Disertacijoje nagrinėjami modeliai, aprašantys dviejų ir trijų reagentų chemines sintezes aukštose temperatūrose. Darbe pristatomos reagentų koncentracijų dinamiką aprašančios diferencialinių lygčių sistemos, sintezės parametrų skaičiavimo metodai bei parametrų paieškos lygiagretinimo algoritmas. Konkretūs skaičiavimai atlikti ir rezultatai pateikti remiantis realių laboratorinių eksperimentų duomenimis itrio aliuminio granato (du reagentai) bei sintetinio kalcio hydroksiapatito (trys reagentai) sintezių atvejais. / The dissertation deals with models describing two- and three-reactant chemical syntheses at high temperatures. The work presents the differential equation systems describing the dynamics of concentrations of reactants, methods for calculation of synthesis parameters, and a parallelization algorithm for faster search of parameters. Concrete calculations were performed and the results presented on the basis of data from real laboratory experiments of syntheses of yttrium aluminum garnet (two reactants) and synthetic calcium hydroxyapatite (three reactants).

Orientadores: Hyun Mo Yang, Norberto Anibal Maidana / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T00:06:51Z (GMT). No. of bitstreams: 1 Malaquias_AngeloMiguel_D.pdf: 3743949 bytes, checksum: d321f27ce84d0589990109a3ee8d2ab3 (MD5) Previous issue date: 2012 / Resumo: Esta tese tem como objetivo abordar, matematicamente, a mutação do vírus da imunodeficiência humana (HIV) por meio de um processo de difusão e advecção. é dividida em três partes: estudo e compreensão do fenômeno biológico; formulação e análise de um primeiro sistema de equações diferenciais ordinárias para estudar o tema e, finalmente, construção e análise de um modelo de equações diferenciais parciais envolvendo a mutação. Os modelos são formulados com base em características biológicas, e procurando, sempre que possível, estabelecer um paralelo entre Biologia e Matemática. Com o modelo de equações diferenciais ordinárias mostrou-se que um sistema imunológico que perde sua capacidade de resposta permite a persistência do vírus HIV no organismo infectado. Também, do modelo com equações diferenciais parciais, concluímos que usar as próprias mutações para combater o vírus pode ser uma alternativa, assim como na idéia de mutagênese letal / Abstract: The aim of this thesis is to study mathematically the mutation of the human immunodeficiency virus (HIV) taking into account the process of diffusion and advection. The thesis is divided in three parts: the current understand of the HIV biology; formulation and analysis of a system of ordinary differential equations to understanding the persistent HIV infection; and, finally, construction and analysis of a model of partial differential equations considering the mutation. The models are formulated based on biological characteristics and whenever it is possible, a parallel between biology and mathematics was established. From system of ordinary differential equations, the persistent HIV infection can be explained by exhausting immune system response. From partial differential equations, the main conclusion is that mutations themselves can be used to fight the virus based on the idea of lethal mutagenesis / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

On considère l'équation de convection--diffusion--réaction instationnaire. On s'intéresse à la dérivation d'estimations d'erreur a posteriori pour la discrétisation de cette équation par la méthode des volumes finis centrés par mailles en espace et un schéma d'Euler implicite en temps. Les estimations, qui sont établies dans la norme d'énergie, bornent l'erreur entre la solution exacte et une solution post-traitée à l'aide de reconstructions $Hdiv$-conformes du flux diffusif et du flux convectif, et d'une reconstruction $H^1_0(Omega)$-conforme du potentiel. On propose un algorithme adaptatif qui permet d'atteindre une précision relative fixée par l'utilisateur en raffinant les maillages adaptativement et en équilibrant les contributions en espace et en temps de l'erreur. On présente également des essais numériques. Enfin, on dérive une estimation d'erreur a posteriori dans la norme d'énergie augmentée d'une norme duale de la dérivée en temps et de la partie antisymétrique de l'opérateur différentiel. Cette nouvelle estimation est robuste dans des régimes dominés par la convection et des bornes inférieures locales en temps et globales en espace sont également obtenues / We consider the time-dependent convection--diffusion--reaction equation. We derive a posteriori error estimates for the discretization of this equation by the cell-centered finite volume scheme in space and a backward Euler scheme in time. The estimates are established in the energy norm and they bound the error between the exact solution and a locally post processed approximate solution, based on $Hdiv$-conforming diffusive and convective flux reconstructions, as well as an $H^1_0(Omega)$-conforming potential reconstruction. We propose an adaptive algorithm which ensures the control of the total error with respect to a user-defined relative precision by refining the meshes adaptively while equilibrating the time and space contributions to the error. We also present numerical experiments. Finally, we derive another a posteriori error estimate in the energy norm augmented by a dual norm of the time derivative and the skew symmetric part of the differential operator. The new estimate is robust in convective-dominated regimes and local-in-time and global-in-space lower bounds are also derived

Orientador: José Luiz Boldrini / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T18:40:32Z (GMT). No. of bitstreams: 1 Oliveira_AndreaGenovesede_M.pdf: 1278255 bytes, checksum: f16ace92e18ff9cf5e8a4f8a66829f47 (MD5) Previous issue date: 2012 / Resumo: Analisamos um sistema não linear parabólico de reação-difusão com duas equações definidas em ]0,T[x'ômega', (0 < T < 'infinito' e Q 'pertence' R³ limitado) e condições de fronteira do tipo Neumann. Tal sistema foi proposto para modelar o movimento de uma população de amebas unicelulares e tem como base o processo de locomoção chamado quimiotaxia positiva, na qual as amebas se movimentam em direção à região de alta concentração de uma certa substância química, que, neste caso, é produzida pelas próprias amebas. Embora adicionando os detalhes técnicos, este trabalho seguiu livremente o método de resolução proposto no artigo de A. Boy, Analysis for a System of Coupled Reaction-Diffusion Parabolic Equations Arising in Biology, Computers Math. Applic. Vol. 32, No. 4, páginas 15-21, 1996 / Abstract: We will be analyzing a nonlinear parabolic reaction diffusion system with two equations, defined in ]0,T[x'omega', (0 < T < 'infinite' and Q 'belongs' R³) with Neumann boundary conditions. This system was proposed in order to model the movement of a population of single-cell amoebae and is based on the process of movement called chemotaxis, in which the amoebae move in the direction of the region of high concentration of a certain chemical substance, which, in this case, is produced by the amoebae themselves.While adding the technical details, this dissertation followed freely the solution method proposed in the paper: A. Boy, Analysis for a System of Coupled Reaction-Diffusion Parabolic Equations Arising in Biology, Computers Math. Applic. Vol. 32, No. 4, pages 15-21, 1996 / Mestrado / Matematica / Mestre em Matemática

Dans cette thèse, nous avons concentré notre étude sur les mécanismes qui génèrent la polarité cellulaire, en particulier dans le cas de la migration cellulaire. Malgré les derniers développements concernant l’observation de l’activité des RhoGTPases, les principes qui dictent la capacité des cellules à coordonner plusieurs modules de signalisation en parallèle ne sont toujours pas compris. L’optogénétique est un outil d’intérêt pour disséquer ces réseaux de signalisation à partir de la création d’une perturbation dont les caractéristiques spatiotemporelles sont contrôlées. Tout d’abord, à partir de la caractérisation des différents processus biophysiques en jeu, nous avons établi les relations quantitatives entre l’illumination et les gradients moléculaires que l’on induit. Nous avons déterminé qu’il est possible de créer des gradients subcellulaires avec une résolution spatiale de l’ordre de 5 μm et temporelle d’environ 3 minutes Ensuite, nous avons utilisé cette approche optogénétique pour contrôler l’activité de Cdc42, Rac1 et RhoA. Nous avons caractérisé les effets subcellulaires de l’activation de ces RhoGTPases en utilisant l’activité de membrane, les changements de forme cellulaire et leurs déplacements comme rapporteurs de la polarisation et de la migration. Nous avons ainsi montré qu’une activation locale de RhoGTPase permet la réorganisation interne des cellules jusqu’à générer un phénotype de migration.Enfin, nous avons caractérisé les effets d’une activation locale de RhoA sur différents acteurs moléculaires comme les points focaux d’adhésion, l’actine et les moteurs moléculaires myosines. Nous avons mesuré alors la dynamique de l’intégration des points focaux dans le cytosquelette et analysé la réponse du réseau d’acto-myosine au cours d’évènements de rétraction.Notre approche optogénétique couple le contrôle d’une perturbation à la mesure de la réponse cellulaire simultanément de manière directe et reproductible. Elle apporte une méthode pour contrôler la polarité cellulaire et une manière de disséquer des réseaux de signalisation à l’échelle subcellulaire. / In this thesis we focus on the mechanisms that establish cell polarization, particularly during cell migration. Despite latest developments that enable visualization of RhoGTPases activity, the underlying principles dictating the cell’s ability to coordinates multiple signaling modules is still unclear. Optogenetic methods have been recognized as promising tools to dissect these intracellular signaling networks by allowing perturbations to be spatially and temporally controlled. We established the quantitative relationship between illumination patterns and the corresponding gradients of induced signaling activity through the characterization of the biophysical properties of CRY2/CIBN. We determined that it is possible to create subcellular gradients of recruited proteins of different shapes of choice up to spatial resolutions of 5μm and temporal ones of ca. 3 minutes.We applied the aforementioned optogenetic approach as a means to perturb the activity of cdc42, Rac1 and RhoA. We characterized the effects of subcellular activation of those RhoGTPases using membrane activity, cell shape changes and cell displacement as reporters of cell polarization and migration. We show that localized activation of RhoGTPases can trigger cellular organization and drive the cell into a migrating state.We also characterized the effects of local activation of RhoA on different cellular effectors as focal adhesion complexes, actin filaments and myosin molecular motors. We measured the dynamics of the newly formed focal adhesion complexes and the acto-myosin complex during retraction events.Altogether, our optogenetic methodology enables simultaneous measurement of the imposed perturbation and the cell response in a straightforward and reproducible way. It provides a quantitative way to control cell polarity and a step forward in the dissection of subcellular signaling networks.

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In this work, we design a linear, two step implicit finite difference method to approximate the solutions of a biological system that describes the interaction between a microbial colony and a surrounding substrate. Three separate models are analyzed, all of which can be described as systems of partial differential equations (PDE)s with nonlinear diffusion and reaction, where the biological colony grows and decays based on the substrate bioavailability. The systems under investigation are all complex models describing the dynamics of biological films. In view of the difficulties to calculate analytical solutions of the models, we design here a numerical technique to consistently approximate the system evolution dynamics, guaranteeing that nonnegative initial conditions will evolve uniquely into new, nonnegative approximations. This property of our technique is established using the theory of M-matrices, which are nonsingular matrices where all the entries of their inverses are positive numbers. We provide numerical simulations to evince the preservation of the nonnegative character of solutions under homogeneous Dirichlet and Neumann boundary conditions. The computational results suggest that the method proposed in this work is stable, and that it also preserves the bounded character of the discrete solutions.

We present the analysis for the higher order continuous Galerkin−Petrov (cGP) time discretization schemes in combination with the one-level local projection stabilization in space applied to time-dependent convection-diffusion-reaction problems. Optimal a priori error estimates will be proved. Numerical studies support the theoretical results. Furthermore, a numerical comparison between continuous Galerkin−Petrov and discontinuous Galerkin time discretization schemes will be given.

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