Physics and mathematics of dispersion-managed optical solitons

We review the main physical and mathematical properties of dispersion-managed (DM) optical solitons. Theory of DM solitons can be presented at two levels of accuracy: first, simple, but nevertheless, quantitative models based on ordinary differential equations governing evolution of the soliton width and phase parameter (the so-called chirp); and second, a comprehensive path-average theory that is capable of describing in detail both the fine structure of DM soliton form and its evolution along the fiber line. An analogy between DM soliton and a macroscopic nonlinear quantum oscillator model is also discussed. © 2003 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

Theoretical Investigation of Intra- and Inter-cellular Spatiotemporal Calcium Patterns in Microcirculation

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and SMC, coupled EC-SMC and a multi-cellular vessel segment with deterministic and stochastic descriptions of the cellular components were developed, and the intra- and inter-cellular spatiotemporal Ca2+ mobilization was examined. Coupled EC-SMC model simulations captured the experimentally observed localized subcellular EC Ca2+ events arising from the opening of EC transient receptor vanilloid 4 (TRPV4) channels and inositol triphosphate receptors (IP3Rs). These localized EC Ca2+ events result in endothelium-derived hyperpolarization (EDH) and Nitric Oxide (NO) production which transmit to the adjacent SMCs to ultimately result in vasodilation. The model examined the effect of heterogeneous distribution of cellular components and channel gating kinetics in determination of the amplitude and spread of the Ca2+ events. The simulations suggested the necessity of co-localization of certain cellular components for modulation of EDH and NO responses. Isolated EC and SMC models captured intracellular Ca2+ wave like activity and predicted the necessity of non-uniform distribution of cellular components for the generation of Ca2+ waves. The simulations also suggested the role of membrane potential dynamics in regulating Ca2+ wave velocity. The multi-cellular vessel segment model examined the underlying mechanisms for the intercellular synchronization of spontaneous oscillatory Ca2+ waves in individual SMC. From local subcellular events to integrated macro-scale behavior at the vessel level, the developed multi-scale models captured basic features of vascular Ca2+ signaling and provide insights for their physiological relevance. The models provide a theoretical framework for assisting investigations on the regulation of vascular tone in health and disease.

Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico

LINS, Filipe C. A. et al. Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico. In: CONGRESSO BRASILEIRO DE PESQUISA E DESENVOLVIMENTO EM PETRÓLEO E GÁS, 5. 2009, Fortaleza, CE. Anais... Fortaleza: CBPDPetro, 2009.

Flexible modeling and estimation for high-dimensional graphs

Thesis (Ph.D.)--University of Washington, 2016-08

Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico

LINS, Filipe C. A. et al. Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico. In: CONGRESSO BRASILEIRO DE PESQUISA E DESENVOLVIMENTO EM PETRÓLEO E GÁS, 5. 2009, Fortaleza, CE. Anais... Fortaleza: CBPDPetro, 2009.

Aplicação da metodologia numérica “fast bounds crack” para uma estimativa eficiente da evolução do tamanho de trinca

A significant part of the life of a mechanical component occurs, the crack propagation stage in fatigue. Currently, it is had several mathematical models to describe the crack growth behavior. These models are classified into two categories in terms of stress range amplitude: constant and variable. In general, these propagation models are formulated as an initial value problem, and from this, the evolution curve of the crack is obtained by applying a numerical method. This dissertation presented the application of the methodology "Fast Bounds Crack" for the establishment of upper and lower bounds functions for model evolution of crack size. The performance of this methodology was evaluated by the relative deviation and computational times, in relation to approximate numerical solutions obtained by the Runge-Kutta method of 4th explicit order (RK4). Has been reached a maximum relative deviation of 5.92% and the computational time was, for examples solved, 130,000 times more higher than achieved by the method RK4. Was performed yet an Engineering application in order to obtain an approximate numerical solution, from the arithmetic mean of the upper and lower bounds obtained in the methodology applied in this work, when you don’t know the law of evolution. The maximum relative error found in this application was 2.08% which proves the efficiency of the methodology "Fast Bounds Crack".

Análise estequiométrica da dinâmica não-linear de redes de reações químicas

Dissertação (mestrado)—Universidade de Brasília, Instituto de Química, Programa de Pós-Graduação em Química, 2016.

Asymptotic stability of a coupled Advection-Diffusion-Reaction system arising in bioreactor processes.

In this work, we perform an asymptotic analysis of a coupled system of two Advection-Diffusion-Reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacterias), called biomass, and a diluted organic contaminant (e.g., nitrates), called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the method of linearization to give sufficient conditions for the asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations.

Search of symmetric composition methods of symmetric integrators

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they increase the order of accuracy of a given basic numerical integration scheme. We will focus on sy-mmetric composition methods involving some basic second order symmetric integrator with different step sizes [17]. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients of these type of methods: the best method of order 8 has 17 stages [24], methods of order 8 and 15 stages were given in [29, 39, 40], 10-order methods of 31, 33 and 35 stages have been also found [24, 34]. In this work some techniques that we have built to obtain 10-order symmetric composition methods of symmetric integrators of s = 31 stages (16 order conditions) are explored. Given some starting coefficients that satisfy the simplest five order conditions, the process followed to obtain the coefficients that satisfy the sixteen order conditions is provided.

Modelagem e simulação de um sistema de bombeio mecânico em poços direcionais utilizando parâmetros concentrados

This work aims presenting the development of a model and computer simulation of a sucker rod pumping system. This system take into account the well geometry, the flow through the tubing, the dynamic behavior of the rod string and the use of a induction motor model. The rod string were modeled using concentrated parameters, allowing the use of ordinary differential equations systems to simulate it s behavior

Quantum integrability as a new method for exact results on N=2 supersymmetric gauge theories and black holes

In this thesis I show a triple new connection we found between quantum integrability, N=2 supersymmetric gauge theories and black holes perturbation theory. I use the approach of the ODE/IM correspondence between Ordinary Differential Equations (ODE) and Integrable Models (IM), first to connect basic integrability functions - the Baxter’s Q, T and Y functions - to the gauge theory periods. This fundamental identification allows several new results for both theories, for example: an exact non linear integral equation (Thermodynamic Bethe Ansatz, TBA) for the gauge periods; an interpretation of the integrability functional relations as new exact R-symmetry relations for the periods; new formulas for the local integrals of motion in terms of gauge periods. This I develop in all details at least for the SU(2) gauge theory with Nf=0,1,2 matter flavours. Still through to the ODE/IM correspondence, I connect the mathematically precise definition of quasinormal modes of black holes (having an important role in gravitational waves’ obervations) with quantization conditions on the Q, Y functions. In this way I also give a mathematical explanation of the recently found connection between quasinormal modes and N=2 supersymmetric gauge theories. Moreover, it follows a new simple and effective method to numerically compute the quasinormal modes - the TBA - which I compare with other standard methods. The spacetimes for which I show these in all details are in the simplest Nf=0 case the D3 brane in the Nf=1,2 case a generalization of extremal Reissner-Nordström (charged) black holes. Then I begin treating also the Nf=3,4 theories and argue on how our integrability-gauge-gravity correspondence can generalize to other types of black holes in either asymptotically flat (Nf=3) or Anti-de-Sitter (Nf=4) spacetime. Finally I begin to show the extension to a 4-fold correspondence with also Conformal Field Theory (CFT), through the renowned AdS/CFT correspondence.

Modeling and simulation of the anode in direct ethanol fuels cells

Mathematical modeling has been extensively applied to the study and development of fuel cells. In this work, the objective is to characterize a mechanistic model for the anode of a direct ethanol fuel cell and perform appropriate simulations. The software Comsol Multiphysics (R) (and the Chemical Engineering Module) was used in this work. The software Comsol Multiphysics (R) is an interactive environment for modeling scientific and engineering applications using partial differential equations (PDEs). Based on the finite element method, it provides speed and accuracy for several applications. The mechanistic model developed here can supply details of the physical system, such as the concentration profiles of the components within the anode and the coverage of the adsorbed species on the electrode surface. Also, the anode overpotential-current relationship can be obtained. To validate the anode model presented in this paper, experimental data obtained with a single fuel cell operating with an ethanol solution at the anode were used. (C) 2008 Elsevier B.V. All rights reserved.

Análise numérica de condensadores do tipo arame-sobre-tubo usados em refrigeradores domésticos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A model for diffusive and displacive phase transitions in steels

Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.