Rozprawy doktorskie na temat „Nonlinear Chemical Dynamics”

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1985.
MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.
Bibliography: leaves 176-186.
by John Abraham Tsamopoulos.
Ph.D.

This work shows that nonlinear dynamic systems are quite different from linear dynamic systems. The usual phase plots of linear and nonlinear dynamical systems are also distinctly different, even before damping or forcing terms are added. It is also shown that the usual phase plot allows for the visualization of unobservable information that is present in the times series. The higher-order phase plots give yet additional information that is not present in the existing methods of plotting the data. Higher-order phase plots were originated and applied for the first time to a dynamical system (Morse oscillator) for the purpose of earlier detection of nonlinear effects. The dynamics of a weakly forced and weakly damped Morse oscillator is examined. The novel tool of higher-order phase plots is used to visualize the importance of the higher harmonics in the phase which are essential for the dynamics to be complicated and dissociative. Expansions of the higher-order phase plots in regions about x$\sp{(n-1)}$ = 0, x$\sp{(n)}$ = 0 are considered and it is shown that there is a topological change that occurs sequentially for each higher-order phase plot. After the topological change, which occurs at a critical value of initial total energy E(0) for a particular value of forcing F, the higher-order phase space structure has a circular loop. As F or E(0) is further increased the phase space trajectory loops an increasing number of times in the higher-order phase plot. It is shown that for F = $1.0\times10\sp{-3}$ the topological change occurs around E(0) = 0.96 for the fifth-order phase plot and around E(0) = 0.94 for the eleventh-order phase plot. This is also illustrated with a series of higher-order phase plots (2$\sp{nd}$-10$\sp{th}$) for F = $1\times10\sp{-3}$ and E(0) = 0.97. These plots indicate that although the 5$\sp{th}$ order phase plot forms loops the 4$\sp{th}$ forms only half-loops. Thus the higher-order phase plots are increasingly sensitive probes of the phase space dynamics as the order increases. Qualitatively this is because, as the order increases, part of each higher-order phase space structure is increasingly close to the point (x$\sp{(n)}$,x$\sp{(n-1)}$) = (0,0). For larger values of F the topological change occurs at a smaller value of E(0) for each higher-order phase plot, as the radius of the loop centered on x$\sp{(n-1)}$ = 0, x$\sp{(n)}$ = 0 is larger. While the phase space trajectory loops the energy is approximately constant with small oscillations. The circular loop in the higher-order phase plot is the higher-order space structure that is expected for the weakly forced and weakly damped free particle. The significance of the circular loop is that the lower the order of the higher-order phase plot in which the phase space trajectory loops, the closer the Morse oscillator is to dissociation. From this viewpoint, the Morse oscillator dissociates when the value of F or E(0) becomes sufficiently large that the topological change occurs in the usual phase plot. That is, the Morse oscillator dissociates when the phase space structure becomes open for the usual phase plot. (Abstract shortened by UMI.)

Interest in the interdisciplinary field of nonlinear dynamics has increased significantly over the past three decades. Nonlinear dynamics is the study of the temporal and spatio-temporal evolution of dynamical systems whose behaviour depends on the values of the key variables in a nonlinear manner. Nonlinear chemical reactions, chemical oscillations and their spatial behaviour play an important part in the field of nonlinear dynamics. This thesis is concerned primarily with those chemical systems which feature the proton, or its counterpart the hydroxide ion, as a main kinetic driving species. A review of the area is presented to provide a background for the developments discussed in this thesis. Experimental and numerical investigation of the methylene glycol-sulfite reaction leads to the development of a complete kinetic model for this system. This new mechanism provides the basis of a reduced model for the design of novel pH oscillators. This reduced model, discussed in chapter 4, is used to design the first organic substrate based, non-redox, pH oscillating reaction, the methylene glycolsulfite-gluconolactone system. In an open reactor this reaction displays large amplitude oscillations in pH which are well modelled with a proposed mechanism. In chapter 5 experimental results of an acid autocatalytic reaction performed in nano-meter size water droplets are presented. The effects of confinement on the kinetics is established and shown to be affected by changes in droplet size and dispersion of droplets. The effect of the microheterogeneties of the microenvironment on reaction-diffusion fronts in this system is also investigated. The results show the propagation of acid fronts with interesting structural instabilities.

Fuel cells are becoming increasingly important in the conversion of our society to clean, and renewable energy sources. However, there are some technical, as well as commercial barriers, which remain to be overcome before the fuel cell industry may be counted a success. One such problem is that of nonlinear current fluctuations, which have been observed under quite general conditions, in solid oxide fuel cells. This thesis attempts to elucidate the mechanisms driving this undesirable be- haviour, by developing a rational mathematical model based on fundamental chemical kinetics, and mass transfer effects, which take place within the porous anode of the fuel cell. A system of nonlinear, coupled ordinary differential equations is derived to describe the reaction and transfer processes associated with this fundamental model. This system is then rationally reduced to a planar dynamical system and the cases of weakly and fully humidified fuel streams are considered. Self-sustained, temporal oscillations are shown to arise through Hopf bifurcations in each case, and key parameter regimes leading to oscillatory behaviour are identified. Experiments have been conducted on commercial fuel cells, with results presented in Chapter 5.

In this thesis we describe the complex array of behaviours of a homogeneous thermotropic nematic liquid crystal in the context of a Landau-de Gennes theory. There exist two parameters that control the behaviour of the system: the temperature and the shear rate, and by employing continuation and bifurcation theory we describe the different time dependent states for the two and three dimensional cases. For the two dimensional case we compute the steady state solution branches finding that the flow favours an in-plane nematic state at higher temperatures, while at lower temperatures it favours a nematic state with preferred direction of alignment perpendicular to the shear plane, the so-called log-rolling state. We have found excellent agreement between the numerical calculations and analytical results in the limit of very low and very large values of the shear rate. The existence of a Takens-Bogdanov bifurcation in the underlying bifurcation diagram organises the steady and the time dependent solutions in the state diagram. The periodic orbits can be either of the wagging type, at intermediate values of the shear rate or of the tumbling type at lower shear rates. We complete the analysis of the two dimensional case, by considering a general planar flow and studying the influences of strain and vorticity in the system. We provide a very detailed account of the behaviour of the liquid crystal in the three dimensional case, when the direction of alignment of the molecules that constitute the liquid crystal is allowed out of the shear plane. We establish that the only out-of-plane steady solution of the system is an anomalous continuum of equilibria, and therefore the Landau-de Gennes model that we are employing is structurally unstable. The time dependent solutions of the liquid crystal fall into one of the following categories: in plane periodic orbits, which are the tumbling and wagging solutions and out-of-plane periodic orbits, the so-called kayaking state. The use of bifurcation theory in the context of nematodynamics allows us to give a complete summary of the nonlinear behaviour of a nematic liquid crystal in a shear flow, for the two and three dimensional cases.

Dissertation (Ph.D.)--Worcester Polytechnic Institute.
Keywords: Parametric optimization; nonlinear dynamics; functional equations; chemical reaction system dynamics; time scale multiplicity; robust control; nonlinear observers; invariant manifold; process monitoring; Lyapunov stability. Includes bibliographical references (leaves 92-98).

La plupart des systèmes non linéaires loin de l'équilibre sont sensibles aux fluctuations internes. Dans ce travail, les effets stochastiques dans des modèles génériques de réaction-diffusion sont étudiés à deux échelles différentes. Dans l'approche mésoscopique, l'évolution du système est gouvernée par une équation maîtresse résolue par des simulations de Monte Carlo cinétique. A l'échelle microscopique, des simulations de dynamique des particules sont réalisées. Ces approches stochastiques sont comparées à des équations macroscopiques, déterministes de réaction-diffusion. Dans l'introduction, les différentes échelles, les concepts concernant les systèmes non linéaires et les méthodes numériques utilisées sont présentés. La première partie du chapitre consacré aux résultats est dédiée à l'étude de la perturbation de la distribution des vitesses des particules induite par la réaction pour un système bistable et la propagation d'un front d'onde. Une équation maîtresse incluant cette perturbation est écrite et comparée à des simulations de la dynamique microscopique. La seconde partie concerne la formation de structures dans les systèmes réaction-diffusion dans le contexte de la biologie du développement. Une méthode pour simuler des structures de Turing à l'échelle microscopique est développée à partir de l'algorithme DSMC (direct simulation Monte Carlo). Ensuite, des expériences consistant à perturber la formation de la colonne vertébrale sont expliquées dans le cadre du mécanisme de Turing. Enfin, un modèle de réaction-diffusion associé à un mécanisme différent, connu sous le nom de "Clock and wavefront", est proposé pour rendre compte de la segmentation
Many nonlinear systems under non-equilibrium conditions are highly sensitive to internal fluctuations. In this dissertation, stochastic effects in some generic reaction-diffusion models are studied using two approaches of different precision. In the mesoscopic approach, evolution of the system is governed by the master equation, which can be solved numerically or used to set up kinetic Monte Carlo simulations. On the microscopic level, particle computer simulations are used. These two stochastic approaches are compared with deterministic, macroscopic reaction-diffusion equations.In the Introduction, key information about the different approaches is presented, together with basics of nonlinear systems and a presentation of numerical algorithms used.The first part of the Results chapter is devoted to studies on reaction-induced perturbation of particle velocity distributions in models of bistability and wave front propagation. A master equation including this perturbation is presented and compared with microscopic simulations.The second part of the Results deals with pattern formation in reaction-diffusion systems in the context of developmental biology. A method for simulating Turing patternsat the microscopic level using the direct simulation Monte Carlo algorithm is developed. Then, experiments consisting of perturbing segmentation of vertebrate embryo’s bodyaxis are explained using the Turing mechanism. Finally, a different possible mechanism of body axis segmentation, the “clock and wavefront” model, is formulated as a reaction-diffusion model

A formação espontânea de padrões espaço-temporais auto-organizados longe do equilíbrio termodinâmico é um comportamento característico de sistemas de reação-transporte. De fato, essa estruturação espacial pode ser entendida como um comportamento coletivo de um grande número de elementos individuais no sistema. Consequentemente o padrão emerge como o resultado da interação entre a dinâmica local dessas subunidades e o mecanismo de acoplamento espacial. Dinâmica não-linear do tipo multi-estável, excitável e oscilatória são exemplos típicos de padrões temporais complexos geralmente associados à estruturação espacial. Nesta tese de doutorado são apresentadas duas frentes de trabalho utilizando-se da dinâmica química não-linear na elucidação de mecanismos reacionais longe do equilíbrio termodinâmico: (a) a investigação da natureza química e efeito do drift nas séries temporais transientes em osciladores eletroquímicos. A análise da evolução temporal do parâmetro de bifurcação foi baseada em um método empírico de estabilização, sendo o acúmulo superficial de espécies oxigenadas o principal responsável pelo drift; (b) o desacoplamento das rotas eletroquímicas paralelas na formação de CO2 pela combinação de experimentos, modelagem e simulações numéricas durante a eletro-oxidação oscilatória de metanol em platina policristalina. O efeito dos ânions perclorato e sulfato nas reações paralelas foi investigado por meio da produção global de CO2 e HCOOCH3. Notavelmente, ânions sulfato inibiram mais fortemente a atividade catalítica proveniente da via direta em contraste com a pequena alteração na via indireta. Em paralelo às duas frentes de trabalho, foi construído um setup experimental com a finalidade de acompanhar a evolução espaço-temporal de uma reação eletroquímica com um sistema de aquisição de dados multicanal. A descrição do processo de confecção da célula e eletrodo de trabalho multicanal, o tratamento de dados e alguns resultados experimentais preliminares são inseridos como um capítulo adicional. A ideia central dessa tese converge na obtenção de informações da cinética química envolvida que não é observada em condições próximas ao equilíbrio termodinâmico. Essa interpretação pode ser utilizada como uma metodologia alternativa no estudo da eletrocatálise em reações químicas complexas.
The spontaneous formation of self-organized spatiotemporal patterns under far from thermodynamic equilibrium conditions is a characteristic behavior in reaction-transport systems. Indeed, this spatial structuration can be understood as a collective behavior of a large number of individual elements in the system. Consequently the pattern emerges as a result of the interaction between the local dynamic of these subunits and the spatial coupling. Multistable, excitable and oscillatory nonlinear dynamics are typical examples of complex temporal patterns usually associated to the spatial structuration. In this doctoral thesis, two work fronts are presented using the nonlinear chemical dynamics in the elucidation of reaction mechanisms under far from thermodynamic equilibrium regime: (a) the investigation of the chemical nature and effect of the drift in the transient time-series in electrochemical oscillators. The analysis of the temporal evolution of the bifurcation parameter was based on an empiric method of stabilization, being the slow accumulation of oxygenated species the main responsible for the drift; (b) the decoupling of the parallel electrochemical routes for CO2 production by a combination of experiments, modeling and numerical simulations during the oscillatory electro-oxidation of methanol on polycrystalline platinum. The effect of perchlorate and sulfate anions in the parallel reactions was investigated by the global production of CO2 and HCOOCH3. Remarkably, sulfate anions inhibited more strongly the catalytic activity from direct pathway in contrast to the small alteration in the indirect pathway. In parallel to the two work fronts, an experimental setup was built in order to obtain a spatiotemporal evolution of a electrochemical reaction with a multichannel data acquisition system. A description of the confection process of the cell and the multichannel working electrode, data treatment and some preliminary experimental results are included as an additional chapter. The main idea of this thesis converges in the obtainment of chemical kinetic information which is not observed in conditions close to the thermodynamic equilibrium. This interpretation might be used as an alternative methodology in the study of electrocatalysis in complex chemical reactions.

Extracellular neuroelectronic interfacing has important applications in the fields of neural prosthetics, biological computation and whole-cell biosensing for drug screening and toxin detection. While the field of neuroelectronic interfacing holds great promise, the recording of high-fidelity signals from extracellular devices has long suffered from the problem of low signal-to-noise ratios and changes in signal shapes due to the presence of highly dispersive dielectric medium in the neuron-microelectrode cleft. This has made it difficult to correlate the extracellularly recorded signals with the intracellular signals recorded using conventional patch-clamp electrophysiology. For bringing about an improvement in the signal-to-noise ratio of the signals recorded on the extracellular microelectrodes and to explore strategies for engineering the neuron-electrode interface there exists a need to model, simulate and characterize the cell-sensor interface to better understand the mechanism of signal transduction across the interface. Efforts to date for modeling the neuron-electrode interface have primarily focused on the use of point or area contact linear equivalent circuit models for a description of the interface with an assumption of passive linearity for the dynamics of the interfacial medium in the cell-electrode cleft. In this dissertation, results are presented from a nonlinear dynamic characterization of the neuroelectronic junction based on Volterra-Wiener modeling which showed that the process of signal transduction at the interface may have nonlinear contributions from the interfacial medium. An optimization based study of linear equivalent circuit models for representing signals recorded at the neuron-electrode interface subsequently proved conclusively that the process of signal transduction across the interface is indeed nonlinear. Following this a theoretical framework for the extraction of the complex nonlinear material parameters of the interfacial medium like the dielectric permittivity, conductivity and diffusivity tensors based on dynamic nonlinear Volterra-Wiener modeling was developed. Within this framework, the use of Gaussian bandlimited white noise for nonlinear impedance spectroscopy was shown to offer considerable advantages over the use of sinusoidal inputs for nonlinear harmonic analysis currently employed in impedance characterization of nonlinear electrochemical systems. Signal transduction at the neuron-microelectrode interface is mediated by the interfacial medium confined to a thin cleft with thickness on the scale of 20-110 nm giving rise to Knudsen numbers (ratio of mean free path to characteristic system length) in the range of 0.015 and 0.003 for ionic electrodiffusion. At these Knudsen numbers, the continuum assumptions made in the use of Poisson-Nernst-Planck system of equations for modeling ionic electrodiffusion are not valid. Therefore, a lattice Boltzmann method (LBM) based multiphysics solver suitable for modeling ionic electrodiffusion at the mesoscale neuron-microelectrode interface was developed. Additionally, a molecular speed dependent relaxation time was proposed for use in the lattice Boltzmann equation. Such a relaxation time holds promise for enhancing the numerical stability of lattice Boltzmann algorithms as it helped recover a physically correct description of microscopic phenomena related to particle collisions governed by their local density on the lattice. Next, using this multiphysics solver simulations were carried out for the charge relaxation dynamics of an electrolytic nanocapacitor with the intention of ultimately employing it for a simulation of the capacitive coupling between the neuron and the planar microelectrode on a microelectrode array (MEA). Simulations of the charge relaxation dynamics for a step potential applied at t = 0 to the capacitor electrodes were carried out for varying conditions of electric double layer (EDL) overlap, solvent viscosity, electrode spacing and ratio of cation to anion diffusivity. For a large EDL overlap, an anomalous plasma-like collective behavior of oscillating ions at a frequency much lower than the plasma frequency of the electrolyte was observed and as such it appears to be purely an effect of nanoscale confinement. Results from these simulations are then discussed in the context of the dynamics of the interfacial medium in the neuron-microelectrode cleft. In conclusion, a synergistic approach to engineering the neuron-microelectrode interface is outlined through a use of the nonlinear dynamic modeling, simulation and characterization tools developed as part of this dissertation research.
Ph.D.
Doctorate
Physics
Sciences
Physics

Thesis (MScIng)--University of Stellenbosch, 2004.
ENGLISH ABSTRACT: As result of the increasingly competitive performance in today’s industrial environment, it has become necessary for production facilities to increase their efficiency. An essential step towards increasing the efficiency of these production facilities is through tighter processes control. Process control is a monitoring and modelling problem, and improvements in these areas will also lead to better process control. Given the difficulties of obtaining theoretical process models, it has become important to identify models from process data. The irregular behaviour of many chemical processes, which do not seem to be inherently stochastic, can be explained by analysing time series data from these systems in terms of their nonlinear dynamics. Since the discovery of time delay embedding for state space analysis of time series, a lot of time has been devoted to the development of techniques to extract information through analysis of the geometrical structure of the attractor underlying the time series. Nearly all of these techniques assume that the dynamical process under question is stationary, i.e. the dynamics of the process did not change during the observation period. The ability to detect dynamic changes in processes, from process data, is crucial to the reliability of these state space techniques. Detecting dynamic changes in processes is also important when using advanced control systems. Process characteristics are always changing, so that model parameters have to be recalibrated, models have to be updated and control settings have to be maintained. More reliable detection of changes in processes will improve the performance and adaptability of process models used in these control systems. This will lead to better automation and enormous cost savings. This work investigates and assesses techniques for detecting dynamical changes in processes, from process data. These measures include the use of multilayer perceptron (MLP) neural networks, nonlinear cross predictions and the correlation dimension statistic.The change detection techniques are evaluated by applying them to three case studies that exhibit (possible) nonstationary behaviour. From the research, it is evident that the performance of process models suffers when there are nonstationarities in the data. This can serve as an indication of changes in the process parameters. The nonlinear cross prediction algorithm gives a better indication of possible nonstationarities in the process data; except for instances where the data series is very short. Exploiting the correlation dimension statistic proved to be the most accurate method of detecting dynamic changes. Apart from positively identifying nonstationary in each of the case studies, it was also able to detect the parameter changes sooner than any other method tested. The way in which this technique is applied, also makes it ideal for online detection of dynamic changes in chemical processes.
AFRIKAANSE OPSOMMING: Dit is belangrik om produksie aanlegte so effektief moontlik te bedryf. Indien nie, staar hulle die moontlikheid van finansiële ondergang in die gesig – veral as gevolg van toenemende mededinging die industrie. Die effektiwiteit van produksie aanlegte kan verhoog word deur verbeterde prosesbeheer. Prosesbeheer is ‘n moniterings en modellerings probleem, en vooruitgang in hierdie areas sal noodwendig ook lei tot beter prosesbeheer. Omdat dit moeilik is om teoretiese proses modelle af te lei, word dit al hoe belangriker om modelle vanuit proses data te identifiseer. Die ongewone optrede van baie chemiese prosesse, wat nie inherent stogasties blyk te wees nie, kan meestal verklaar word deur tydreeks data vanaf hierdie prosesse te analiseer in terme van hul nie-liniêre dinamika. Sedert die ontdekking van tydreeksontvouing vir toestandveranderlike stelsels, is baie tyd daaraan spandeer om tegnieke te ontwikkel wat inligting uit tydreekse kan onttrek deur die onderliggende geometriese struktuur van die attraktor te bestudeer. Byna al hierdie tegnieke aanvaar dat die dinamiese proses stationêr is, m.a.w dat die dinamika van die proses nie verander het tydens die observasie periode nie. Die vermoë om hierdie dinamiese proses veranderinge te kan identifiseer, is daarom baie belangrik. Ook in gevorderde beheerstelsels is vroegtydige identifisering van dinamiese veranderinge in prosesse belangrik. Proses karakteristieke is altyd besig om te verander, sodat model parameters herkalibreer moet word, modelle opgedateer moet word en beheer setpunte onderhou moet word. Meer betroubare tegnieke om veranderinge in prosesse te identifiseer sal die aanpasbaarheid van proses modelle in hierdie beheerstelsels verbeter. Dit sal lei tot beter outomatisering en sodoende lei tot enorme kostebesparings. Hierdie werk ondersoek tegnieke om dinamiese veranderinge in prosesse te identifiseer, deur die analise van proses data. Die tegnieke wat gebruik word sluit die volgende in:multilaag-perseptron neurale netwerke, nie-liniêre kruisvoorspelling statistieke en die korrelasie dimensie statistiek. Die tegnieke is op drie gevallestudies toegepas om te sien of hulle die dinamiese veranderinge in die data kan identifiseer. Vanuit die navorsing is dit duidelik dat proses modelle nadelig beinvloed word deur niestationêre data. Dit kan dien as ‘n indikasie van veranderinge in die proses parameters. Die nie-liniêre kruisvoorspellings algoritme gee ‘n beter indikasie van dinamiese veranderinge in die proses data, behalwe waar die tydreeks baie kort is. Toepassings van die korrelasie dimensie statistiek gee die beste resultate. Hierdie tegniek kon dinamiese veranderinge vinniger as enige ander tegniek identifiseer, en die manier waarop dit gebruik word maak dit ideaal vir die identifisering van dinamiese veranderinge in chemiese prosesse.

Recent advances in DNA computing have greatly facilitated the design of biomolecular circuitry based on toehold-mediated DNA strand displacement (DSD) reactions. The synthesis of biomolecular circuits for controlling molecular-scale processes is an important goal of synthetic biology with a wide range of in vitro and in vivo applications. In this thesis, new results are presented on how chemical reaction networks (CRNs) can be used as a programming language to implement commonly used linear and nonlinear system theoretic operators that can be further utilised in combination to form complex biomolecular circuits. Within the same framework, the design of an important class of nonlinear feedback controller, i.e. a quasi sliding mode (QSM) feedback controller, is proposed. The closed loop response of the nonlinear QSM controller is shown to outperform a traditional linear proportional+integrator (PI) controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs. An important issue to consider in this design process for synthetic circuits is the effect of biological and experimental uncertainties on the functionality and reliability of the overall circuit. In the case of biomolecular feedback control circuits, such uncertainties could lead to a range of adverse effects, including achieving wrong concentration levels, sluggish performance and even instability. In this thesis, the robustness properties of two biomolecular feedback controllers; PI and QSM, subject to uncertainties in the experimentally implemented rates of their underlying chemical reactions, and to variations in accumulative time delays in the process to be controlled, are analysed. The simulation results show that the proposed QSM controller is significantly more robust against investigated uncertainties, highlighting its potential as a practically implementable biomolecular feedback controller for future synthetic biology applications. Finally, the thesis presents new results on the design of biomolecular feedback controllers using the set of chemical reactions underlying covalent modification cycles.

We report progress made on an analytic investigation of low-frequency cardiorespiratory variability in humans. The work is based on an existing physiological model of chemically-mediated blood-gas control via the central and peripheral chemoreceptors, that of Grodins, Buell & Bart (1967). Scaling and simplification of the Grodins model yields a rich variety of dynamical subsets; the thesis focusses on the dynamics obtained under the normoxic assumption (i.e., when oxygen is decoupled from the system). In general, the method of asymptotic reduction yields submodels that validate or invalidate numerous (and more heuristic) extant efforts in the literature. Some of the physiologically-relevant behaviour obtained here has therefore been reported before, but a large number of features are reported for the first time. A particular novelty is the explicit demonstration of cardiorespiratory coupling via chemosensory control. The physiology and literature reviewed in Chapters 1 and 2 set the stage for the investigation. Chapter 3 scales and simplifies the Grodins model; Chapters 4, 5, 6 consider carbon dioxide dynamics at the central chemoreceptor. Chapter 7 begins analysis of the dynamics mediated by the peripheral receptor. Essentially all of the dynamical behaviour is due to the effect of time delays occurring within the conservation relations (which are ordinary differential equations). The pathophysiology highlighted by the analysis is considerable, and includes central nervous system disorders, heart failure, metabolic diseases, lung disorders, vascular pathologies, physiological changes during sleep, and ascent to high altitude. Chapter 8 concludes the thesis with a summary of achievements and directions for further work.

Thesis (MScIng)--University of Stellenbosch, 2003.
ENGLISH ABSTRACT: Physical systems encountered in process engineering are invariably ill-defined, multivariate, and exhibit complex nonlinear dynamical behaviour. The increasing demands for better process efficiency and high product quality have led to the development and implementation of advanced control strategies in process plants. These modern control strategies are based on the use of a mathematical model defined for the process. Traditionally, linear models have been used to approximate the dynamics of processes whereas most processes are governed by nonlinear mechanisms. Since linear systems theory is well-established whereas nonlinear systems theory is not, recent developments in nonlinear dynamical systems theory present opportunities for improved approaches in modelling these process systems. It is now known that a nonlinear description of a process can be obtained from using time-delayed copies reconstructed from measurements taken from the process. Due to low signal to noise ratios associated with measured data it is logical to exploit redundant information in multivariate time signals taken from the systems in reconstructing the underlying dynamics. This study investigated the extension of univariate nonlinear time series analysis to the situation where multivariate measurements are available. Using simulated data from a coupled continuously stirred tank reactor and measured data from a flotation process system, the comparative advantages of using multivariate and univariate state space reconstructions were investigated. With respect to detection of nonlinearity multivariate surrogate analysis were found to give potentially robust results because of preservation of cross-correlations among components in the surrogate data. Multivariate local linear models showed a deterministic structure in both small and large neighbourhood sizes whereas for scalar embeddings determinism was defined only in smaller neighbourhood sizes. Non-uniform multivariate embeddings gave local linear models that resembled models from a trivial reconstruction of the original state space variables. With regard to global nonlinear modelling, multivariate embeddings gave models with better predictability irrespective of the model class used. Further improvements in the performance of models were obtained for multivariate non-uniform embeddings. A relatively new statistical learning algorithm, the least-squares support vector machine (LSSVM), was evaluated using multilayer perceptrons (MLP) as a benchmark in modelling nonlinear time series using simulated and plant data. It was observed that in the absence of autocorrelations in the variables and sparse data LSSVMs performed better than MLPs. Simulation of trained models gave consistent results for the LSSVMs, which was not the case for MLPs. However, the computational costs incurred in training the LSSVM model was significantly higher than for MLPs. LSSVMs were found to be insensitive to dimensionality reduction methods whereas the performance of MLPs degraded with increasing complexity of the dimension reduction method. No relative merits were found for using complex subspace dimension reduction methods for the data used. No general conclusions could be drawn with respect to the relative superiority of one class of models method over the other. Spatiotemporal structures are routinely observed in many chemical systems, such as reactive-diffusion and other pattern forming systems. We investigated the modelling of spatiotemporal time series using the coupled logistic map lattice as a case study. It was found that including both spatial and temporal information improved the performance of the fitted models. However, the superiority of spatiotemporal embeddings over individual time series was found to be defined for certain choices of the spatial and temporal embedding parameters.
AFRIKAANSE OPSOMMING: Fisiese stelsels wat in prosesingenieurswese voorkom is dikwels nie goed gedefinieer nie, multiveranderlik en vertoon komplekse nie-lineˆere gedrag. Toenemende vereistes vir ho¨e prosesdoeltreffendheid en produkgehalte het gelei tot die ontwikkeling en implementering van gevorderde beheerstrategie¨e vir prosesaanlegte. Hierdie morderne beheerstrategie¨e is gebaseer op die gebruik van wiskundige prosesmodelle. Lineˆere modelle word gewoonlik ontwikkel, al is die onderliggende prosesmeganismes in die algemeen nie-lineˆere, aangesien lineˆere stetselteorie goed gevestig is, en nie-line¨ere stelselteorie nie. Onlangse verwikkelinge in die teorie van nie-lineˆeredinamiese stelsels bied egter geleenthede vir verbeterde modellering van prosesstelsels. Dit is bekend dat ‘n nie-lineˆere beskrywing van ‘n progses verkry kan word deur tydvertraagde kopie¨e van metings van die prosesse te rekonstrueer. Met die lae seintot- geraasverhoudings wat met gemete data geassosieer word, is dit logies om die oortollige informasie in meerveranderlike seine te benut tydens die rekonstruksie van die onderliggende prosesdinamika. In die tesis is die uitbreiding van enkel-veranderlike nie-lineˆere tydreeksontleding na meer-veranderlike stelsels ondersoek. Met data van twee aaneengeskakelde gesimuleerde geroerde tenkreaktore en werklike data van ‘n flottasieproses, is die meriete van enkel- en meerveranderlike rekonstruksies van toestandruimtes ondersoek. Meerveranderlike surrogaatdata-ontleding het nie-lineariteite in die data op ‘n meer robuuste wyse ge¨ıdentifiseer, a.g.v. die behoud van kruis-korrelasies in die komponente van die data. Meerveranderlike lokale lineˆere modelle het ‘n deterministiese struktuur in beide klein en groot naasliggende omgewings ge¨ıdentifiseer, terwyl enkelveranderlike metodes dit slegs vir klein naasliggende omgewings kon doen. Nie-uniforme meerveranderlike inbeddings het lokale lineˆere modelle gegenereer wat soos globale modelle afkomstig van triviale rekonstruksies van die data gelyk het. M.b.t globale nie-lineˆere modellering, het meerveranderlike inbedding deurgaans beter modelle opgelewer. Verdere verbetering in die prestasie van modelle kon verkry word d.m.v. meerveranderlike nie-uniforme inbedding. ‘n Relatief nuwe statistiese algoritme, die kleinste-kwadrate-steunvektormasjien (KKSVM) is ge¨evalueer teenoor multilaag-perseptrons (MLP) as ‘n standaard vir die modellering van nie-lineˆere tydreekse, deur gebruik te maak van gesimuleerde en werklike aanlegdata. Daar is gevind dat die KKSVM beter presteer het as die MLPs wanneer die opeenvolgende waarnemings swak gekorreleer en min was relatief tot die aantal veranderlikes. Die KKSVMs het beduidend langer geneem as die MLPs om te ontwikkel. Hulle was ook minder sensitief vir die metodes wat gevolg is om die dimensionaliteit van die data te verlaag, anders as die MLPs. Ook is gevind dat meer komplekse metodes tot die verlaging van die dimensionaliteit weinig nut gehad het. Geen algemene gevolgtrekkings kan egter gemaak word m.b.t die verskillende modelle nie. Ruimtelik-temporale strukture word algemeen waargeneem in baie chemiese stelsels, soos reaktiewe diffusie e.a. patroonvormende sisteme. Die modellering van ruimtelik-temporale stelsels is bestudeer aan die hand van ‘n gekoppelde logistiese projeksierooster. Insluiting van beide die ruimtelike en temporale inligting het tot beduidend beter modelle gelei, solank as wat di´e inligting op die regte wyse ontsluit is.

Thesis (Ph. D.)--Ohio State University, 2004.
Title from first page of PDF file. Document formatted into pages; contains xiv, 117 p. : ill. (some col.). Advisors: Bhavik R. Bakshi and Prem K. Goel, Department of Chemical Engineering. Includes bibliographical references (p. 114-117).

A neutralizacao de pH e utilizada nas industrias, para garantir o descarte seguro de euentes. As plantas de neutralizacao de pH sao um problema complexo de controle, visto que a planta segue um modelo nao-linear e apresenta caractersticas variantes no tempo, o que demanda sua correta modelagem para o projeto de sistemas de controle ecientes. No entanto, a teoria referente a modelagem de pH nao e facilmente aplicada na pratica, resultando frequentemente em modelos que nao predizem corretamente o comportamento dinamico da planta. O primeiro objetivo deste trabalho foi modelar matematicamente a Planta Piloto de Neutralizacao de pH do Laboratorio de Controle de Processos Industriais (LCPI), utilizando uma metodologia que possa ser aplicada para obter o modelo matematico de outras plantas de neutralizacao de pH. Inicialmente a Planta Piloto de Neutralizacao de pH do LCPI foi modelada de acordo com a abordagem fenomenologica, utilizando-se os princpios de conservacao de massa, da eletroneutralidade e os conceitos de equilbrio qumico. Em seguida, o modelo foi ajustado aos dados experimentais do processo (abordagem emprica), utilizando-se curvas de titulacao dos inuentes e distribuicoes de tempos de residencia do reator. Atraves de experimentos, vericou-se que o modelo representou, de forma satisfatoria, a dinamica real da Planta Piloto de Neutralizacao de pH do LCPI. Ademais, este modelo foi utilizado para alcancar o segundo objetivo deste trabalho: projetar um sistema de controle de pH, o qual foi composto por um observador nao-linear e um controlador baseado em modelo. Esta estrutura de controle foi testada experimentalmente, onde certicou-se que os requisitos de controle foram satisfeitos.
The pH neutralization is used in industry to discard properly the wastewater, ensuring the environment preservation. The pH neutralization is a complex control problem, as the model of the plant presents a strong nonlinearity and time varying characteristics, which demands a proper modeling in order to design ecient control systems. However, the application of the theory related to pH modeling is not a trivial task and may result in models that can not predict the plant dynamics. The rst objective of this research was to model the pH Neutralization Pilot Plant, of the Laboratory of Industrial Processes Control (LCPI), using a methodology that could be replicated to model other pH neutralization plants. Initially, the pH Neutralization Pilot Plant was modeled with the phenomenological approach, utilizing rst principles, such as the mass conservation, electroneutrality and chemical equilibrium. Moreover, the model was adjusted to represent the process observed data (empirical approach), as its titration curves of the inuent streams and its reactor residence time distribution. Through experiments, it was veried that the model could represent adequately the real process dynamics. Furthermore, this model was used to achieve the second objective of this research: to design a pH control system, which was composed of a nonlinear observer and a modelbased control. This control structure was tested experimentally, ensuring that the control requirements were satised.

Optimization has enabled automated applications in chemical manufacturing such as advanced control and scheduling. These applications have demonstrated enormous benefit over the last few decades and continue to be researched and refined. However, these applications have been developed separately with uncoordinated objectives. This dissertation investigates the unification of scheduling and control optimization schemes. The current practice is compared to early-concept, light integrations, and deeper integrations. This quantitative comparison of economic impacts encourages further investigation and tighter integration. A novel approach combines scheduling and control into a single application that can be used online. This approach implements the discrete-time paradigm from the scheduling community, which matches the approach of the control community. The application is restricted to quadratic form, and is intended as a replacement for systems with linear control. A novel approach to linear time-scaling is introduced to demonstrate the value of including scaled production rates, even with simplified equation forms. The approach successfully demonstrates significant benefit. Finally, the modeling constraints are lifted from the discrete-time approach. Time dependent constraints and parameters (like time-of-day energy pricing) are introduced, enabled by the discrete-time approach, and demonstrate even greater economic value. The more difficult problem calls for further exploration into the relaxation of integer variables and initialization techniques for faster, more reliable solutions. These applications are also capable of replacing both scheduling and control simultaneously. A generic CSTR application is used throughout as a case study on which the integrated optimization schemes are implemented. CSTRs are a common model for applications in most chemical engineering industries, from food and beverage, to petroleum and pharmaceuticals. In the included case study results, segregated control and scheduling schemes are shown to be 30+% less profitable than fully unified approaches during operational periods around severe disturbances. Further, inclusion of time-dependent parameters and constraints improved the open-loop profitability by an additional 13%.

In recent years, Polymer Electrolyte Membrane Fuel Cells (PEMFC) have attracted much attention due to their potential as a clean power source for many applications, including automotive, portable and stationary devices. This resulted in a tremendous technological progress, such as the development of new membranes and electro-catalysts or the improvement of electrode structures. However, in order to compete within the most attractive markets, the PEMFC technologies did not reach all the required characteristics yet, in particular in terms of cost and durability.Because of the strong coupling between different physicochemical phenomena, the interpretation of experimental observations is difficult, and analysis through modeling becomes crucial to elucidate the degradation and failure mechanisms, andto help improving both PEMFC electrochemical performance and durability.The development of a theoretical tool is essential for industrials and the scientific community to evaluate the PEMFC degradation and to predict itsperformance and durability in function of the materials properties and in a diversity of operating conditions. This manuscript summarizes my scientific research efforts in this exciting topic during the last 9 years in France, including my invention of the MEMEPhys multiscale simulation package,developed on the basis of my childhood passion for the New Technologies for Energyin Argentina. My perspectives of adapting this approach to other electrochemical systems such as water electrolyzers and batteries are also discussed.

The focus of this dissertation is on modeling and analysis of prototype problems of reacting flows interacting with surfaces or in porous media. In particular, flammability limits of gaseous and condensed fuels, complex nonlinear dynamics of flames, and deposition of thin membranes within porous substrates have been studied. The regime of self-sustained methane-air combustion has been first identified in the parameter space of strain rate-fuel flow rate, for a gaseous diffusion flame. Additionally, the regime of absolute stability, where heat losses at the surface do not extinguish a flame, has also been mapped. It has been found that the critical extinction mass pyrolysis rate is insensitive to thermo-transpo-kinetic details at high values of modified Damköhler numbers, whereas is very sensitive at low values. Selected comparisons with experimental results have been made to validate our numerical predictions. The regime of oscillatory instabilities in hydrogen-air combustion was systematically mapped for the first time for premixed and diffusion flames. It has been demonstrated that premixed hydrogen-air flames exhibit complex dynamics including chaos at high pressures. The interplay of autocatalytic chemistry with transport, reaction exothermicity, and flow, inherent to distributed flames, has been identified to be the cause for the observed chaotic dynamics. Finally, a multiscale computational framework for deposition of films within porous substrates is developed and applied to the opposed flow geometry. The model captures transport of reactants through the pores described by the dusty gas model, homogeneous reaction of the organometallic precursor producing an intermediate species, nucleation (treated stochastically), and growth of the film as a moving boundary problem. Adaptive mesh refinement is used to resolve length scales varying from nanometers to one millimeter. The numerical results provide insight into how to confine thin films within substrates and control their thickness. For example, it has been found that the location of the metal deposit within the porous substrate is essentially determined by the relative concentrations of H2 and the organometallic precursor. Additionally, it is shown that the interplay of nucleation and growth kinetics determines the morphology of the deposit at short time scales.

Thesis (Ph. D.)--Florida State University, 2003.
Advisor: Dr. Oliver Steinbock, Florida State University, College of Arts and Sciences, Dept. of Chemistry and Biochemistry. Title and description from dissertation home page (Aug. 27, 2004). Includes bibliographical references.

Celem niniejszej pracy było zbadanie wybranych przykładów zjawisk dynamicznych niestabilności, występujących w homogenicznych układach chemicznych z udziałem nadtlenku wodoru. Rozprawa jest podzielona na dwie główne części. Pierwsza część, oparta na danych literaturowych, zawiera podstawowe informacje na temat kinetyki chemicznej i dyna miki nieliniowej. Przedstawiony jest także bieżący stan wiedzy na temat oscylatorów chemicznych z udz iałem nadtlenku wodoru. Druga część rozprawy, eksperyment alna, omawia przeprowadzone przeze mnie badania i otrzymane wyniki. W części literaturowej rozprawy przedstawiono szczegółową charakterystykę dwóch oscylacyjnych układów chemicznych z udziałem nadtlenku wodoru. Reakcja w pierwszym ukł adzie polega na utleni aniu jonów rodankowych przez nadtlenek wodoru w środowisku zasadowych w obecności katalizator miedziowego. Zachowanie oscylacyjne układu H 2 O 2 – NaSCN – NaOH – CuSO 4 jest obserwowane zarówno w warunkach przepływowych jak i bez przepływu. Postęp reakcji można monitorować za pomocą różnych metod analitycznych, np. poprzez pomiary absorbancji lub potencjału różnych elektrod wskaźnikowych. Drugi z opisanych chemicznych oscylatorów jest r eakcją przebiegającą w układzie H 2 O 2 – Na 2 S 2 O 3 – H 2 SO 4 – CuSO 4 . Zastąpienie jonów rodankowych przez tiosiarczanowe i zamiana środowiska na kwasowe sprawia, że mimo powierzchownego podobieństwa do poprzedniego układu, reakcja ta wykazuje zachowanie oscylacyjne jedynie w reaktorze przepływowym. Co więcej, reakcja ta jest także oscylatorem pH, w odróżnieniu o d reakcji w układzie rodankowym, która to zachowywała praktycznie stała wartość pH w trakcie trwania reakcji. Część literaturowa pracy zawiera także omówienie podstawowych pojęć kinetyki chemiczne j i przedstawia teorię kompleksu aktywnego. Wprowadzone są pojęcia nieliniowej dynamiki i teorii bifurkacji. Omówione zostały także metody analizy układów dynamicznych i modeli kinetycznych, takie jak liniowa analiza stabilności, teoria sieci i teoria indeksów. Jako uzupełnienie tematyki związanej z układami dynamicznymi przedstawione są także podstawy teorii chaosu deterministycznego. Ze względu na kluczowa rolę, jaką w moich badaniach odegrały zarówno modelowania numeryczne jak i pomiary potencjałowe, omówione zostały także podstawowe metody numerycznego rozwiązywania równań różniczkowych oraz koncepcja potencjału mieszanego elektrody. Część druga rozprawy zawiera wyniki przeprowadzonych przeze mnie badań. Część ta rozpoczyna się od krótkiego opis u celów badawczych oraz wyliczenia użyte j aparatury i odczynników. Kolejne rozdziały szczegółowo przedstawiają przeprowadzone badania, które zostały nakreślone we wstępie. Pierwszym opisanym problemem badawczym jest zagadnienie konstrukcji modeli kinetycznych reakcji oraz ich dalszej redukcji, a ż do otrzymania modelu skrajnie uproszczonego, zwanego minimalnym oscylatorem reakcji. Badania te zrealizowałem na przykładzie reakcji H 2 O 2 – NaSCN – NaOH – CuSO 4 , której prosty model kinetyczny, składający się z 9 równań kinetycznych, został skonstruowany wcześniej w naszym zespole badawczym. Moim celem było przedstawienie sposobu uproszczenia tego modelu. Stosując podejście w dużej mierze intuicyjne, uzupełnione także formalnymi metodami analitycznymi, zapropon owałem układ zredukowany do postaci 5 równań kinetycznych. Stosując metodologię teorii sieci wykazałem, że zachowanie oscylacyjne układu nie zostało na drodze przeprowadzonej redukcji wytracone, co wprost udowodniłem za pomocą modelowania numerycznego. Dalsze badania numeryczne pokazały, że model 5 z miennych jest jakościowo równoważny modelowi 9 zmiennych. Zachowana została charakterysty ka stanów stacjonarnych układu , a obydwa modele wykazały półilościową zgodność parametrów wymodelowanych oscylacji (okres i amplituda). Następnie przeprowadzone został y pomiary spektrofotometryczne i potencjometryczne, które posłużyły ocenie trafności przewidywań teoretycznych. Model 5 zmiennych pozwolił między innymi półilościowo opisać sigmoidalną zależność amplitudy oscylacji od stężenia katalizatora miedziowego. Półilościowo oddane zostały także parametry oscylacji absorbancji w eksperymencie chemicznym. Kolejnym etapem badań była próba dalszego uproszczenia modelu kinetycznego, mająca na celu otrzymanie tak zwanego minimalnego oscylatora reakcji. Eliminując zbęd ne reakcje, lub wprowadzając ich efektywny ekwiwalent, zredukowałem model 5 zmiennych do układu zawierającego jedynie 3 równania kinetyczne. Kluczowymi elementami modelu, odpowiedzialnymi za generowanie zachowania oscylacyjnego jest pętla autokatalitycznego sprzężenia zwrot nego oraz układ odpowiednio opóźnionych względem niej sprzężeń zwrotnych ujemnych. Elementy te zostały w modelu 3 zmiennych zachowane. Otrzymany układ modelowy wykazuje zachowanie oscylacyjne, o parametrach podobnych do tych obserwowanych w eksperymencie spektrofotometrycznym. Z e względu jednak na jego skrajnie uproszczony charakter, zgodność ta jest co najwyżej jakościowa. Otrzymany układ został sprowadzony do postaci bezwymiarowej, co pozwoliło zredukować liczbę parametrów kontrolnych or az wykazać, że modelu tego nie można dalej zredukować. Zastosowanie np. przybliżenia adiabatycznego w celu dalszej redukcji zaproponowanego modelu wiąże się z wytraceni em jego oscylacyjnej charakterystyki. Otrzymany układ może być zatem nazwany minimalnym oscylatorem reakcji w układzie nadtlenek wodoru – rodanek sodu. Dalsze badania dynamicznych niestabilności poświęcone były zagadnieniu otrzymywania struktur czasoprzestrzennych w reakcji w układzie nadtlenek wodoru – tiosiarczan sodu. Wstępne eksperymenty prowadzone w reaktorze cienkowarstwowym bez mieszania wykazały, że w warunkach izotermicznych reakcja ta nie generuje zauważalnych struktur czasoprzestrzennych . Dalsze badania wykazały, że strukturę taką można w układzie reakcyjnym wygenerować w warunka ch nieizotermicznych. Przyłożenie zewnętrznego gradientu temperatury do reaktora cienkowarst wowego pozwoliło w obecności barwnika pH zaobserwować strukturę o charakterze wędrującego fr ontu podwyższonego pH. Zabieg ten powoduje przestrzenne zróżnicowanie ki netyki reakcji, co z kolei jest przyczyną powstania trywialnej struktury czasoprzestrzennej. Hipoteza, że gł ówną przyczyną powstawania zaobserwowanej struktury została zweryfikowana za pomocą eksperymentów prowadzonych w termostatowanym reaktorze z mieszan iem. Doświadczenia ten pozwoliły wyznaczyć zależność okresu indukcji, rozumianego jako czas od zainicjowania reakcji do momentu zmiany koloru przez wskaźnik pH, oraz okresu trwania fazy podwyższonego pH od temperat ury. Wyznaczona została także formalna energia aktywacji reakcji. Otrzymane dane okazały się dobr ze korelować z przebiegiem eksperymentu w reaktorze cienkowarstwowym. Badania zostały uzupełnione prz ez studium modelu kinetycznego reakcji. Model literaturowy został przeze mnie roz budowany o człony z wiązane ze zmierzoną energią aktywacji, przejawiającą się w wyrażeniach arr heniusowskich na stałą szybkości reakcji. Tak skonstruowany model kinetyczny pozwolił poprawnie odtworzyć pr zebieg powstawania zaobserwowanej, barwnej struktury czasoprzestrzennej. W toku dalszej dyskusji otrzymanych wyników wykazałem, że główną przyczyną powstawania struktury czasoprzes trzennej jest zewnętrzny gradient temperatury, modyfikujący lokalną kinetykę reakcji. Co więcej, wykazałem też, że niektóre elementy modelu reakcja – dyfuzja użytego do opisu zjawiska, takie jak dyfuzja masy w przestrzeni czy ewolucja czasowa temperatury, mogą być w rozważaniach zaniedbane bez jednoczesnej straty zgodności przewidywań modelowych z doświadczeniem. Zastosowane przeze mnie przybliżenia pozwoliły formalnie zredukować układ cząstkowych równań różniczk owych do układu równań zwyczajnych. Przybliżenia te są w tym przypadku dobrze spełnione z powodu względnie krótkiej skali czasowej procesu. Mimo bardzo uproszczonej struktury, z aproponowany mode l pozwolił ilościowo odzwierciedlić przebieg eksperymentu chemicznego w reaktorz e cienkowarstwowym. Ostatnia część badań została poświęcona zagadnieniu przesunięcia fazowego w układzie H 2 O 2 – Na 2 S 2 O 3 – H 2 SO 4 – CuSO 4 , które można zaobserwować między odpowiedziami elektrod wskaźnikowych zastosowanych do monitorowania postępu reakcji w termostatowanym reaktorz e przepływowym. Oscylacyjne przebiegi potencjałów wskazywanych przez elektrody Pt, pH i jonoselektywną względem jonów Cu(II) wykazują przesunięcie fazowe względem siebie. O znacza to, że maksima potencjałów ustalających się na tych elektrodach nie występują równocz eśnie. Zbadałem zależność przesunięcia fazowego od różnych czynników, takich jak stężenia reagentów, temp eratura i parametr przepływu strumienia zasilającego reaktor. Dla ustalonej temperatury , kluczowym dla zachowania układu parametrem okazał się być parametr przepływu. Jest on także parametrem bifurkacji, co oznacza, że oscylacje chemiczne w układzie występują jedynie dla jego wartości z pewnego optymalnego przedziału. Dalsze badania wykazały, że wartość przesunięcia fazowego (obliczana jako różnica między położeniami ekstremów potencjałów elektrod, znormaliz owana przez okres oscylacji) zależy w przybliżeniu parabolicznie od wartości parametru przepływu. Maksymalne wartości przesunięcia fazowego osiągane są w układzie dla przepływów odpowiadając ych punktom bifurkacji, w których zachowanie oscylacyjne powstaje lub zanika. Dla wyjaśn ienia zaobserwowanego zjawis ka wystarczający okazał się być model kinetyczny reakcji dostępny w literatur ze, rozbudowany przeze mnie o reakcje chemiczne opisujące dynamikę zmian stężenia form Cu(I) i Cu( II). Zaproponowany przeze mnie model pozwala bezpośrednio odtworzyć przebiegi potencjałów rejestrowanych za pomocą elektrod pH i jonoselektywnej. Dzięki zastosowaniu formal izmu potencjału mieszanego możliwe jest także wymodelowanie potencjału elektrody Pt. Zaproponowany model pozwolił półilościowo odtworzyć obserwowane w eksperymencie przebiegi potencjałów elektrodowych, jak i paraboliczną zależność przesunięcia fazowego od parametru przepływu. Przeprowadzone badania pozwoliły wykazać, że w badaniach dynamiki reakcji oscylacyjnych użyteczne może być stosowanie równocześnie kilku różnych sensorów lub metod analitycznych. Praca zwieńczona jest krótkim podsumowaniem i zwięzłym przedstawieniem wniosków wynikających z przeprowadzonych badań. Dwa ostatnie rozdziały rozprawy zawierają listę źródeł, z których zostały zapożyczone ilustracje użyte w pracy, oraz bibliografię.

A thorough understanding of pharmaceutical and therapeutic products and materials is important for an improved quality of life. By probing the complex behaviors and properties of these systems, new insights can allow for a better understanding of current treatments, improved design and synthesis of new drug products, and the development of new treatments for various health conditions. Often, the impact of these new insights are limited by current technology and instrumentation and by the methods in which existing data is processed. Additionally, current standards for characterization of pharmaceuticals and therapeutics are time-consuming and can delay the timeline in which these products become available to the consumer. By addressing the limitations in current instrumentation and data science methods, faster and improved characterization is possible.

In this thesis appropriate statistical methods to overcome two types of problems that occur during parameter estimation in chemical engineering systems are studied. The first problem is having too many parameters to estimate from limited available data, assuming that the model structure is correct, while the second problem involves estimating unmeasured disturbances, assuming that enough data are available for parameter estimation. In the first part of this thesis, a model is developed to predict rates of undesirable reactions during the finishing stage of nylon 66 production. This model has too many parameters to estimate (56 unknown parameters) and not having enough data to reliably estimating all of the parameters. Statistical techniques are used to determine that 43 of 56 parameters should be estimated. The proposed model matches the data well. In the second part of this thesis, techniques are proposed for estimating parameters in Stochastic Differential Equations (SDEs). SDEs are fundamental dynamic models that take into account process disturbances and model mismatch. Three new approximate maximum likelihood methods are developed for estimating parameters in SDE models. First, an Approximate Expectation Maximization (AEM) algorithm is developed for estimating model parameters and process disturbance intensities when measurement noise variance is known. Then, a Fully-Laplace Approximation Expectation Maximization (FLAEM) algorithm is proposed for simultaneous estimation of model parameters, process disturbance intensities and measurement noise variances in nonlinear SDEs. Finally, a Laplace Approximation Maximum Likelihood Estimation (LAMLE) algorithm is developed for estimating measurement noise variances along with model parameters and disturbance intensities in nonlinear SDEs. The effectiveness of the proposed algorithms is compared with a maximum-likelihood based method. For the CSTR examples studied, the proposed algorithms provide more accurate estimates for the parameters. Additionally, it is shown that the performance of LAMLE is superior to the performance of FLAEM. SDE models and associated parameter estimates obtained using the proposed techniques will help engineers who implement on-line state estimation and process monitoring schemes.
Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2013-12-23 15:12:35.738

Thesis (Ph. D.)--University of Notre Dame, 2006.
Thesis directed by Mark A. Stadtherr for the Department of Chemical and Biomolecular Engineering. "May 2006." Includes bibliographical references (leaves 239-253).