Thesis--Ph. D., University of Hong Kong, 1987.

Thesis (Ph.D.) - University of Glasgow, 2008. / Ph.D. thesis submitted to the Faculty of Information and Mathematical Sciences, Department of Statistics, 2008. Includes bibliographical references. Print version also available.

Made available in DSpace on 2015-05-14T13:21:37Z (GMT). No. of bitstreams: 1 parte1.pdf: 2426440 bytes, checksum: ed3c18b465357e2c561cffbd380b983f (MD5) Previous issue date: 2008-07-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The chemiluminescence (CL) of luminol-cobalt(II) reaction has been used in analytical systems for capillary electrophoresis, chromatography, -TAS (microTotal Analysis System), etc. Even with the diversity of applications, the steps of this reaction have not been completely elucidated and have been still a subject of research and controversy. Many works reported only to the isolated studies of the influence of each variable in the luminol-cobalt(II) reaction and, as such studies do not consider the interactions among variables, they do not exploit the total performance of this reaction in order to increase the chemiluminescent intensity (ICL). In this context, the use of an experimental design and a ChemiLumimetric Flow-Batch System (CLFBS) is proposed in this work in order to study and to optimize this reaction, aiming at to develop an automatic method to determine vitamin B12 (VB12) in drugs. For optimization purpose, a 24 factorial design was carried out fixing the cobalt concentration at 3.0 g L-1 and varying the concentration of luminol, hydrogen peroxide, sodium hydroxide and the order of mixture of these reagents. Sixteen assays were performed in five replicates, generating a total of eighty experiments. The analysis using normal plot of the experimental design revealed that the luminol concentration and the order of mixture of the reagents are variables more important than the NaOH or H2O2 concentrations to luminol-cobalt(II) reaction. These two parameters were responsible to enhance the chemiluminescent signal in about 80%. Another study was carried out in order to evaluate the CLFBS performance by using the optimized variables which were suggested by the factorial design study. Calibration curves were built by using standard solution of Co(II) and VB12 and the analytical parameters for Co(II) curve were: ΔICL = -21.39 +1771.37[Co2+] (r2 = 0.9996), LD and LQ = 12.0 ng L-1, RSD = 1.8% (n = 5), analytical sensitivity = 1947.29 W/g L-1; and VB12 curve were: ΔICL = -186.71 + 12.90 [VB12] (r2 = 0.9999), LD = 14.53 mg L-1 and LQ = 14.70 mg L-1, RSD = 2.1% (n = 4) and analytical sensitivity = 10.76 W/μg L-1. The results of the vitamin B12 analysis in drug samples employing the luminol-cobalt(II) reaction and CLFBS were enough satisfactory. Relative errors smaller than 4% were obtained by using curve calibration or standard addition method. The recovery studies yield very good values, which were of 97 to 103%. In addition, a good agreement was obtained when a drug sample was analyzed by the proposed and the reference (HPLC) method. Thus, the automatic chemilumimetric method, which was here developed and optimized, can be considered a promising alternative to quality control of vitamin B12 in drugs. / A quimiluminescência (QL) da reação luminol-cobalto(II) vem sendo empregada em sistemas analíticos de eletroforese capilar, cromatografia, -TAS (microTotal Analysis System), etc. Mesmo com a diversidade de aplicações, essa reação possui etapas pouco elucidadas que continuam sendo alvo de pesquisas e polêmicas. Muitos trabalhos relatam apenas estudos isolados da influência de cada variável na reação luminol-cobalto(II) e, por não considerar as interações entre as variáveis, estes estudos não exploram ao máximo a performance analítica desta reação. Neste contexto, foi proposto neste trabalho o uso de um planejamento experimental e de um Sistema Quimilumimétrico Fluxo-Batelada (SQLFB) para o estudo e a otimização desta reação com vista a desenvolver um método automático para a determinação de vitamina B12 (VB12) em medicamentos. Na otimização, foi utilizado um planejamento fatorial 24 em que foi mantido constante a concentração de cobalto(II) em 3,0 g L-1 enquanto variou-se as concentrações de luminol, peróxido de hidrogênio, hidróxido de sódio e a ordem de mistura destes constituintes. Foram efetuados dezesseis ensaios em quintuplicata, perfazendo um total de 80 experimentos realizados. A análise usando o gráfico normal do planejamento experimental revelou que a concentração de luminol ([Lu]) e a ordem da mistura (OM) dos reagentes são variáveis mais importante do que a concentração de NaOH e H2O2 para a reação luminol-cobalto(II). Ambas variáveis [Lu] e OM foram responsáveis por aumentar o sinal quimiluminescente em cerca de 80%. Um outro estudo foi realizado para avaliar a performance do SQLFB, empregando as variáveis otimizadas que foram sugeridas pelo estudo do planejamento fatorial. Curvas de calibração foram construídas utilizando soluções padrão de Co(II) e de VB12 e os parâmetros analíticos para a curva Co(II) foram: ΔIQL=-21,39+1771,37[Co2+](r2 = 0,9996), LD=1,54 ng L-1 e LQ=5,13 ng L-1, DPR=1,8% (n=5) e sensibilidade analítica=1947,29 Watts/μg L-1; e para a curva VB12 foram: ΔIQL= -186,71 + 12,90[VB12] (r2 = 0,9999), LD=0,89 μg L-1 e LQ = 2,98 μg L-1, DPR=2,1% (n=4) e sensibilidade analítica=10,76 Watts/μg L-1. Os resultados obtidos nas análises de vitamina B12 em medicamentos empregando a reação luminol-cobalto(II) e o SQLFB foram bastante satisfatórios. Erros relativos menores do que 4% foram obtidos empregando as técnicas de curva de calibração e de adição de padrão. Em estudos de recuperação, os valores foram também muito bons, ficando entre 97 e 103%. Além disso, uma boa concordância entre os resultados foi obtida quando uma amostra foi analisada empregando o método aqui proposto e o método de referência (HPLC). Portanto, o método quimilumimétrico automático aqui desenvolvido e otimizado pode ser considerado uma alternativa promissora para o controle de qualidade de vitamina B12 em medicamentos.

This thesis addresses issues related to the simulation and optimization of the injection molding of short fiber-reinforced plastics (SFRPs). The injection molding process is modeled by a two phase flow problem. The simulation of the two phase flow is accompanied by the solution of the Folgar-Tucker equation (FTE) for the simulation of the moments of fiber orientation densities. The FTE requires the solution of the so called 'closure problem'', i.e. the representation of the 4th order moments in terms of the 2nd order moments. In the absence of fiber-fiber interactions and isotropic initial fiber density, the FTE admits an analytical solution in terms of elliptic integrals. From these elliptic integrals, the closure problem can be solved by a simple numerical inversion. Part of this work derives approximate inverses and analytical inverses for special cases of fiber orientation densities. Furthermore a method is presented to generate rational functions for the computation of arbitrary moments in terms of the 2nd order closure parameters. Another part of this work treats the determination of effective material properties for SFRPs by the use of FFT-based homogenization methods. For these methods a novel discretization scheme, the 'staggered grid'' method, was developed and successfully tested. Furthermore the so called 'composite voxel'' approach was extended to nonlinear elasticity, which improves the approximation of material properties at the interfaces and allows the reduction of the model order by several magnitudes compared to classical approaches. Related the homogenization we investigate optimal experimental designs to robustly determine effective elastic properties of SFRPs with the least number of computer simulations. Finally we deal with the topology optimization of injection molded parts, by extending classical SIMP-based topology optimization with an approximate model for the fiber orientations. Along with the compliance minimization by topology optimization we also present a simple shape optimization method for compensation of part warpage for an black-box production process.:Acknowledgments v Abstract vii Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Nomenclature 3 Chapter 2. Numerical simulation of SFRP injection molding 5 2.1 Introduction 5 2.2 Injection molding technology 5 2.3 Process simulation 6 2.4 Governing equations 8 2.5 Numerical implementation 18 2.6 Numerical examples 25 2.7 Conclusions and outlook 27 Chapter 3. Numerical and analytical methods for the exact closure of the Folgar-Tucker equation 35 3.1 Introduction 35 3.2 The ACG as solution of Jeffery's equation 35 3.3 The exact closure 36 3.4 Carlson-type elliptic integrals 37 3.5 Inversion of R_D-system 40 3.6 Moment tensors of the angular central Gaussian distribution on the n-sphere 49 3.7 Experimental evidence for ACG distribution hypothesis 54 3.8 Conclusions and outlook 60 Chapter 4. Homogenization of SFRP materials 63 4.1 Introduction 63 4.2 Microscopic and macroscopic model of SFRP materials 63 4.3 Effective linear elastic properties 65 4.4 The staggered grid method 68 4.5 Model order reduction by composite voxels 80 4.6 Optimal experimental design for parameter identification 93 Chapter 5. Optimization of parts produced by SFRP injection molding 103 5.1 Topology optimization 103 5.2 Warpage compensation 110 Chapter 6. Conclusions and perspectives 115 Appendix A. Appendix 117 A.1 Evaluation of R_D in Python 117 A.2 Approximate inverse for R_D in Python 117 A.3 Inversion of R_D using Newton's/Halley's method in Python 117 A.4 Inversion of R_D using fixed point method in Python 119 A.5 Moment computation using SymPy 120 A.6 Fiber collision test 122 A.7 OED calculation of the weighting matrix 123 A.8 OED Jacobian of objective and constraints 123 Appendix B. Theses 125 Bibliography 127 / Diese Arbeit befasst sich mit Fragen der Simulation und Optimierung des Spritzgießens von kurzfaserverstärkten Kunststoffen (SFRPs). Der Spritzgussprozess wird durch ein Zweiphasen-Fließproblem modelliert. Die Simulation des Zweiphasenflusses wird von der Lösung der Folgar-Tucker-Gleichung (FTE) zur Simulation der Momente der Faserorientierungsdichten begleitet. Die FTE erfordert die Lösung des sogenannten 'Abschlussproblems'', d. h. die Darstellung der Momente 4. Ordnung in Form der Momente 2. Ordnung. In Abwesenheit von Faser-Faser-Wechselwirkungen und anfänglich isotroper Faserdichte lässt die FTE eine analytische Lösung durch elliptische Integrale zu. Aus diesen elliptischen Integralen kann das Abschlussproblem durch eine einfache numerische Inversion gelöst werden. Ein Teil dieser Arbeit leitet approximative Inverse und analytische Inverse für spezielle Fälle von Faserorientierungsdichten her. Weiterhin wird eine Methode vorgestellt, um rationale Funktionen für die Berechnung beliebiger Momente in Bezug auf die Abschlussparameter 2. Ordnung zu generieren. Ein weiterer Teil dieser Arbeit befasst sich mit der Bestimmung effektiver Materialeigenschaften für SFRPs durch FFT-basierte Homogenisierungsmethoden. Für diese Methoden wurde ein neuartiges Diskretisierungsschema 'staggerd grid'' entwickelt und erfolgreich getestet. Darüber hinaus wurde der sogenannte 'composite voxel''-Ansatz auf die nichtlineare Elastizität ausgedehnt, was die Approximation der Materialeigenschaften an den Grenzflächen verbessert und die Reduzierung der Modellordnung um mehrere Größenordnungen im Vergleich zu klassischen Ansätzen ermöglicht. Im Zusammenhang mit der Homogenisierung untersuchen wir optimale experimentelle Designs, um die effektiven elastischen Eigenschaften von SFRPs mit der geringsten Anzahl von Computersimulationen zuverlässig zu bestimmen. Schließlich beschäftigen wir uns mit der Topologieoptimierung von Spritzgussteilen, indem wir die klassische SIMP-basierte Topologieoptimierung um ein Näherungsmodell für die Faserorientierungen erweitern. Neben der Compliance-Minimierung durch Topologieoptimierung stellen wir eine einfache Formoptimierungsmethode zur Kompensation von Teileverzug für einen Black-Box-Produktionsprozess vor.:Acknowledgments v Abstract vii Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Nomenclature 3 Chapter 2. Numerical simulation of SFRP injection molding 5 2.1 Introduction 5 2.2 Injection molding technology 5 2.3 Process simulation 6 2.4 Governing equations 8 2.5 Numerical implementation 18 2.6 Numerical examples 25 2.7 Conclusions and outlook 27 Chapter 3. Numerical and analytical methods for the exact closure of the Folgar-Tucker equation 35 3.1 Introduction 35 3.2 The ACG as solution of Jeffery's equation 35 3.3 The exact closure 36 3.4 Carlson-type elliptic integrals 37 3.5 Inversion of R_D-system 40 3.6 Moment tensors of the angular central Gaussian distribution on the n-sphere 49 3.7 Experimental evidence for ACG distribution hypothesis 54 3.8 Conclusions and outlook 60 Chapter 4. Homogenization of SFRP materials 63 4.1 Introduction 63 4.2 Microscopic and macroscopic model of SFRP materials 63 4.3 Effective linear elastic properties 65 4.4 The staggered grid method 68 4.5 Model order reduction by composite voxels 80 4.6 Optimal experimental design for parameter identification 93 Chapter 5. Optimization of parts produced by SFRP injection molding 103 5.1 Topology optimization 103 5.2 Warpage compensation 110 Chapter 6. Conclusions and perspectives 115 Appendix A. Appendix 117 A.1 Evaluation of R_D in Python 117 A.2 Approximate inverse for R_D in Python 117 A.3 Inversion of R_D using Newton's/Halley's method in Python 117 A.4 Inversion of R_D using fixed point method in Python 119 A.5 Moment computation using SymPy 120 A.6 Fiber collision test 122 A.7 OED calculation of the weighting matrix 123 A.8 OED Jacobian of objective and constraints 123 Appendix B. Theses 125 Bibliography 127