Cette thèse est consacrée à l’enrichissement du modèle mathématique classique des structures intelligentes, en tenant compte des effets thermiques, et à son étude analytique et numérique. Il s'agit typiquement de structures se présentant sous forme de capteurs ou actionneurs, piézoélectriques et/ou magnétostrictifs, dont les propriétés dépendent de la température. On présente d'abord des résultats d'existence et unicité concernant deux problèmes posés sur un domaine tridimensionnel : le problème dynamique et le problème quasi-statique. A partir du problème quasi-statique on déduit un modèle bidimensionnel de plaque grâce à la méthode des développements asymptotiques en considérant quatre types différents de conditions aux limites, chacun visant à modéliser un comportement de type capteur et/ou actionneur. Chacun des quatre problèmes se découple en un problème membranaire et un problème de flexion. Ce dernier est un problème d'évolution qui tient compte d'un effet d'inertie de rotation. On focalise ensuite notre attention sur ce problème et on en présente une étude mathématique et numérique. L'analyse numérique est complétée avec des tests effectués sous l'environnement FreeFEM++. / This thesis is devoted to the enrichment of the usual mathematical model of smart structures, by taking into account thermal effects, and to its mathematical and numerical study. By the expression "smart structures" we refer to structures acting as sensors or actuators, whose properties depend on the temperature. We present at first the results of existence and uniqueness concerning two problems posed on a three-dimensional domain: the dynamic problem and the quasi-static problem. Based on the quasi-static problem, we infer a two-dimensional plate model by means of the asymptotic expansion method by considering four different sets of boundary conditions, each one featuring a sensor-like or an actuator-like behavior. Each of the four problems decouples into a membrane problem and a flexural problem. The latter is an evolution problem that accounts for a rotational inertia effect. Attention is then focused on this problem by presenting a mathematical and numerical study of it. Our numerical analysis is complemented with numerical tests carried out under the FreeFEM++ environment.

Calculating the price of an option commonly uses numerical methods and can becomputationally heavy. In general, longer computations result in a more precisresult. As such, improving existing models or creating new models have been thefocus in the research field. More recently the focus has instead shifted towardcreating neural networks that can predict the price of a given option directly.This thesis instead studied how the number of time-steps parameter can beoptimized, with regard to precision of the resulting price, and then predict theoptimal number of time-steps for other options. The number of time-stepsparameter determines the computation time of one of the most common models inoption pricing, the Cox-Ross-Rubinstein model (CRR). Two different methodsfor determining the optimal number of time-steps were created and tested. Bothmodels use neural networks to learn the relationship between the input variablesand the output. The first method tried to predict the optimal number oftime-steps directly. The other method instead tried to predict the parameters ofan envelope around the oscillations of the option pricing method. It wasdiscovered that the second method improved the performance of the neuralnetworks tasked with predicting the optimal number of time-steps. It was furtherdiscovered that even though the best neural network that was found significantlyoutperformed the benchmark method, there was no significant difference incalculation times, most likely because the range of log moneyness and pricesthat were used. It was also noted that the neural network tended tounderestimate the parameter and that might not be a desirable property of asystem in charge of estimating a price in the financial sector.

Inferring and anticipation of genetic networks based on experimental data and environmental measurements is a challenging research problem of mathematical modeling. In this thesis, we discuss gene-environment network models whose dynamics are represented by a class of time-continuous systems of ordinary differential equations containing unknown parameters to be optimized. Accordingly, time-discrete version of that model class is studied and improved by using different numerical methods. In this aspect, 3rd-order Heun&rsquo / s method and 4th-order classical Runge-Kutta method are newly introduced, iteration formulas are derived and corresponding matrix algebras are newly obtained. We use nonlinear mixed-integer programming for the parameter estimation and present the solution of a constrained and regularized given mixed-integer problem. By using this solution and applying the 3rd-order Heun&rsquo / s and 4th-order classical Runge-Kutta methods in the timediscretized model, we generate corresponding time-series of gene-expressions by this thesis. Two illustrative numerical examples are studied newly with an artificial data set and a realworld data set which expresses a real phenomenon. All the obtained approximate results are compared to see the goodness of the new schemes. Different step-size analysis and sensitivity tests are also investigated to obtain more accurate and stable predictions of time-series results for a better service in the real-world application areas. The presented time-continuous and time-discrete dynamical models are identified based on given data, and studied by means of an analytical theory and stability theories of rarefication, regularization and robustification.

Orientador: Philippe Remy Bernard Devloo / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-13T10:14:35Z (GMT). No. of bitstreams: 1 Lucci_PauloCesardeAlvarenga_M.pdf: 6661587 bytes, checksum: b77bb456093ce1f153056c6b2fa89626 (MD5) Previous issue date: 2009 / Resumo: Este trabalho é dedicado ao desenvolvimento de uma metodologia específica de mapeamento curvo aplicável a qualquer tipo de elemento geométrico regular. Trata-se de uma generalização do modelo matemático de representação geométrica apresentado em 1967 por Steven Anson Coons, denominado "Bilinearly Blended Coons Patches", o qual ajusta uma superfície retangular em um contorno delimitado por quatro curvas arbitrárias. A generalização proposta permitirá a utilização deste tipo de interpolação geométrica em elementos de qualquer topologia, através de uma sistemática única e consistente. / Abstract: In this work a methodology is developed for mathematical representation of curved domains, applicable to any type of finite element geometry. This methodology is a generalization of the mathematical model of a geometric representation presented in 1967 by Steven Anson Coons, called "Bilinearly Blended Coons Patches", which patch a rectangular surface in four arbitrary boundary curves. The proposed methodology is a kind of geometric transfinite interpolation applicable to elements of any topology, using a single and consistent systematic. / Mestrado / Estruturas / Mestre em Engenharia Civil