyond the European and American options, which include Barrier, Asian, Basket and Forward options. However, this semi-analytic perturbative approach is effective for longer maturities and unstable when pricing is done close to maturity. As a result a more accurate technique, the decomposition pricing approach that gives explicit analytic first- and second-order pricing and implied volatility formulae is discussed as one of the current alternatives. Here, the method is only employed for European options but an extension to other options could be an idea for further research. The only requirements for this method are integrability and regularity of the stochastic volatility process. Corrections to [3] remarkable work are discussed here. / AFRIKAANSE OPSOMMING: Hierdie werk gebruik steuringstegnieke om finansiële afgeleide instrumente in ’n stogastiese wisselvalligheid raamwerk te prys en te verskans. Fouque et al. [44] gemodelleer wisselvalligheid as ’n funksie van twee prosesse wat op verskillende tyd-skale werk. Een proses is verantwoordelik vir die vinnig-wisselende eienskap van die wisselvalligheid en stem ooreen met die stadiger tyd-skaal en die tweede is vir stadig-wisselende fluktuasies of ’n vinniger tyd-skaal. Die voormalige is ’n Ergodiese-Markov-proses en die laasgenoemde is ’n sterk oplossing vir ’n Lipschitz stogastiese differensiaalvergelyking. Hierdie werk behels hoofsaaklik modellering, analise en skattingstegnieke, wat die konsep van terugkeer to die gemiddelde van die wisseling gebruik. Die benadering wat gebruik word is rubuust in die sin dat dit nie ’n aanname van ’n spesifieke wisselvalligheid model maak nie. Deur singulêre en reëlmatige steuringstegnieke te gebruik op die PDV kan ’n eerste-orde pryskorreksie aan die Black-Scholes opsie-waardasiemodel afgelei word. Belangrike groeperings van mark parameters is geïdentifiseer en hul geskatte waardes van mark data is uiters doeltreffend en stabiel. Die geïmpliseerde onbestendigheid word uitgedruk as ’n lineêre (affiene) funksie van die log-geldkarakter-tot-verval verhouding, en kan maklik gekalibreer word deur gegroepeerde mark parameters te beraam van die waargenome geïmpliseerde wisselvalligheids vlak. Wat belangrik is, is dat dieselfde gegroepeerde parameters gebruik kan word om ander komplekse afgeleide instrumente buite die Europese en Amerikaanse opsies te prys, dié sluit in Barrier, Asiatiese, Basket en Stuur opsies. Hierdie semi-analitiese steurings benadering is effektief vir langer termyne en onstabiel wanneer pryse naby aan die vervaldatum beraam word. As gevolg hiervan is ’n meer akkurate tegniek, die ontbinding prys benadering wat eksplisiete analitiese eerste- en tweede-orde pryse en geïmpliseerde wisselvalligheid formules gee as een van die huidige alternatiewe bespreek. Hier word slegs die metode vir Europese opsies gebruik, maar ’n uitbreiding na ander opsies kan’n idee vir verdere navorsing wees. Die enigste vereistes vir hierdie metode is integreerbaarheid en reëlmatigheid van die stogastiese wisselvalligheid proses. Korreksies tot [3] se noemenswaardige werk word ook hier bespreek.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 328-332. / by Marcel Coderch i Collell. / Ph.D.

Resonant Magnetic Perturbation (RMP) fields produced by external control coils are considered a viable option for the suppression of Edge Localized Modes (ELMs) in present and future tokamaks. Repeated reversals of the toroidal phase of the I-coil magnetic field in RMP shot 147170 on DIII-D has generated uniquely different edge pedestal profiles, implying different edge transport phenomena. The causes, trends, and implications of RMP toroidal phase reversal on edge transport is analyzed by comparing various parameters at 0 and 60 degree toroidal phases, with an I-coil mode number of n=3. An analysis of diffusive and non-diffusive transport effects of these magnetic perturbations it the plasma edge pedestal for this RMP shot is characterized by interpreting the ion and electron heat diffusivities, angular momentum transport frequencies, ion diffusion coefficients, and pinch velocities for both phases.

One of the difficulties of human figure tracking is that humans move their bodies in complex, non-linear ways. An effective computational model of human motion could therefore be of great benefit in figure tracking. We are interested in the use of a class of dynamic models called switching linear dynamic systems for figure tracking. This thesis makes two contributions. First, we present an empirical analysis of some of the technical issues involved with applying linear dynamic systems to figure tracking. The lack of high-level theory in this area makes this type of empirical study valuable and necessary. We show that sensitivity of these models to perturbations in input is a central issue in their application to figure tracking. We also compare different types of LDS models and identification algorithms. Second, we describe 2-DAFT, a flexible software framework we have created for figure tracking. 2-DAFT encapsulates data and code involved in different parts of the tracking problem in a number of modules. This architecture leads to flexibility and makes it easy to implement new tracking algorithms.

This thesis investigates the generation of second harmonic bulk waves in the presence of a free boundary. Second harmonic waves have proven to be useful in the field of nondestructive evaluation to detect fatigue in a material at an early stage. Since most experimental setups include a free surface, the influence of such a boundary is of significant practical interest. As a result, the objective of this research is to develop a quantitative understanding of the complete process of second harmonic generation at a free boundary. This research shows that the interaction of primary waves (with each other) in the nonlinear framework leads to the generation of second harmonic bulk waves. We distinguish between self-interaction of a single primary wave and the cross-interaction of two different primary waves. The proposed approach uses the perturbation method to solve the nonlinear equations of motion, and shows two fundamentally different solutions. In the case of resonance, the secondary waves grow with propagation distance. This is the most important practical case, since the growing amplitudes of these waves should be easier to experimentally measure. In the second, non-resonant case, the amplitudes of the secondary waves are constant. The complete process of second harmonic generation is analyzed for an incident Pand an incident SV-wave, with the primary and secondary fields given. Finally, the degenerate case of normal incidence is presented. Normal and oblique incidence are compared with regard to their feasibility in experimental setups. The specific behavior of second harmonic waves propagating in aluminum is numerically determined. These results enable a variety of physical insights and conclusions to be drawn from the analytical and numerical investigations.

Orientadores: Marcelo da Silva Montenegro, Massimo Grossi / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T13:53:15Z (GMT). No. of bitstreams: 1 Neves_SergioLeandroNascimento_D.pdf: 694748 bytes, checksum: 52d4109b562640e98c9a0a6098d9cb46 (MD5) Previous issue date: 2012 / Resumo: Neste trabalho, consideramos uma classe de problemas de Neumann com perturbação singular e fazemos um estudo do número de soluções do tipo "single peak" que se concentram em um mesmo ponto. Estudamos casos de concentração no interior e na fronteira do domínio. Obtemos um resultado de multiplicidade exata que relaciona o número de tais soluções com o número de zeros estáveis de um campo vetorial associado / Abstract: In this work, we consider a class of Neumann problems with singular perturbation and we study the number of single peak solutions which concentrate at the same point. We study concentration in the interior and at the boundary of the domain. We obtain an exact multiplicity result which relates the number of such solutions with the number of stable zeros of an associated vector field. / Doutorado / Matematica / Doutor em Matemática

Phonon anharmonicity is critical for describing various phenomena in crystals, including lattice thermal conductivity, thermal expansion, structural phase transitions, and many others. Including anharmonicity in the calculation of condensed matter observables developed rapidly in the past decade. First-principles computation of cubic phonon interactions have been performed in many systems, and the quartic interactions have begun to receive more attention. In this study, reliable Hamiltonians are constructed purely in terms of quadratic, cubic, and quartic irreducible derivatives, which are calculated efficiently and precisely using the lone and bundled irreducible derivative approaches (LID and BID). The resulting Hamiltonians give rise to a nontrivial many-phonon problem which requires some approximation in order to compute observables. We implemented self-consistent diagrammatic approaches to evaluate the phonon self-energy, including the Hartree-Fock approximation for phonons and quasiparticle perturbation theory, where both the 4-phonon loop and the real part of the 3-phonon bubble are employed during self-consistency. Additionally, we implemented molecular dynamics in order to yield the numerically exact solution in the classical limit. The molecular dynamics solution is robust for directly comparing to experimental results at sufficiently high temperatures, and for assessing our diagrammatic approaches in the classical limit. Anharmonic vibrational Hamiltonians were constructed for CaF₂, ThO₂, and UO₂. Diagrammatic approaches were used to evaluate the phonon self-energy, yielding the phonon lineshifts and linewidths and the thermal conductivity within the relaxation time approximation. Our systematic results allowed us to resolve the paradox of why first-principles phonon linewidths strongly disagree with results extracted from inelastic neutron scattering (INS). We demonstrated that the finite region in reciprocal space required in INS data analysis, the 𝑞-voxel, must be explicitly accounted for within the calculation in order to draw a meaningful comparison. We also demonstrated that the 𝑞-voxel is important to properly compare the spectrum measured in inelastic X-ray scattering (IXS), despite the fact that the ?-voxel is much smaller. Accounting for the 𝑞-voxel, we obtained good agreement for the scattering function linewidths up to intermediate temperatures. Additionally, good agreement was obtained for the thermal conductivity. Another topic we addressed is translation symmetry breaking caused by factors such as defects, chemical disorders, and magnetic order. These phenomena will lead to shifts and a broadening of the phonon spectrum, and formally the single-particle Green’s function encodes these effects. However, it is often desirable to obtain an approximate non-interacting spectrum that contains the effective shifts of the phonon frequencies, allowing straightforward comparison with experimentally measured scattering peak locations. Such an effective phonon dispersion can be obtained using a band unfolding technique, and in this study, we formulated unfolding in the context of irreducible derivatives. We showcased the unfolding of phonons in UZr₂, where chemical disorder is present, and compared the results with experimental IXS data. Additionally, we extended the unfolding technique to anharmonic terms and demonstrated this using 3rd and 4th order terms in the antiferromagnetic phase of UO₂.

Active queue management (AQM) techniques for congestion control in Internet Protocol (IP) networks have been designed using both heuristic and analytical methods. But so far, there has been found no AQM scheme designed in the realm of stochastic optimization. Of the many options available in this arena, the gradient-based stochastic approximation method using Infintesimal Perturbation Analysis (IPA) gradient estimators within the Stochastic Fluid Model (SFM) framework is very promising. The research outlined in this thesis provides the theoretical basis and foundational layer for the development of IPA-based AQM schemes. Algorithms for computing the IPA gradient estimators for loss volume and queue workload were derived for the following cases: a single-stage queue with instantaneous, additive loss-feedback, a single-stage queue with instantaneous, additive loss-feedback and an unresponsive competing flow, a single-stage queue with delayed, additive loss-feedback, and a multi-stage tandem network of $m$ queues with instantaneous, additive loss-feedback. For all cases, the IPA gradient estimators were derived with the control parameter, $ heta$, being the buffer-limits of the queue(s). For the single-stage case and the multi-stage case with instantaneous, additive loss-feedback, the IPA gradient estimators for when the control parameter, $ heta$, is the loss-feedback constant, were also derived. Sensitivity analyses and optimizations were performed with control parameter, $ heta$, being the buffer-limits of the queue(s), as well as the loss-feedback constant.