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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
11

Electrochemical partitioning of actinides and rare earths in molten salt and cadmium solvents : activity coefficients and equilibrium simulation /

Bechtel, Tom B. January 1997 (has links)
Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 180-182). Also available on the Internet.
12

Molecular Dynamics Study of Novel Cryoprotectants and of CO2 Capture by sI Clathrate Hydrates

Nohra, Michael January 2012 (has links)
The first project in this work used classical molecular dynamics to study the ice recrystallization inhibition potential of a series of carbohydrates and alcochols, using the hydration index, partial molar volumes and isothermal compressibilities as parameters for measuring their cryogenic efficacy. Unfortunately, after 8 months of testing, this work demonstrates that the accuracy and precision of the density extracted from simulations is not sufficient in providing accurate partial molar volumes. As a result, this work clearly demonstrates that current classical molecular dynamics technology cannot probe the volumetric properties of interest with sufficient accuracy to aid in the research and development of novel cryoprotectants.The second project in this work used molecular dynamics simulations to evaluate the Gibbs free energy change of substituting CO2 in sI clathrate hydrates by N2,CH4, SO2 and H2S flue gas impurities under conditions proposed for CO2 capture (273 K, 10 bar). Our results demonstrate that CO2 substitutions by N2 in the small sI cages were thermodynamically favored. This substitution is problematic in terms of efficient CO2 capture, since the small cages make up 25% of the sI clathrate cages, therefore a significant amount of energy could be spent on removing N2 from the flue gas rather than CO2. The thermodynamics of CO2 substitution by CH4, SO2 and H2S in sI clathrate hydrates was also examined. The substitution of CO2 by these gases in both the small and large cages were determined to be favorable. This suggests that these gases may also disrupt the CO2 capture by sI clathrate hydrates if they are present in large concentrations in the combustion flue stream. Similar substitution thermodynamics at 200 K and 10 bar were also studied. With one exception, we found that the substitution free energies do not significantly change and do not alter the sign of thermodynamics. Thus, using a lower capture temperature does not significantly change the substitution free energies and their implications for CO2 capture by sI clathrate hydrates.
13

Aplicação de métodos de otimização no cálculo de equilíbrio de misturas de biodiesel com utilização de metodologias rigorosas para estimativa de propriedades termodinâmicas / Application of optimization methods in equilibrium calculation of biodiesel blends with use of rigorous methodologies for estimation of thermodynamic properties

Borghi, Daniela de Freitas, 1983- 12 December 2014 (has links)
Orientadores: Reginaldo Guirardello, Charlles Rubber de Almeida Abreu / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química / Made available in DSpace on 2018-08-26T16:13:40Z (GMT). No. of bitstreams: 1 Borghi_DanieladeFreitas_D.pdf: 3030117 bytes, checksum: b4aac454256a7b9c27deaa4219de53e7 (MD5) Previous issue date: 2014 / Resumo: Atualmente, a produção de biodiesel tem sido objeto de estudo em diversos países devido à previsão de exaustão das fontes petrolíferas e também às suas características, já que este combustível possui vantagens ambientais em relação à emissão de gases poluentes. Trata-se de uma fonte de energia renovável e as matérias-primas para a sua produção são abundantes no Brasil. O biodiesel é produzido através da transesterificação de gordura animal ou óleo vegetal. Porém, os reagentes (óleo e etanol/metanol) e os produtos (éster metílico/etílico de ácidos graxos e glicerol) são parcialmente solúveis durante o processo. Assim, o conhecimento do equilíbrio de fases das misturas envolvidas em sua produção é um fator importante na otimização das condições da reação e da separação final dos produtos. Dentro deste contexto, o presente trabalho teve como objetivo realizar cálculos de equilíbrio de misturas de compostos envolvidos nos processos de produção de biodiesel, utilizando técnicas de otimização global. A modelagem matemática requer o conhecimento de propriedades termoquímicas de todas as espécies envolvidas e do equilíbrio de fases do sistema. Tais informações foram obtidas a partir do uso de uma metodologia utilizando o software Gaussian 03 e o método COSMO-SAC. E o equilíbrio de fases foi realizado através da minimização da energia de Gibbs do sistema. Foram obtidos perfis sigma a serem utilizados no método COSMO-SAC através do software MOPAC. Eles foram comparados com os perfis sigma de um banco de dados do grupo Virginia Tech (VT-2005) e percebeu-se que, apesar de apresentarem diferenças, qualitativamente eles possuem muitas semelhanças. Foi verificada a eficiência do modelo COSMO-SAC em predizer os coeficientes de atividade de uma mistura binária de metanol e glicerol e observou-se que os desvios médios absolutos entre os valores experimentais e os calculados estão acima de 27%, o que é um desvio muito alto. Além disso, utilizou-se a metodologia da minimização da energia de Gibbs para a realização do cálculo de equilíbrio de fases de misturas binárias contendo água, metanol e glicerol, com o auxílio da ferramenta computacional GAMS. Os desvios médios absolutos obtidos variaram de 1,55 a 7,96%, dependendo da mistura. Portanto, este modelo ainda precisa de refinamentos para se tornar uma ferramenta confiável / Abstract: Biodiesel production has been studied in several countries due to the forecast of petroleum sources depletion and to its characteristics, since this fuel has environmental advantages due to lower pollutant gas emissions. It is a renewable source of energy and raw materials for its production are abundant in Brazil. Biodiesel is produced by transesterification of vegetable oils or animal fat. However, reagents (oil and ethanol/methanol) and products (fatty acids ethyl/methyl ester and glycerol) are partially soluble in the process. Therefore, knowledge of the phase equilibrium mixtures involved in its production is an important factor in optimizing the reaction conditions and separation of the final products. In this context, this work aims to perform equilibrium calculations of mixtures of compounds involved in the biodiesel production process using global optimization techniques. Mathematical modeling requires the knowledge of thermochemical properties of all the species involved and the phase equilibrium of the system. Such information was obtained with a methodology using the Gaussian 03 software and COSMO-SAC method. The phase equilibrium was achieved by minimizing the Gibbs energy of the system. Sigma profiles to be used in COSMO-SAC method were obtained using the MOPAC software. It was compared with the sigma profiles from Virginia Tech group database (VT-2005) and it was realized that, despite having differences, qualitatively it is similar. The efficiency of COSMO-SAC model to predict the activity coefficients of a binary mixture of methanol and glycerol was verified and it was found that the average absolute deviation between experimental and calculated values are above 27%, a very high value. In addition, a methodology of Gibbs energy minimization we used to perform the calculation of the phase equilibrium of binary mixtures containing water, methanol and glycerol, with the GAMS software. The mean absolute deviations obtained ranged from 1.55 to 7.96% depending on the mixure. Therefore, this model still needs refinements to become a reliable tool / Doutorado / Engenharia Química / Doutora em Engenharia Quimica
14

Effect Of Interfacial Top Electrode Layer On The Performance Of Niobium Oxide Based Resistive Random Access Memory

Manjunath, Vishal Jain 11 July 2019 (has links)
No description available.
15

Advancing Computational High-Temperature Materials Thermodynamics with Machine Learning

Gharakhanyan, Vahe January 2024 (has links)
Mitigating climate change necessitates a rapid transition away from fossil fuels and toward renewable carbon-neutral energy sources such as wind and solar. This doctoral research addresses fundamental limitations of first-principles computational methods for the design and discovery of new processes and materials to accelerate industrial decarbonization and the global transition to a clean and sustainable energy economy by developing practical methods that build on thermodynamics and leverage foundational advances in machine learning. Recent breakthroughs in artificial intelligence for materials design and discovery aim to screen entire material libraries for desirable properties and to predict novel materials with target properties. Because of the scarcity of available thermodynamic data, designing materials for thermodynamic conditions far away from absolute zero temperature and pressure has proven particularly challenging. In principle, machine learning can speed up materials modeling by providing surrogate models, learning the relationship between structure/composition features and material properties, and training the model to predict desired properties. Due to a lack of experimental data, these models rely heavily on synthetic data from first-principles approaches such as electronic density functional theory. Designing high-temperature processes is also problematic because of the intrinsic limitations of conventional density functional theory calculations, which are strictly correct only at zero temperature. To overcome these data and methodological limitations, I integrated thermodynamic relationships with machine learning models to augment results from first-principles calculations. Additionally, I identified materials descriptor spaces that provide natural representations of structures and compositions for materials discovery. Chapter 1 introduces in more detail the motivation for this doctoral research and for the combination of computational materials thermodynamics and machine learning. Chapter 2 reviews computational materials science methods that I employed. Chapter 3 showcases how the melting temperatures of materials can be predicted with a combination of electronic structure theory and machine learning. In Chapter 4, our approach for Gibbs free energy predictions is discussed. Chapter 5 deals with the representation learning of materials, dimensionality reduction, quantifying the information content of materials representation spaces, and constructing property-aware materials descriptors. I conclude the thesis with a summary and a discussion of future directions.
16

Application of the Entropy Concept to Thermodynamics and Life Sciences: Evolution Parallels Thermodynamics, Cellulose Hydrolysis Thermodynamics, and Ordered and Disordered Vacancies Thermodynamics

Popovic, Marko 01 June 2018 (has links)
Entropy, first introduced in thermodynamics, is used in a wide range of fields. Chapter 1 discusses some important theoretical and practical aspects of entropy: what is entropy, is it subjective or objective, and how to properly apply it to living organisms. Chapter 2 presents applications of entropy to evolution. Chapter 3 shows how cellulosic biofuel production can be improved. Chapter 4 shows how lattice vacancies influence the thermodynamic properties of materials. To determine the nature of thermodynamic entropy, Chapters 1 and 2 describe the roots, the conceptual history of entropy, as well as its path of development and application. From the viewpoint of physics, thermal entropy is a measure of useless energy stored in a system resulting from thermal motion of particles. Thermal entropy is a non-negative objective property. The negentropy concept, while mathematically correct, is physically misleading. This dissertation hypothesizes that concepts from thermodynamics and statistical mechanics can be used to define statistical measurements, similar to thermodynamic entropy, to summarize the convergence of processes driven by random inputs subject to deterministic constraints. A primary example discussed here is evolution in biological systems. As discussed in this dissertation, the first and second laws of thermodynamics do not translate directly into parallel laws for the biome. But, the fundamental principles on which thermodynamic entropy is based are also true for information. Based on these principles, it is shown that adaptation and evolution are stochastically deterministic. Chapter 3 discusses the hydrolysis of cellulose to glucose, which is a key reaction in renewable energy from biomass and in mineralization of soil organic matter to CO2. Conditional thermodynamic parameters, ΔhydG', ΔhydH', and ΔhydS', and equilibrium glucose concentrations are reported for the reaction C6H10O5(cellulose) + H2O(l) ⇄ C6H12O6(aq) as functions of temperature from 0 to 100°C. Activity coefficients of aqueous glucose solution were determined as a function of temperature. The results suggest that producing cellulosic biofuels at higher temperatures will result in higher conversion. Chapter 4 presents the data and a theory relating the linear term in the low temperature heat capacity to lattice vacancy concentration. The theory gives a quantitative result for disordered vacancies, but overestimates the contribution from ordered vacancies because ordering leads to a decreased influence of vacancies on heat capacity.
17

Aplicação de simulated annealing para o calculo de equilibrio de fases de misturas complexas / Simulated annealing applied to the calculation of phase equilibria for a complex misture

Jesus, Lorena Brancaglião de 27 February 2007 (has links)
Orientadores: Reginaldo Guirardello, Lucio Cardozo-Filho / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-09T05:19:46Z (GMT). No. of bitstreams: 1 Jesus_LorenaBrancagliaode_M.pdf: 1007051 bytes, checksum: 2881509687072c829010312b1b5653e0 (MD5) Previous issue date: 2007 / Resumo: O conhecimento do equilíbrio de fases é de grande importância no projeto e análise de uma grande variedade de processos químicos, incluindo reatores e unidades de separação. É o caso, por exemplo, da indústria de produção de óleos vegetais e de produção de ácido cítrico. Geralmente, sistemas de interesse da indústria alimentícia são formados por muitos componentes. A determinação e o cálculo das propriedades termodinâmicas e do equilíbrio de fases, nesses casos, são bastante complicados. Devido à natureza não-convexa e não-linear de modelos termodinâmicos, necessários para descrever o problema do equilíbrio de fases, há um grande interesse na aplicação de técnicas de otimização para descrever o comportamento do equilíbrio. Problemas de otimização global, técnicas rápidas, seguras e robustas que têm certo grau de confiança para achar a solução global não foram ainda completamente desenvolvidos. Por isso, estudos desses métodos têm sido foco na simulação e otimização na engenharia química. Este trabalho tem como objetivo o estudo e aplicação de um método de busca estocástica para otimização global no cálculo do equilíbrio de fases de misturas complexas de sistemas de interesse da industria alimentícia. O método de busca estocástica utilizado é o algoritmo ¿simulated annealing¿ (SA) devido à sua principal vantagem em poder evitar mínimos locais (teoricamente) e de ser de fácil aplicação. A determinação do equilíbrio de fases é feita pela minimização da energia livre de Gibbs do sistema. Para a representação termodinâmica de misturas complexas de interesse da indústria alimentícia foram empregados os modelos NRTL (Non-Random-Two-Liquid) e UNIQUAC (UNIversal QUAsi-Chemical). Os dados experimentais utilizados como estudo de caso foram obtidos na literatura e foram caracterizados por meio de pseudo-componentes, uma vez que são formados por muitas substâncias diferentes. Os resultados obtidos para os casos estudados demonstraram que a aplicação da técnica de SA para minimização global da energia livre de Gibbs permite, juntamente com os modelos NRTL e UNIQUAC, a representação confiável dos dados experimentais em tempos muito bons de execução. Além disso, a técnica de SA mostrou-se robusta levando a resultados de mínimo global independentemente da estimativa inicial, mesmo para casos fortemente não-lineares e não-convexos / Abstract: In many industrial processes, during the phase of refining and separation, products form very complex mixtures. It is the case, for example, of the vegetal oil and citric acid industries. As these mixtures are formed by many components, determination and calculation of thermodynamic properties and phase equilibrium are very complicated. In this way, the use of the most rigorous methods able to calculate the phase equilibrium and to analyse the stability of phases of these mixtures becomes necessary. In this work, the determination of phase equilibrium is done by minimization of the Gibbs free energy of the system. The NRTL (Non-Random-Two-Liquid) and UNIQUAC (UNIversal QUAsi-Chemical) models were used for the thermodynamic representation of the complex mixtures, which were characterized by means of pseudo-components. Under conditions of constant temperature and pressure, the necessary and sufficient condition for a multiphase and multicomponent system to reach the equilibrium is that the Gibbs free energy is a global minimum. Based on this principle, equilibrium problems can be formulated and solved as otimization problems. The objective function for these problems is generaly highly nonlinear and usually nonconvex, and methods of global optimization are generally necessary for its minimization. The technique of global optimization studied and applied in this work is a method of random search named Simulated Annealing (SA), whose main advantages are the ability to avoid local minimum and the ease of application. The results obtained for the studied cases have demonstrated that the application of the technique of SA for global minimization of the Gibbs free energy, together with the models NRTL and UNIQUAC, allows a reliable representation of the experimental data in very short execution times. Moreover, the SA technique was robust, leading to the global minima independently of the initial estimate even for highly nonlinear and nonconvex cases / Mestrado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química
18

Análise termodinâmica da transformação de biomassa em combustíveis utilizando técnicas de otimização global / Thermodynamic analysis of biomass transformation in fuels using global optimization techniques

Freitas, Antonio Carlos Daltro de, 1986- 28 April 2015 (has links)
Orientador: Reginaldo Guirardello / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química / Made available in DSpace on 2018-08-27T12:37:15Z (GMT). No. of bitstreams: 1 Freitas_AntonioCarlosDaltrode_D.pdf: 6856921 bytes, checksum: 9a39352c311e27b7f5ddb44084565f2e (MD5) Previous issue date: 2015 / Resumo: Há um crescente interesse por fontes alternativas de energia limpa, segura e renovável, e por tecnologias de transformação destas fontes em combustíveis. Dentre esses processos, a reação de gaseificação utilizando água supercrítica (SCWG), visando a produção de hidrogênio e a reação de síntese de Fischer-Tropsch (FT) visando a produção de combustíveis líquidos, vêm ocupando papel de destaque. Nesse contexto, essa tese teve como objetivo realizar a análise termodinâmica das reações envolvidas na transformação de biomassa em combustíveis, utilizando para isso, técnicas de otimização global. Foram aplicadas as metodologias de minimização da energia de Gibbs para sistemas com pressão e temperatura constantes e de maximização da entropia para sistemas com pressão e entalpia constantes. Os problemas foram formulados na forma de programações lineares e não lineares, e as metodologias propostas foram implementadas e resolvidas no software GAMS. Primeiramente foi realizada a análise termodinâmica da transformação de diferentes fontes renováveis de energia, tais como etanol, glicerol, glicose, celulose, lignina, bagaço de cana de açúcar e biomassa microalgal, em hidrogênio ou gás de síntese por meio da reação de SCWG. Posteriormente o uso do gás de síntese produzido, foi termodinamicamente avaliado visando a produção de combustíveis líquidos, por meio da reação de síntese de Fischer-Tropsch. Com esse trabalho, contribuímos com uma maior elucidação das condições reacionais mais favoráveis para cada um dos processos analisados, estudando ainda estratégias para se obter uma maior conversão dos reagentes e aumentar a produtividade dos compostos de interesse, além de verificar o comportamento energético dos sistemas associados / Abstract: There is a growing interest in alternative sources of clean, safe and renewable energy, and in technologies for processing these sources into fuels. Among these processes, the supercritical water gasification (SCWG) reaction, for hydrogen production, and the Fischer-Tropsch (FT) synthesis reaction, for liquid fuels production, have occupied a prominent role. In this context, this thesis performed the thermodynamic analysis of reactions involved in the transformation of biomass into fuels, using for it, global optimization techniques. Methodologies are applied to minimize Gibbs energy, in systems with constant pressure and temperature, and maximize the entropy, in systems with constant pressure and enthalpy. The problems are formulated in the form of linear and nonlinear programming, and the proposed methodologies are implemented and solved in the software GAMS. The thermodynamic analysis of the transformation of different sources such as ethanol, glycerol, glucose, cellulose, lignin, sugarcane bagasse and microalgal biomass in hydrogen or syngas, through the SCWG reaction are performed first. Later, the use of syngas produced are thermodynamically evaluated for the production of liquid fuels by the Fischer-Tropsch synthesis reaction. With this work we contribute to a further elucidation of the more favorable reaction conditions for each of the cases examined, also considering strategies to increase the conversion of reactants and the productivity of the desired products, as well as the realization of the energy characterization of the processe / Doutorado / Engenharia Química / Doutor em Engenharia Química
19

Characterization of Ionic Liquid Solvents Using a Temperature Independent, Ion-Specific Abraham Parameter Model

Stephens, Timothy W. 12 1900 (has links)
Experimental data for the logarithm of the gas-to-ionic liquid partition coefficient (log K) have been compiled from the published literature for over 40 ionic liquids over a wide temperature range. Temperature independent correlations based on the Gibbs free energy equation utilizing known Abraham solvation model parameters have been derived for the prediction of log K for 12 ionic liquids to within a standard deviation of 0.114 log units over a temperature range of over 60 K. Temperature independent log K correlations have also been derived from correlations of molar enthalpies of solvation and molar entropies of solvation, each within standard deviations of 4.044 kJ mol-1 and 5.338 J mol-1 K-1, respectively. In addition, molar enthalpies of solvation and molar entropies of solvation can be predicted from the Abraham coefficients in the temperature independent log K correlations to within similar standard deviations. Temperature independent, ion specific coefficients have been determined for 26 cations and 15 anions for the prediction of log K over a temperature range of at least 60 K to within a standard deviation of 0.159 log units.
20

Análise global da estabilidade termodinâmica de misturas: um estudo com o método do conjunto gerador / Global analysis of the thermodynamic stability of mixtures: a study with the method of generating set

Joviana Sartori de Souza 13 December 2010 (has links)
O cálculo do equilíbrio de fases é um problema de grande importância em processos da engenharia, como, por exemplo, na separação por destilação, em processos de extração e simulação da recuperação terciária de petróleo, entre outros. Mas para resolvê-lo é aconselhável que se estude a priori a estabilidade termodinâmica do sistema, a qual consiste em determinar se uma dada mistura se apresenta em uma ou mais fases. Tal problema pode ser abordado como um problema de otimização, conhecido como a minimização da função distância do plano tangente à energia livre de Gibbs molar, onde modelos termodinâmicos, de natureza não convexa e não linear, são utilizados para descrevê-lo. Esse fato tem motivado um grande interesse em técnicas de otimização robustas e eficientes para a resolução de problemas relacionados com a termodinâmica do equilíbrio de fases. Como tem sido ressaltado na literatura, para proporcionar uma completa predição do equilíbrio de fases, faz-se necessário não apenas a determinação do minimizador global da função objetivo do teste de estabilidade, mas também a obtenção de todos os seus pontos estacionários. Assim, o desenvolvimento de metodologias para essa tarefa desafiadora tem se tornado uma nova área de pesquisa da otimização global aplicada à termodinâmica do equilíbrio, com interesses comuns na engenharia química e na engenharia do petróleo. O foco do presente trabalho é uma nova metodologia para resolver o problema do teste de estabilidade. Para isso, usa-se o chamado método do conjunto gerador para realizar buscas do tipo local em uma rede de pontos previamente gerada por buscas globais efetuadas com uma metaheurística populacional, no caso o método do enxame de partículas.Para se obter mais de um ponto estacionário, minimizam-se funções de mérito polarizadas, cujos pólos são os pontos previamente encontrados. A metodologia proposta foi testada na análise de quatorze misturas polares previamente consideradas na literatura. Os resultados mostraram que o método proposto é robusto e eficiente a ponto de encontrar, além do minimizador global, todos os pontos estacionários apontados previamente na literatura, sendo também capaz de detectar, em duas misturas ternárias estudadas, pontos estacionários não obtidos pelo chamado método de análise intervalar, uma técnica confiável e muito difundida na literatura. A análise do teste de estabilidade pela simples utilização do método do enxame de partículas associado à técnica de polarização mencionada acima, para a obtenção de mais de um ponto estacionário (sem a busca local feita pelo método do conjunto gerador em uma dada rede de pontos), constitui outra metodologia para a resolução do problema de interesse. Essa utilização é uma novidade secundária deste trabalho. Tal metodologia simplificada exibiu também uma grande robustez, sendo capaz de encontrar todos os pontos estacionários pesquisados. No entanto, quando comparada com a abordagem mais geral proposta aqui, observou-se que tal simplificação pode, em alguns casos onde a função de mérito apresenta uma geometria mais complexa, consumir um tempo de máquina relativamente grande, dessa forma é menos eficiente. / The phase equilibrium calculation is an important problem in engineering processes, for example, in the separation by distillation, in extraction processes, and simulation of the tertiary petroleum recovery, among others applications. But, before this calculation is advisable a phase stability analysis, which will determine if a given mixture presents one or more phases. Such stability analysis can be approached as an optimization problem, called the minimization of the tangent plane distance function to molar Gibbs free energy, where thermodynamic models, with a non-convex and also non-linear nature, are used to describe this problem. Such fact has been motivating a large interest in robust and efficient techniques for optimization of problems related with the phase equilibrium thermodynamics. As has been highlighted in the literature, in order to provide a complete prediction of the phase equilibrium, the determination of the global minimizer of the objective function related with the stability test is not enough. Is also necessary the obtaining of all its stationary points. Thus, the development of methodologies for this challenging task became a new research area of global optimization applied to the phase equilibrium thermodynamics, with common interests in chemical and petroleum engineering. The focus of the present work is a new methodology to solve the stability test problem. For such, here it is used the called Generating Set Search method, which accomplishes local searches in points of a net previously generated by an evolutionary methaheuristic, the Particle Swarm algorithm. To obtain more than one stationary point, polarized merit functions are minimized, where the poles of such merit functions are the points previously found. The methodology proposal was tested in the analysis of fourteen polar mixtures, previously considered in the literature. The results showed that the proposed method is robust and efficient, being capable to find all stationary points previously indicated in the literature, besides the global minimizers. For two ternary mixtures, it was noticed that this method detected some stationary points not obtained before by the interval analysis method, a reliable technique very diffused in the literature. The stability analysis using only the Particle Swarm algorithm together with the polarization technique (without the local search done by the Generating Set Search method) constitutes other methodology for the resolution of the problem considered here. That use is a secondary novelty of this work. This simplified methodology exhibited also a significant robustness, being capable to find all the stationary points. However, when compared with the more general approach proposed here, in some cases, where the merit function presents a more complex geometry, it was observed that such simplification can consume a relatively large computational time. Therefore, the simplified methodology is less efficient.

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