A computational study of ionic liquids used in the production of fuels and biofuels

For the past decades it has been a worldwide concern to reduce the emission of harmful gases released during the combustion of fossil fuels. This goal has been addressed through the reduction of sulfur-containing compounds, and the replacement of fossil fuels by biofuels, such as bioethanol, produced in large scale from biomass. For this purpose, a new class of solvents, the Ionic Liquids (ILs), has been applied, aiming at developing new processes and replacing common organic solvents in the current processes. ILs can be composed by a large number of different combinations of cations and anions, which confer unique but desired properties to ILs. The ability of fine-tuning the properties of ILs to meet the requirements of a specific application range by mixing different cations and anions arises as the most relevant aspect for rendering ILs so attractive to researchers. Nonetheless, due to the huge number of possible combinations between the ions it is required the use of cheap predictive approaches for anticipating how they will act in a given situation. Molecular dynamics (MD) simulation is a statistical mechanics computational approach, based on Newton’s equations of motion, which can be used to study macroscopic systems at the atomic level, through the prediction of their properties, and other structural information. In the case of ILs, MD simulations have been extensively applied. The slow dynamics associated to ILs constitutes a challenge for their correct description that requires improvements and developments of existent force fields, as well as larger computational efforts (longer times of simulation). The present document reports studies based on MD simulations devoted to disclose the mechanisms of interaction established by ILs in systems representative of fuel and biofuels streams, and at biomass pre-treatment process. Hence, MD simulations were used to evaluate different systems composed of ILs and thiophene, benzene, water, ethanol and also glucose molecules. For the latter molecules, it was carried out a study aiming to ascertain the performance of a recently proposed force field (GROMOS 56ACARBO) to reproduce the dynamic behavior of such molecules in aqueous solution. The results here reported reveal that the interactions established by ILs are dependent on the individual characteristics of each IL. Generally, the polar character of ILs is deterministic in their propensity to interact with the other molecules. Although it is unquestionable the advantage of using MD simulations, it is necessary to recognize the need for improvements and developments of force fields, not only for a successful description of ILs, but also for other relevant compounds such as the carbohydrates.

Majorantes para a ordem de subgrafos induzidos k-regulares

Muitos dos problemas de otimização em grafos reduzem-se à determinação de um subconjunto de vértices de cardinalidade máxima que induza um subgrafo k-regular. Uma vez que a determinação da ordem de um subgrafo induzido k-regular de maior ordem é, em geral, um problema NP-difícil, são deduzidos novos majorantes, a determinar em tempo polinomial, que em muitos casos constituam boas aproximações das respetivas soluções ótimas. Introduzem-se majorantes espetrais usando uma abordagem baseada em técnicas de programação convexa e estabelecem-se condições necessárias e suficientes para que sejam atingidos. Adicionalmente, introduzem-se majorantes baseados no espetro das matrizes de adjacência, laplaciana e laplaciana sem sinal. É ainda apresentado um algoritmo não polinomial para a determinação de umsubconjunto de vértices de umgrafo que induz umsubgrafo k-regular de ordem máxima para uma classe particular de grafos. Finalmente, faz-se um estudo computacional comparativo com vários majorantes e apresentam-se algumas conclusões.

Computational methods in the fractional calculus of variations and optimal control

The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their efficiency. Direct and indirect methods in solving fractional variational problems are studied in detail. Furthermore, optimality conditions are discussed for different types of unconstrained and constrained variational problems and for fractional optimal control problems. The introduced numerical methods are employed to solve some illustrative examples.

Polyhedral study of mixed integer sets arising from inventory problems

“Branch-and-cut” algorithm is one of the most efficient exact approaches to solve mixed integer programs. This algorithm combines the advantages of a pure branch-and-bound approach and cutting planes scheme. Branch-and-cut algorithm computes the linear programming relaxation of the problem at each node of the search tree which is improved by the use of cuts, i.e. by the inclusion of valid inequalities. It should be taken into account that selection of strongest cuts is crucial for their effective use in branch-and-cut algorithm. In this thesis, we focus on the derivation and use of cutting planes to solve general mixed integer problems, and in particular inventory problems combined with other problems such as distribution, supplier selection, vehicle routing, etc. In order to achieve this goal, we first consider substructures (relaxations) of such problems which are obtained by the coherent loss of information. The polyhedral structure of those simpler mixed integer sets is studied to derive strong valid inequalities. Finally those strong inequalities are included in the cutting plane algorithms to solve the general mixed integer problems. We study three mixed integer sets in this dissertation. The first two mixed integer sets arise as a subproblem of the lot-sizing with supplier selection, the network design and the vendor-managed inventory routing problems. These sets are variants of the well-known single node fixed-charge network set where a binary or integer variable is associated with the node. The third set occurs as a subproblem of mixed integer sets where incompatibility between binary variables is considered. We generate families of valid inequalities for those sets, identify classes of facet-defining inequalities, and discuss the separation problems associated with the inequalities. Then cutting plane frameworks are implemented to solve some mixed integer programs. Preliminary computational experiments are presented in this direction.