The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator.

During the last decade, the use of time scales as a means of unifying and extending results about various types of dynamic equations has proven to be both prolific and fruitful. Many classical results from the theories of differential and difference equations have time scale analogues. In this thesis we derive new oscillation criteria for second order dynamic equations on time scales.

Neste trabalho, estudamos alguns colóides magnéticos dos tipos iônico e surfactado com partículas de estrutura tipo espinélio. Usamos a técnica de varredura-Z para investigar as amostras nas escalas de tempo de femtossegundos e milissegundos. Medimos o índice de refração não-linear nas duas escalas de tempo. Na escala de milissegundos todas as amostras apresentaram comportamento tipo lente divergente, e os valores obtidos são da ordem de 10^(-7) cm^2/W. Na escala de femtossegundos, as amostras iônicas apresentaram comportamento tipo lente convergente, com valores típicos do índice de refração não-linear da ordem de 10^(11) cm^2/W. Também medimos a absorção não-linear na escala de tempo de femtossegundos. Os valores obtidos são da ordem de 10^2 cm/GW. Com os dados obtidos na escala de femtossegundos calculamos a susceptibilidade elétrica de terceira ordem (chi(3)). O módulo de chi(3) encontrado é da ordem de 10^(-17) m^2/V^2 (ou 10^(-9) esu). Obtivemos evidências experimentais da contribuição da susceptibilidade elétrica de quinta-ordem nas medidas de absorção não-linear. Verificamos a presença do efeito de tamanho das partículas no valor de chi(3) ao estudar partículas de mesma composição e de diâmetros diferentes. / In this work, we studied some magnetic colloids of kind ionic and surfacted with particles of spinel struture. We used the Z-Scan technique to investigate the samples in the time scales of femto- and milliseconds. We measured the nonlinear refractive index in both time scales. In the scale of milliseconds all samples showed divergent-lens-type behavior, and the obtained values are of order of 10^(-7) cm^2/W. In the femtoseconds scale, the ionic-type samples have convergent-lens-type behavior, with the typical values of order of 10^(11) cm^2/W. Also we measured the nonlinear absorption in the femtoseconds time scale. The obtained values are of order of 10^2 cm/GW. With the data obtained in the femtoseconds time scale we calculated the third-order electric susceptibilities (chi(3)). The found modulus of chi(3) is of order of 10^(-17) m^2/V^2 (or 10^(-9) esu). We obtained experimental evidences that fifth-order electric susceptibilities can contribute to the measurements of nonlinear absorption. We observed the dependence of particles\' size effect in the values of chi(3) in the studies of particles of the same composition and different diameters.

The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The reliable prediction of turbulent non-equilibrium flows is of high academic and industrial interest in several engineering fields. Most turbulent flows are often predicted using single-time-scale Reynolds-Averaged-Navier-Stokes (RANS) turbulence models which assume the flows can be modelled through a single time or length scale which is an admittedly incorrect assumption. Therefore they are not expected to capture the lag in the response of the turbulence in non-equilibrium flows. In attempts to improve prediction of these flows, by taking into consideration some features of the turbulent kinetic energy spectrum, the multiple-time-scale models arose. A number of two-scale models have been proposed, but so far their use has been rather limited.This work thus focusses on the development of two-time-scale approaches. Two two-time-scale linear-eddy-viscosity models, referred to as NT1 and NT2 models, have been developed and the initial stages of the development of two-time-scale non-linear-eddy-viscosity models are also reported. The models' coefficients have been determined through asymptotic analysis of decaying grid turbulence, homogeneous shear flows and the flow in a boundary layer in local equilibrium. Three other important features of these models are that there is consistent partition of the large and the small scales for all above limiting cases, model sensitivity to the partition and production rate ratios and sensitivity of the eddy viscosity sensitive to the mean strain rates.The models developed have been tested through computations of a wide range of flows such as homogeneous shear and normally strained flows, fully developed channel flows, zero-pressure-gradient, adverse-pressure-gradient, favourable-pressure-gradient and oscillatory boundary layer flows, fully developed oscillatory and ramp up pipe flows and steady and pulsated backward-facing-step flows.The proposed NT1 and NT2 two-scale models have been shown to perform well in all test cases, being, among the benchmarked models tested, the models which best performed in the wide range of dimensionless shear values of homogeneous shear flows, the only linear-eddy-viscosity models which predicted well the turbulent kinetic energy in the normally strained cases and the only models which showed satisfactory sensitivity in predicting correctly the reattachment point in the unsteady backward facing step cases with different forcing frequencies. Although the development of the two-time-scale non-linear-eddy-viscosity models is still in progress, the interim versions proposed here have resulted in predictions of the Reynolds normal stresses similar to those of much more complex models in all test cases studied and in predictions of the turbulent kinetic energy in normally strained flows which are better than those of the other models tested in this study.

[pt] Estendemos o formalismo de Fokker-Planck que foi usado previamente para descrever, a partir de primeiros princípios, o comportamento de um gás granular em esfriamento, com potencial de contato Hertziano e força de atrito viscoelástica o qual resulta em um sistema com coeficiente de restituição que depende da velocidade. Nesta tese é estudado, também a partir de primeiros princípios, o caso mais geral, o de um estado estacionário com energia cinética finita e fora do equilíbrio, devido ao acoplamento a um mecanismo externo de alimentação de energia. Estende- se assim a validade do resultado prévio. / [en] We extend the Fokker-Planck formalism used previously to describe the behavior of a cooling granular gas, with a Hertzian contact potential and viscoelastic radial friction, giving a velocity dependent coeficient of restitution. In this thesis, we study the more general case of a steady-state with finite kinetic, energy and far from equilibrium, due to the coupling to an external energy- feeding mechanism, also from first-principles, and extend the validity of the former results.

Since the 1980s, hemlock-dominated forests (Tsuga canadensis) of central New England have been increasingly infested by the invasive pest hemlock woolly adelgid (HWA, Adelges tsugae), predominantly resulting in its replacement by black birch-dominated forests (Betula lenta). To date there has been no long-term empirical analysis of HWA effects on forest carbon (C) cycling due to forest transition from hemlock to black birch. To address this question, I measured the C pools in five stand types at varying ages and stages of HWA infestation in Massachusetts and Connecticut. I also measured C fluxes in aboveground net primary production (ANPP) and soil respiration, and studied the drivers of these fluxes viz. litter production, rates of foliar decomposition, soil exoenzyme activity, temperature sensitivity of soil respiration and nitrogen (N) cycling. The mass of C stored in recovering forests was resilient to HWA infestation but the location of these stocks varied among stand types. There was a transition of C from live biomass in healthy, unaffected secondary hemlock forests to coarse woody debris (CWD) in recently girdled forests intended to simulate the effect of HWA on hemlock loss. Twenty years post-HWA infestation, however, ANPP was very high and there was a large increase in biomass-C pools in aggrading black stand types. C pools in mature, secondary black birch stand types ~135 years since pastureland abandonment were as large as those in primary hemlock stand types ~235 years of age, suggesting recovery of C storage within one century of HWA infestation. Soil respiration rates were positively correlated with inputs of hardwood leaf litter, fine root biomass and exoenzyme activity. Stand-type variations in ANPP were positively correlated with annual N requirements and N uptake from the soil. Nitrogen-use efficiency was highest in the girdled and post-HWA infestation stand types where ANPP was dominated by wood production which has a wide C:N ratio. Similar trends were found in soil respiration, but not to the same degree as that of ANPP. Collectively, my results indicate that southern New England forests C storage is highly resilient to the HWA-induced losses of hemlock, suggesting that these ecosystems will continue to be sinks for atmospheric carbon dioxide.

" The chemical engineering literature is dominated by physical and (bio)-chemical processes that exhibit complex nonlinear behavior, and as a consequence, the associated requirements of their analysis, optimization, control and monitoring pose considerable challenges in the face of emerging competitive pressures on the chemical, petrochemical and pharmaceutical industries. The above operational requirements are now increasingly imposed on processes that exhibit inherently nonlinear behavior over a wide range of operating conditions, rendering the employment of linear process control and monitoring methods rather inadequate. At the same time, increased research efforts are now concentrated on the development of new process control and supervisory systems that could be digitally implemented with the aid of powerful computer software codes. In particular, it is widely recognized that the important objective of process performance reliability can be met through a comprehensive framework for process control and monitoring. From: (i) a process safety point of view, the more reliable the process control and monitoring scheme employed and the earlier the detection of an operationally hazardous problem, the greater the intervening power of the process engineering team to correct it and restore operational order (ii) a product quality point of view, the earlier detection of an operational problem might prevent the unnecessary production of o-spec products, and subsequently minimize cost. The present work proposes a new methodological perspective and a novel set of systematic analytical tools aiming at the synthesis and tuning of well-performing digital controllers and the development of monitoring algorithms for nonlinear processes. In particular, the main thematic and research axis traced are: (i) The systematic integrated synthesis and tuning of advanced model-based digital controllers using techniques conceptually inspired by Zubov’s advanced stability theory. (ii) The rigorous quantitative characterization and monitoring of the asymptotic behavior of complex nonlinear processes using the notion of invariant manifolds and functional equations theory. (iii) The systematic design of nonlinear state observer-based process monitoring systems to accurately reconstruct unmeasurable process variables in the presence of time-scale multiplicity. (iv) The design of robust nonlinear digital observers for chemical reaction systems in the presence of model uncertainty. "

Hlavním zájmem diplomové práce je studium zobecněné nabla Laplaceové transformace na časových škálach a její jednoznačnosti, včetně důkazu jednoznačnosti a aplikace jednoznačnosti v zlomkovém kalkulu na časových škálach.

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