O estudo e observação de Sistemas Químicos Oscilantes vêm se destacando como importante campo de pesquisa da ciência química contemporânea. Tais sistemas têm como comportamento notório principal a variação periódica da concentração de um intermediário de reação química. Sua compreensão vem estimulando debates que transcendem o escopo químico e estabelecem relações com outras disciplinas científicas, e mais marcadamente, o estudo de sistemas complexos em geral. O ensino de sistemas químicos oscilantes, em específico, e de sistemas complexos, em geral, se apresenta na atualidade como desafio necessário e estimulante. Neste trabalho optou-se por tentar contribuir neste esforço, utilizando-se da noção de obstáculos epistemológicos inicialmente estabelecida pelo filósofo francês Gastón Bachelard. O conceito de obstáculos epistemológicos apresentou-se nas últimas décadas como importante ferramenta na abordagem das relações de ensino-aprendizagem de conceitos das ciências contemporâneas. Existem diferentes tipos de obstáculos epistemológicos, entre eles: experiência primeira, conhecimento geral, obstáculo verbal, conhecimento unitário e pragmático e obstáculo animista. Neste trabalho surge a proposta de utilizar a noção de obstáculo epistemológico voltada ao ensino de conceitos da complexidade pertinentes aos Sistemas Químicos Oscilantes. Foram analisadas as presenças de obstáculos epistemológicos em textos didáticos de ensino de sistemas químicos oscilantes. Os textos didáticos escolhidos foram artigos científicos da área de ensino de química voltados ao ensino de sistemas químicos oscilantes, livros didáticos usados em cursos de graduação e livros de divulgação científica. Foram analisados os conteúdos integrais de sete artigos científicos da área de ensino de química voltados ao tema reações químicas oscilantes. Foram também analisadas as seções referentes a reações químicas oscilantes de quatro livros didáticos utilizados em cursos de graduação da USP devotadas ao ensino de sistemas caóticos. Foram também analisadas as seções referentes a reações químicas oscilantes de quatro livros de divulgação científica que abordaram o tema sistemas químicos oscilantes. Foram encontrados grande número de obstáculos da experiência primeira e obstáculos animistas em livros didáticos e um grande número de obstáculos verbais em livros de divulgação científica. Todos os tipos de obstáculos epistemológicos listados foram identificados ao menos uma vez em algum dos textos. Demonstrou-se a viabilidade de aplicação do conceito de obstáculos epistemológicos em textos didáticos de ensino de sistemas químicos oscilantes. / The study and observation of Oscillating Chemical Systems have been highlighted as an important research field of chemical science contemporary. Such systems are notorious behavior as the main periodic variation of the concentration of an intermediate chemical reaction. Your understanding is stimulating debates that transcend the scope of chemical and establish relationships with other scientific disciplines, and most notably, the study of complex systems in general. The teaching of chemical oscillating systems, in particular, and complex systems in general, is presented nowadays as necessary and stimulating challenge. In this work it was decided to try to contribute in this effort, using the notion of epistemological obstacles initially established by the philosopher Gaston Bachelard. The concept of epistemological obstacle presented itself in recent decades as an important tool in addressing the relationships of teaching and learning of contemporary science concepts. There are different kinds of epistemological obstacles, among them: first experience, geral knowledge, verbal obstacle, pragmatic and unitary knowledge and animist obstacle . This work comes propose to use the notion of epistemological obstacle to teach the complexity of concepts relevant to oscillating chemical system .We analyzed the presence of epistemological obstacles in textbooks that have teaching oscillating chemical systems. The selected texts were scientific articles in the area of chemical education aimed at teaching oscillating chemical systems, books used in undergraduate and some popular science books. We analyzed the entire contents of seven papers in the area of chemical education geared to the theme oscillating chemical reactions. We also analyzed the sections pertaining to oscillating chemical reactions of four textbooks used in undergraduate courses devoted to teaching the chaotic systems at USP . We also analyzed the sections pertaining to oscillating chemical reactions of four popular science books that addressed the issue of oscillating chemical systems. We found many first experiences and animists obstacles in textbooks and a large number of verbal obstacles in popular science books. All kinds of epistemological obstacles identified were listed at least once at some of the texts. The results confirm the feasibility of applying the concept of epistemological obstacles in textbooks teaching oscillating chemical systems.

Lee Ho-Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 71-72). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Table of Contents --- p.iv / List of Tables --- p.vi / List of Figures --- p.vii / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Gaussian´ؤ3 Method --- p.1 / Chapter 1.2 --- "The G2++, a Modified Gaussian-2 Method" --- p.2 / Chapter 1.3 --- Density Functional Theory (DFT) --- p.2 / Chapter 1.4 --- Calculation of Thermodynamical Data --- p.3 / Chapter 1.5 --- Remark on the Location of Equilibrium and Transition Structures --- p.3 / Chapter 1.6 --- Natural Bond Orbital (NBO) Analysis --- p.3 / Chapter 1.7 --- Scope of the Thesis --- p.4 / Chapter 1.8 --- References --- p.4 / Chapter Chapter 2 --- Structures and Energetics of C3H6S+´Ø Isomers: A Gaussian-3 ab initio Study --- p.6 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Methods of Calculation --- p.8 / Chapter 2.3 --- Results and Discussion --- p.8 / Chapter 2.4 --- Conclusion --- p.21 / Chapter 2.5 --- Publication Note --- p.21 / Chapter 2.6 --- References --- p.22 / Chapter Chapter 3 --- A Gaussian-3 Study of the C3H6S Isomers and the Dissociation Channels of Diradical ´ØCH2CH2SCH2´Ø and Its Radical Cation ´ØCH2CH2SCH2+ --- p.24 / Chapter 3.1 --- Introduction --- p.24 / Chapter 3.2 --- Methods of Calculation --- p.25 / Chapter 3.3 --- Results and Discussion --- p.26 / Chapter 3.3.1 --- Structures and Energetics of C3H6S Isomers --- p.26 / Chapter 3.3.2 --- Dissociation Channels of ´ØCH2CH2SCH2´Ø and ´ØCH2CH2SCH2+ --- p.34 / Chapter 3.4 --- Conclusion --- p.40 / Chapter 3.5 --- Publication Note --- p.41 / Chapter 3.6 --- References --- p.41 / Chapter Chapter 4 --- Computational Study on the Electrocyclic Reactions of [16]Annulene --- p.43 / Chapter 4.1 --- Introduction --- p.43 / Chapter 4.2 --- Methods of Calculation --- p.45 / Chapter 4.3 --- Results and Discussion --- p.45 / Chapter 4.3.1 --- Reaction (1) --- p.49 / Chapter 4.3.2 --- Reaction (2) --- p.50 / Chapter 4.3.3 --- Reaction (3) --- p.52 / Chapter 4.3.4 --- Overall Reaction --- p.53 / Chapter 4.4 --- Conclusion --- p.54 / Chapter 4.5 --- Publication Note --- p.55 / Chapter 4.6 --- References --- p.55 / Chapter Chapter 5 --- Computational Study on the Structures and Stabilities of Some Hypothetical Silicon Nanotubes --- p.57 / Chapter 5.1 --- Introduction --- p.57 / Chapter 5.2 --- Model Design and Methods of Calculation --- p.59 / Chapter 5.3 --- Results and Discussion --- p.59 / Chapter 5.3.1 --- "Armchair (n,n) SiNTs" --- p.60 / Chapter 5.3.2 --- "Zigzag (n,0) SiNTs" --- p.61 / Chapter 5.3.3 --- "Chiral (n,m) SiNTs" --- p.65 / Chapter 5.3.4 --- Stabilities of SiNTs at Elevated Temperature --- p.69 / Chapter 5.4 --- Conclusion --- p.70 / Chapter 5.5 --- References --- p.71 / Chapter Chapter 6 --- Conclusion --- p.73 / Appendix A --- p.74 / Appendix B --- p.76 / Appendix C --- p.77

The exact and phaseless variants of auxiliary-field quantum Monte Carlo (AFQMC) have been shown to be capable of producing accurate ground-state energies for a wide variety of systems including those which exhibit substantial electron correlation effects. The first chapter of this thesis will provide an overview of the relevant electronic structure problem, and the phaseless AFQMC (ph-AFQMC) methodology. The computational cost of performing these calculations has to date been relatively high, impeding many important applications of these approaches. In Chapter 2 we present a correlated sampling methodology for AFQMC which relies on error cancellation to dramatically accelerate the calculation of energy differences of relevance to chemical transformations. In particular, we show that our correlated sampling-based ph-AFQMC approach is capable of calculating redox properties, deprotonation free energies, and hydrogen abstraction energies in an efficient manner without sacrificing accuracy. We validate the computational protocol by calculating the ionization potentials and electron affinities of the atoms contained in the G2 test set and then proceed to utilize a composite method, which treats fixed-geometry processes with correlated sampling-based AFQMC and relaxation energies via MP2, to compute the ionization potential, deprotonation free energy, and the O-H bond dissociation energy of methanol, all to within chemical accuracy. We show that the efficiency of correlated sampling relative to uncorrelated calculations increases with system and basis set size and that correlated sampling greatly reduces the required number of random walkers to achieve a target statistical error. This translates to reductions in wall-times by factors of 55, 25, and 24 for the ionization potential of the K atom, the deprotonation of methanol, and hydrogen abstraction from the O-H bond of methanol, respectively. In Chapter 3 we present an implementation of ph-AFQMC utilizing graphical processing units (GPUs). The AFQMC method is recast in terms of matrix operations which are spread across thousands of processing cores and are executed in batches using custom Compute Unified Device Architecture kernels and the hardware-optimized cuBLAS matrix library. Algorithmic advances include a batched Sherman-Morrison-Woodbury algorithm to quickly update matrix determinants and inverses, density-fitting of the two-electron integrals, an energy algorithm involving a high-dimensional precomputed tensor, and the use of single-precision floating point arithmetic. These strategies result in dramatic reductions in wall-times for both single- and multi-determinant trial wavefunctions. For typical calculations we find speed-ups of roughly two orders of magnitude using just a single GPU card. Furthermore, we achieve near-unity parallel efficiency using 8 GPU cards on a single node, and can reach moderate system sizes via a local memory-slicing approach. We illustrate the robustness of our implementation on hydrogen chains of increasing length, and through the calculation of all-electron ionization potentials of the first-row transition metal atoms. We compare long imaginary-time calculations utilizing a population control algorithm with our previously published correlated sampling approach, and show that the latter improves not only the efficiency but also the accuracy of the computed ionization potentials. Taken together, the GPU implementation combined with correlated sampling provides a compelling computational method that will broaden the application of ph-AFQMC to the description of realistic correlated electronic systems. In Chapter 4 the bond dissociation energies of a set of 44 3d transition metal-containing diatomics are computed with ph-AFQMC utilizing the correlated sampling technique. We investigate molecules with H, N, O, F, Cl, and S ligands, including those in the 3dMLBE20 database first compiled by Truhlar and co-workers with calculated and experimental values that have since been revised by various groups. In order to make a direct comparison of the accuracy of our ph-AFQMC calculations with previously published results from 10 DFT functionals, CCSD(T), and icMR-CCSD(T), we establish an objective selection protocol which utilizes the most recent experimental results except for a few cases with well-specified discrepancies. With the remaining set of 41 molecules, we find that ph-AFQMC gives robust agreement with experiment superior to that of all other methods, with a mean absolute error (MAE) of 1.4(4) kcal/mol and maximum error of 3(3) kcal/mol (parenthesis account for reported experimental uncertainties and the statistical errors of our ph-AFQMC calculations). In comparison, CCSD(T) and B97, the best performing DFT functional considered here, have MAEs of 2.8 and 3.7 kcal/mol, respectively, and maximum errors in excess of 17 kcal/mol (for the CoS diatomic). While a larger and more diverse data set would be required to demonstrate that ph-AFQMC is truly a benchmark method for transition metal systems, our results indicate that the method has tremendous potential, exhibiting unprecedented consistency and accuracy compared to other approximate quantum chemical approaches. The energy gap between the lowest-lying singlet and triplet states is an important quantity in chemical photocatalysis, with relevant applications ranging from triplet fusion in optical upconversion to the design of organic light-emitting devices. The ab initio prediction of singlet-triplet (ST) gaps is challenging due to the potentially biradical nature of the involved states, combined with the potentially large size of relevant molecules. In Chapter 5, we show that ph-AFQMC can accurately predict ST gaps for chemical systems with singlet states of highly biradical nature, including a set of 13 small molecules and the ortho-, meta-, and para- isomers of benzyne. With respect to gas-phase experiments, ph-AFQMC using CASSCF trial wavefunctions achieves a mean averaged error of ~1 kcal/mol. Furthermore, we find that in the context of a spin-projection technique, ph-AFQMC using unrestricted single-determinant trial wavefunctions, which can be readily obtained for even very large systems, produces equivalently high accuracy. We proceed to show that this scalable methodology is capable of yielding accurate ST gaps for all linear polyacenes for which experimental measurements exist, i.e. naphthalene, anthracene, tetracene, and pentacene. Our results suggest a protocol for selecting either unrestricted Hartree-Fock or Kohn-Sham orbitals for the single-determinant trial wavefunction, based on the extent of spin-contamination. These findings provide a reliable computational tool with which to investigate specific photochemical processes involving large molecules that may have substantial biradical character. We compute the ST gaps for a set of anthracene derivatives which are potential triplet-triplet annihilators for optical upconversion, and compare our ph-AFQMC predictions with those from DFT and CCSD(T) methods. We conclude with a discussion of ongoing projects, further methodological improvements on the horizon, and future applications of ph-AFQMC to chemical systems of interest in the fields of biology, drug-discovery, catalysis, and condensed matter physics.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 93-103).

O estudo e observação de Sistemas Químicos Oscilantes vêm se destacando como importante campo de pesquisa da ciência química contemporânea. Tais sistemas têm como comportamento notório principal a variação periódica da concentração de um intermediário de reação química. Sua compreensão vem estimulando debates que transcendem o escopo químico e estabelecem relações com outras disciplinas científicas, e mais marcadamente, o estudo de sistemas complexos em geral. O ensino de sistemas químicos oscilantes, em específico, e de sistemas complexos, em geral, se apresenta na atualidade como desafio necessário e estimulante. Neste trabalho optou-se por tentar contribuir neste esforço, utilizando-se da noção de obstáculos epistemológicos inicialmente estabelecida pelo filósofo francês Gastón Bachelard. O conceito de obstáculos epistemológicos apresentou-se nas últimas décadas como importante ferramenta na abordagem das relações de ensino-aprendizagem de conceitos das ciências contemporâneas. Existem diferentes tipos de obstáculos epistemológicos, entre eles: experiência primeira, conhecimento geral, obstáculo verbal, conhecimento unitário e pragmático e obstáculo animista. Neste trabalho surge a proposta de utilizar a noção de obstáculo epistemológico voltada ao ensino de conceitos da complexidade pertinentes aos Sistemas Químicos Oscilantes. Foram analisadas as presenças de obstáculos epistemológicos em textos didáticos de ensino de sistemas químicos oscilantes. Os textos didáticos escolhidos foram artigos científicos da área de ensino de química voltados ao ensino de sistemas químicos oscilantes, livros didáticos usados em cursos de graduação e livros de divulgação científica. Foram analisados os conteúdos integrais de sete artigos científicos da área de ensino de química voltados ao tema reações químicas oscilantes. Foram também analisadas as seções referentes a reações químicas oscilantes de quatro livros didáticos utilizados em cursos de graduação da USP devotadas ao ensino de sistemas caóticos. Foram também analisadas as seções referentes a reações químicas oscilantes de quatro livros de divulgação científica que abordaram o tema sistemas químicos oscilantes. Foram encontrados grande número de obstáculos da experiência primeira e obstáculos animistas em livros didáticos e um grande número de obstáculos verbais em livros de divulgação científica. Todos os tipos de obstáculos epistemológicos listados foram identificados ao menos uma vez em algum dos textos. Demonstrou-se a viabilidade de aplicação do conceito de obstáculos epistemológicos em textos didáticos de ensino de sistemas químicos oscilantes. / The study and observation of Oscillating Chemical Systems have been highlighted as an important research field of chemical science contemporary. Such systems are notorious behavior as the main periodic variation of the concentration of an intermediate chemical reaction. Your understanding is stimulating debates that transcend the scope of chemical and establish relationships with other scientific disciplines, and most notably, the study of complex systems in general. The teaching of chemical oscillating systems, in particular, and complex systems in general, is presented nowadays as necessary and stimulating challenge. In this work it was decided to try to contribute in this effort, using the notion of epistemological obstacles initially established by the philosopher Gaston Bachelard. The concept of epistemological obstacle presented itself in recent decades as an important tool in addressing the relationships of teaching and learning of contemporary science concepts. There are different kinds of epistemological obstacles, among them: first experience, geral knowledge, verbal obstacle, pragmatic and unitary knowledge and animist obstacle . This work comes propose to use the notion of epistemological obstacle to teach the complexity of concepts relevant to oscillating chemical system .We analyzed the presence of epistemological obstacles in textbooks that have teaching oscillating chemical systems. The selected texts were scientific articles in the area of chemical education aimed at teaching oscillating chemical systems, books used in undergraduate and some popular science books. We analyzed the entire contents of seven papers in the area of chemical education geared to the theme oscillating chemical reactions. We also analyzed the sections pertaining to oscillating chemical reactions of four textbooks used in undergraduate courses devoted to teaching the chaotic systems at USP . We also analyzed the sections pertaining to oscillating chemical reactions of four popular science books that addressed the issue of oscillating chemical systems. We found many first experiences and animists obstacles in textbooks and a large number of verbal obstacles in popular science books. All kinds of epistemological obstacles identified were listed at least once at some of the texts. The results confirm the feasibility of applying the concept of epistemological obstacles in textbooks teaching oscillating chemical systems.

In biochemically reactive systems with small copy numbers of one or more reactant molecules, stochastic effects dominate the dynamics. In the first part of this thesis, we design novel efficient simulation techniques for a reliable and fast estimation of various statistical quantities for stochastic biological and chemical systems under the framework of Stochastic Reaction Networks. In the first work, we propose a novel hybrid multilevel Monte Carlo (MLMC) estimator, for systems characterized by having simultaneously fast and slow timescales. Our hybrid multilevel estimator uses a novel split-step implicit tau-leap scheme at the coarse levels, where the explicit tau-leap method is not applicable due to numerical instability issues. In a second work, we address another challenge present in this context called the high kurtosis phenomenon, observed at the deep levels of the MLMC estimator. We propose a novel approach that combines the MLMC method with a pathwise-dependent importance sampling technique for simulating the coupled paths. Our theoretical estimates and numerical analysis show that our method improves the robustness and complexity of the multilevel estimator, with a negligible additional cost. In the second part of this thesis, we design novel methods for pricing financial derivatives. Option pricing is usually challenging due to: 1) The high dimensionality of the input space, and 2) The low regularity of the integrand on the input parameters. We address these challenges by developing different techniques for smoothing the integrand to uncover the available regularity. Then, we approximate the resulting integrals using hierarchical quadrature methods combined with Brownian bridge construction and Richardson extrapolation. In the first work, we apply our approach to efficiently price options under the rough Bergomi model. This model exhibits several numerical and theoretical challenges, implying classical numerical methods for pricing being either inapplicable or computationally expensive. In a second work, we design a numerical smoothing technique for cases where analytic smoothing is impossible. Our analysis shows that adaptive sparse grids’ quadrature combined with numerical smoothing outperforms the Monte Carlo approach. Furthermore, our numerical smoothing improves the robustness and the complexity of the MLMC estimator, particularly when estimating density functions.

The implementation of a new curriculum is a challenging issue to educators in many countries. In this country training for an implementation of a curriculum is done in one week and it takes a form of one a size fits all. The study investigated how I transform my content knowledge when teaching a new topic in the new curriculum. The aim of this study was to carry a self- study of how I transformed my content knowledge when teaching energy resources and its uses to make it comprehensible to learners. The following research question guided the study:  How did my PCK develop as I developed the broad content of the energy resources and its uses into focused, teachable and comprehensible content?  How did my planning and reflecting on practice change as I participated in the process of planning, developing and implementing the lesson plans? When teachers teach, they draw upon knowledge of their subject matter, general pedagogy as well as context. This could be improved by the contribution of the concept of pedagogical content knowledge where content and pedagogy are blended. Therefore, for this study I have chosen PCK as a theoretical framework because I will be looking at how my content knowledge can be transformed into content knowledge for teaching. The study employed a qualitative research, which uses multiple realities that are socially constructed through collective and individual definitions of the situations. It is a self –study focusing on my own teaching and intending to improve my practice as a teacher. The focus is myself teaching two grade 11 classes in a township school. Khumalo M. iv Data was collected in a form of concept maps, reflective journals, lesson plan and CoRE s and PaPeRs. CoRes and PaPe-Rs were used to capture and portray my PCK. The methodological tools used to document and portray my Pedagogical Content Knowledge when teaching energy and resources, used representations called Content Representation (CoRe) and Pedagogical and Professional – experience Repertoires (PaP-eRs). The CoRe elaborated on my construction of content, which framed the topic and each Pa-PeR, was a narrative derived from the classroom observations and the journal. Findings in this study indicate that using the CoRe and PaPeR as a tool to portray PCK helps in the development of content knowledge. Some elements of PCK could be identified and the implementation of developed lessons led to insight into my teaching. Learners participated more freely and develop confidence when home language was used. I gained confidence using the CoRe to develop lessons.

The South African government that was elected in 1994 made tremendous changes in the Education system. The new government came up with the new curriculum for Basic Education (grade R- 12). The new curriculum had new topics in physical science. This made me as a teacher doubt whether I would be able to teach new topics. During my time as a student, I was not taught mining at school or college. As a result, I decided to do a self study in order to investigate how I would learn gold mining as a topic in order for me to be able to teach it to my learners. My study involved studying my own teaching practice while learning and also finding out the key things that made me understand the content knowledge involved in the topic of gold mining. The self study was done in order to ensure that I understood the content knowledge and how best to teach it to the learners. I used a collaboration team, reflective journal, group interviews classroom observation and learners’ responses to collect data. The participants were my grade 11 learners and myself. My data was analysed using a PCK model, CoRes and PaPeRs. I had to learn the content knowledge and transform it to make it understandable to learners. I designed lessons using the prior knowledge of learners and integrating Physical Science and Geography. Lessons did not go as smoothly as I had expected. Learners wanted some of their existing knowledge to be included. The classroom activities depended entirely on the relationship between the teacher and learners. I carried out my study bearing in mind that implementation of the new curriculum depends not only on classroom interactions (DoE, 2002) but most importantly on the content knowledge that the teacher has and how it is transformed. Learners taught me to understand gold mining from the geographical point of view as well from the scientific point of view. From the beginning of the study they were really excited and were looking forward to new things. Using the learners’ science prior knowledge helped me design lessons that allowed me to learn to be a facilitator.

An engineering method has been developed for calculating the blowdown of agent from a pressurized dry chemical fire suppression system supply cylinder, and the flow rate of agent through a piping delivery system. Its goal is to provide the means to determine the blowdown time and agent delivery capabilities of pre-engineered and simple engineered systems. The method is based on the treatment of the two-phase powder-gas flow as an equivalent fluid with thermodynamic properties that account for agent composition and the relative proportions of agent and gas propellant. The mixture is treated as compressible, and the expansion in the supply tank is assumed isentropic. A key assumption in the model is that the agent (powder) mass fraction remains constant, in both the tank and delivery system. Laboratory tests were conducted to examine the validity of the model and its assumptions. Simple systems were discharged to measure pressures in the cylinder and nozzle inlet during discharge, and the mass of agent discharged. A 0.43 cubic foot cylinder containing 0-25 lbm of either sodium bicarbonate or moammonium phosphate, pressurized at up to 300 psig of nitrogen, was discharged, either alone, or with an 8-foot length of piping and a single nozzle. For the cylinder by itself, gas alone pressurized to 300 psig discharged in 1.5 seconds, while 25 lbm of sodium bicarbonate agent pressurized to 300 psig discharged in 5.2 seconds with 0.10 lbm of agent remaining in the cylinder after discharge. There was no significant difference in the discharge times or residual masses in the cylinder after discharge between the sodium bicarbonate and monoammonium phosphate agents. For a cylinder-pipe-nozzle system, gas-alone discharges pressurized to 300 psig took 7 seconds, while 25 lbm of sodium bicarbonate agent pressurized to 300 psig discharged in 26 seconds with 0.64 lbm of residual agent in the cylinder after discharge. Predictions generated by the model were compared with test results. Cylinder alone gas-only discharge model predictions agreed well with test data for the full duration of tests using a discharge coefficient of 0.380 to characterize the gas flow through the dip tube / valve assembly; a simple isentropic analytical model gave a good prediction using a discharge coefficient of 0.430. Gas-solids predictions using a discharge coefficient of 0.500 agreed well with test data up to the observed inflection point near the end of discharge. This inflection point is caused by the agent in the cylinder reaching the bottom of the dip tube, resulting in reduced flow of agent from the cylinder, and thus reducing the mass fraction of the flow. Cylinder-pipe-nozzle model discharge predictions for gas-only discharges agreed well with test data for the full duration of tests using a discharge coefficient of 0.470 for the 0.173-inch diameter nozzle used in the testing. Model predictions agreed well with the gas-solids mixture test data up to the inflection point, using a discharge coefficient of 0.999. The constant mass fraction assumption results in residual agent mass predictions of 2.0 lbm or more after discharge. Test data shows 0.6 lbm or less of residual. This residual discrepancy, and the presence of the inflection point observed in solids-gas tests, suggests that the constant mass fraction assumption is not adequate to accurately model agent discharge from the cylinder. Using an appropriate discharge coefficient, the model can be used to determine approximate discharge times for simple systems.

The present work aims at studying the coupling between hydrodynamic fingering instabilities and chemical reactions at the interface between two miscible solutions. Hydrodynamic deformations of interfaces between two reactive fluids as well as flows induced by chemical reactions at the front between two initially steady fluids are encountered frequently in combustion, petroleum, chemical and pharmaceutical engineering. Most of the time, concrete applications imply a very large number of variables so that an understanding of the fundamental processes of chemo-hydrodynamic coupling is out of reach. Our goal is here to analyze a much simpler model system in which only one mechanism of hydrodynamic instability is at play and for which the chemical reactions can be modeled by a one or two-variable model. <p><p>Buoyantly unstable, autocatalytic chemical fronts, are one such model system, which can be used as prototype to study the effects of the coupling between chemical reactions and hydrodynamic fingering instabilities. Fingering processes occur whenever a fluid of high mobility displaces a less mobile one in a porous medium. The initially planar interface looses then stability and a cellular fingering deformation of the interface is observed. Such an instability has been observed, for instance, in the iodate-arsenous acid and chlorite-tetrathionate reactions, autocatalytic redox reactions known to produce a change of density across a traveling front. Fingering happens there when the heavier solution lies on top of the lighter one in the gravity field. <p> <p>Our theoretical contribution to the analysis of fingering of chemical fronts focuses on different points which we detail in this thesis along the following outline. In chapter 2, we introduce fingering phenomena occurring in porous media and distinguish the situation of viscous and density fingering of pure non reactive fluids. Chapter 3 reviews the literature on coupling between fingering and chemical reactions before studying the linear stability conditions as well as nonlinear dynamics of density fingering of isothermal iodate-arsenous acid fronts. This prototype nonlinear redox reaction is the first one on which experimental results on fingering in spatially extended set-ups have been obtained. We next analyze in chapter 4 the density fingering of another front producing autocatalytic system i.e. the chlorite-tetrathionate reaction in order to address the influence of the chemical kinetics on the dynamics observed. The influence of the exothermicity of the reaction is then presented in chapter 5. Eventually, chapter 6 analyzes what happens if the kinetics is now bistable and further compares the situation of both viscous and density fingering of bistable fronts. We then conclude and present suggestions for future work in this subject at the frontier between nonlinear chemistry, hydrodynamics and engineering. <p> / Agrégation de l'enseignement supérieur, Orientation sciences / info:eu-repo/semantics/nonPublished