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The analysis of broadened x-ray diffraction profiles provides a useful insight into the structural properties of materials, including crystallite size and inhomogenous strain. In this work a general method for analysing broadened x-ray diffraction profiles is developed. The proposed method consists of a two-fold maximum entropy (MaxEnt) approach. Conventional deconvolution/inversion methods presently in common use are analysed and shown not to preserve the positivity of the specimen profile; these methods usually result in ill-conditioning of the solution profile. It is shown that the MaxEnt method preserves the positivity of the specimen profile and the underlying size and strain distributions, while determining the maximally noncommital solution. Moreover, the MaxEnt method incorporates any available a priori information and quantifies the uncertainties of the specimen profile and the size and strain distributions. Numerical simulations are used to demonstrate that the MaxEnt method can be applied at two levels: firstly, to determine the specimen profile, and secondly to calculate the size or strain distribution, as well as their average values. The simulations include both sizeand strain-broadened specimen profiles. The experimental conditions under which the data is recorded are also simulated by introducing instrumental broadening, a background level and statistical noise to produce the observed profile. The integrity of the MaxEnt results is checked by comparing them with the traditional results and examining problems such as deconvolving in the presence of noisy data, using non-ideal instrument profiles, and the effects of truncation and background estimation in the observed profile. The MaxEnt analysis is also applied to alumina x-ray diffraction data. It is found that the problems of determining the specimen profile, column-length and strain distributions can be solved using the MaxEnt method, with superior results compared with traditional methods. Finally, the issues of defining the a priori information in each problem and correctly characterising the instrument profile are shown to be critically important in profile analysis.

Thesis (Ph. D.)--University of Technology, Sydney, 1999.

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (leaves 155-161).

Made available in DSpace on 2014-06-11T19:32:22Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-11-20Bitstream added on 2014-06-13T18:43:41Z : No. of bitstreams: 1 mendes_rra_dr_guara.pdf: 1241082 bytes, checksum: 7ae1222297e09f373622dfd724d0cbd5 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Esta tese apresenta uma proposta inovadora com base no DOE (Design of Experiments) para tratar a otimização de portfólios multiobjetivos utilizando uma abordagem híbrida que combina arranjos de experimentos do tipo Misturas (Mixture Design of Experiments – MDE) e funções Desirability para se encontrar um portfólio ótimo modelado pelo algoritmo ARMA–GARCH. Neste tipo de estratégia experimental, as proporções investidas em cada ativo do portfólio são tratadas como fatores de um arranjo de misturas adequado para o tratamento de portfólios em geral. Ao invés de utilizar a tradicional programação matemática de portfólios de média variância (MVP), o conceito da função desirability é aqui utilizado para resolver problemas de otimização não linear multiobjetiva para a predição de valores condicionais de retorno (média), risco (variância) e entropia com suas respectivas superfícies de resposta estimadas pelo MDE. Para evitar a falta de diversificação dos portfólios, o princípio da Máxima Entropia de Shannon é incorporado ao modelo de otimização. O método fatorial de ajuste da função desirability proposto nesta tese aperfeiçoa o desempenho do algoritmo desirability conduzindo a uma eficiente alocação dos ativos no portfólio. Esta abordagem também permite a inclusão da aversão ao risco na rotina de otimização e engloba as interações (efeitos não lineares) dos efeitos entre diversos ativos enquanto reduz o esforço computacional requerido para resolver o problema de otimização não linear restrito. Para avaliar a viabilidade proposta, o método foi testado com dados reais de séries semanais do mercado mundial de preços spot de petróleo bruto. Os resultados numéricos demonstram a adequação da proposta / This thesis presents a new Design of Experiments (DOE)–based approach to treat multi– objective portfolio optimization combining Mixture Design of Experiments (MDE) and Desirability functions to find an optimal portfolio modeled by ARMA–GARCH algorithm. In this kind of experimental strategy, the design factors are treated as proportions in a mixture system considered quite adequate for treating portfolios in general. Instead of using traditional MVP mathematical programming, the concept of desirability function is here used to solve multiobjective nonlinear objective optimization problem for the predicted conditional values of return (mean), risk (variance) and entropy with their respective response surfaces estimated by MDE. To avoid the portfolio’s lack of diversity, the principle of Shannon’s maximum entropy is embodied in the optimization model. The computer–aided desirability tuning method proposed in this paper improves the desirability algorithm performance leading to an efficient assets allocation. This approach also allows the inclusion of risk aversion in the optimization routine and encompasses the interaction (nonlinear) effects among the several assets while reduces the computational effort required to solve the constrained nonlinear optimization problem. To assess the proposal feasibility, the method is tested with a real data set formed by weekly world crude oil spot prices. The numerical results verify the proposal’s adequacy

Orientador: Anderson Paulo de Paiva / Coorientador: Pedro Paulo Balestrassi / Banca: Marcela Aparecida Guerreira Machado de Freitas / Banca: Antonio Fernando Branco Costa / Banca: Rafael Coradi Leme / Banca: João Roberto Ferreira / Resumo: Esta tese apresenta uma proposta inovadora com base no DOE (Design of Experiments) para tratar a otimização de portfólios multiobjetivos utilizando uma abordagem híbrida que combina arranjos de experimentos do tipo Misturas (Mixture Design of Experiments - MDE) e funções Desirability para se encontrar um portfólio ótimo modelado pelo algoritmo ARMA-GARCH. Neste tipo de estratégia experimental, as proporções investidas em cada ativo do portfólio são tratadas como fatores de um arranjo de misturas adequado para o tratamento de portfólios em geral. Ao invés de utilizar a tradicional programação matemática de portfólios de média variância (MVP), o conceito da função desirability é aqui utilizado para resolver problemas de otimização não linear multiobjetiva para a predição de valores condicionais de retorno (média), risco (variância) e entropia com suas respectivas superfícies de resposta estimadas pelo MDE. Para evitar a falta de diversificação dos portfólios, o princípio da Máxima Entropia de Shannon é incorporado ao modelo de otimização. O método fatorial de ajuste da função desirability proposto nesta tese aperfeiçoa o desempenho do algoritmo desirability conduzindo a uma eficiente alocação dos ativos no portfólio. Esta abordagem também permite a inclusão da aversão ao risco na rotina de otimização e engloba as interações (efeitos não lineares) dos efeitos entre diversos ativos enquanto reduz o esforço computacional requerido para resolver o problema de otimização não linear restrito. Para avaliar a viabilidade proposta, o método foi testado com dados reais de séries semanais do mercado mundial de preços spot de petróleo bruto. Os resultados numéricos demonstram a adequação da proposta / Abstract: This thesis presents a new Design of Experiments (DOE)-based approach to treat multi- objective portfolio optimization combining Mixture Design of Experiments (MDE) and Desirability functions to find an optimal portfolio modeled by ARMA-GARCH algorithm. In this kind of experimental strategy, the design factors are treated as proportions in a mixture system considered quite adequate for treating portfolios in general. Instead of using traditional MVP mathematical programming, the concept of desirability function is here used to solve multiobjective nonlinear objective optimization problem for the predicted conditional values of return (mean), risk (variance) and entropy with their respective response surfaces estimated by MDE. To avoid the portfolio's lack of diversity, the principle of Shannon's maximum entropy is embodied in the optimization model. The computer-aided desirability tuning method proposed in this paper improves the desirability algorithm performance leading to an efficient assets allocation. This approach also allows the inclusion of risk aversion in the optimization routine and encompasses the interaction (nonlinear) effects among the several assets while reduces the computational effort required to solve the constrained nonlinear optimization problem. To assess the proposal feasibility, the method is tested with a real data set formed by weekly world crude oil spot prices. The numerical results verify the proposal's adequacy / Doutor

Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2009 / Fluid Mechanics is the study of fluids either at rest (fluids static) or in motion (fluids dynamics and kinematics) and the subsequent effects of the fluids upon the boundaries which may be either solid surfaces or interfaces with other fluids. It is worth noting that both gases and liquids are classified as fluids according to Batchelor [8]. Fluids, unlike solids, lack ability to offer sustained resistance to a deforming force. Thus, a fluid is a substance which deforms continuously under the action of shearing forces, however small they may be. Deformation is caused by shearing forces - forces that act tangentially to the surfaces to which they are applied according to Douglas et al. [23].

The basic objective of this paper is to compare two entropy formulae used as objective functions in spatial intreraction modelling. This is carried out by comparing some attributes of the interaction models derived from both of them. The comparison results in the design of the third formula, which, however, represents a slight modification of one of them. (author's abstract) / Series: Discussion Papers of the Institute for Economic Geography and GIScience

Local Maximum Entropy (LME) method is an approximation technique which has been known to have good approximation characteristics. This is due to its non-negative shape functions and the weak Kronecker delta property which allow the solutions to be continuous and smooth as compared to the Moving Least Square method (MLS) which is used in the Element Free Galerkin method (EFG). The method is based on a convex optimisation scheme where a non-linear equation is solved with the help of a Newton algorithm, implemented in an in-house code called SESKA. In this study, the aim is to compare LME and MLS and highlight the differences. Preliminary benchmark tests of LME are found to be very conclusive. The method is able to approximate deformation of a cantilever beam with higher accuracy as compared to MLS. Moreover, its rapid convergence rate, based on a Cook's membrane problem, demonstrated that it requires a relatively coarser mesh to reach the exact solution. With those encouraging results, LME is then applied to a larger non-linear cardiac mechanics problem. That is simulating a healthy and a myocardial infarcted canine left ventricle (LV) during one heart beat. The LV is idealised by a prolate spheroidal ellipsoid. It undergoes expansion during the diastolic phase, addressed by a non-linear passive stress model which incorporates the transversely isotropic properties of the material. The contraction, during the systolic phase, is simulated by Guccione's active stress model. The infarct region is considered to be non-contractile and twice as stiff as the healthy tissue. The material loss, especially during the necrotic phase, is incorporated by the use of a homogenisation approach. Firstly, the loss of the contraction ability of the infarct region counteracts the overall contraction behaviour by a bulging deformation where the occurrence of high stresses are noted. Secondly, with regards to the behaviour of LME, it is found to feature high convergence rate and a decrease in computation time with respect to MLS. However, it is also observed that LME is quite sensitive to the nodal spacing in particular for an unstructured nodal distribution where it produces results that are completely unreliable.

Structural material fatigue is a leading cause of failure and has motivated fatigue-resistant design to eliminate risks to human lives. Intrinsic microstructural features alter fatigue deformation mechanisms so profoundly that, essentially, fatigue properties of structural materials become deviant. With this in mind, we initiated this project to investigate the microstructural effect on fatigue behavior of potential structural high entropy alloys. With a better understanding of the effect of microstructure features on fatigue properties, the ultimate goal was to engineer the microstructure to enhance the fatigue life of structural materials. The effects of two major deformation mechanisms presented here are twinning-induced fatigue crack retardation, and transformation-induced fatigue crack retardation. The fundamental principle of both mechanisms is to delay the fatigue crack propagation rate by altering the work hardening ability locally within the crack plastic zone. In ultrafine grained triplex Al0.3CoCrFeNi, nano-sized deformation twins were observed during cyclic loading in FCC matrix due to low stacking fault energy (SFE). The work-hardening ability of the material near the crack was sustained with the formation of twins according to Considere's criteria. Further, due to the ultrafine-grained (UFG) nature of the material, fatigue runout stress was enhanced. In a coarse-grained, dual-phase high entropy alloy, persistent slip bands formed in FCC matrix during cyclic loading due mainly to the slight composition change that affects the SFE in the FCC matrix and eventually alters the deformation mechanism. Another way known to alter an alloy's work hardening (WH) ability is transformation-induced plasticity (TRIP). In some alloys, phase transformation happens due to strain localization, which alters the work-hardening ability. iii In a fine-grained, dual-phase metastable high entropy alloy, gamma (f.c.c.) to epsilon (h.c.p.) transformation occurred in the plastic zone that was induced from cracks. Thus, we designed a Cu-containing FeMnCoCrSi high entropy alloy that exhibited a normalized fatigue ratio of ~ 0.62 UTS (ultimate tensile strength). Our design approach was based on (a) engineering the gamma phase stability to attain sustained work hardening through delayed gamma (f.c.c.) to epsilon (h.c.p.) transformation to hinder fatigue crack propagation, (b) incorporating an ultrafine-grained microstructure to delay crack initiation, and (c) forming deformation twins to reduce the crack propagation rate. We verified that a UFG gamma dominant microstructure could provide opportunities for exceptional fatigue resistance, as sustained WH activity strengthened the material locally in the crack plastic zone, thereby validating our expectation that the combination of UFG and TRIP is a path to design the next generation of fatigue-resistant alloys.