Hybrid modeling of convective laminar flow in a permeable tube associated with the cross-flow process

The confined flows in tubes with permeable surfaces arc associated to tangential filtration processes (microfiltration or ultrafiltration). The complexity of the phenomena do not allow for the development of exact analytical solutions, however, approximate solutions are of great interest for the calculation of the transmembrane outflow and estimate of the concentration, polarization phenomenon. In the present work, the generalized integral transform technique (GITT) was employed in solving the laminar and permanent flow in permeable tubes of Newtonian and incompressible fluid. The mathematical formulation employed the parabolic differential equation of chemical species conservation (convective-diffusive equation). The velocity profiles for the entrance region flow, which are found in the connective terms of the equation, were assessed by solutions obtained from literature. The velocity at the permeable wall was considered uniform, with the concentration at the tube wall regarded as variable with an axial position. A computational methodology using global error control was applied to determine the concentration in the wall and concentration boundary layer thickness. The results obtained for the local transmembrane flux and the concentration boundary layer thickness were compared against others in literature. (C) 2007 Elsevier B.V. All rights reserved.

Determination of the components of the gyration tensor of quartz by oblique incidence transmission two-modulator generalized ellipsometry

The two independent components of the gyration tensor of quartz, g11 and g33, have been spectroscopically measured using a transmission two-modulator generalized ellipsometer. The method is used to determine the optical activity in crystals in directions other than the optic axis, where the linear birefringence is much larger than the optical activity.

The Klein-Gordon equation in a domain with time-dependent boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time-dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.

Acoustic scattering : high frequency boundary element methods and unified transform methods

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A. S. Fokas and co-authors, analysing particular instances of this method, proposed by J. A. De-Santo and co-authors, for problems of acoustic scattering by diffraction gratings.

Mapeamento de ambientes estruturados com extração de informações geométricas através de dados sensoriais

The objective of this thesis is proposes a method for a mobile robot to build a hybrid map of an indoor, semi-structured environment. The topological part of this map deals with spatial relationships among rooms and corridors. It is a topology-based map, where the edges of the graph are rooms or corridors, and each link between two distinct edges represents a door. The metric part of the map consists in a set of parameters. These parameters describe a geometric figure which adapts to the free space of the local environment. This figure is calculated by a set of points which sample the boundaries of the local free space. These points are obtained with range sensors and with knowledge about the robot s pose. A method based on generalized Hough transform is applied to this set of points in order to obtain the geomtric figure. The building of the hybrid map is an incremental procedure. It is accomplished while the robot explores the environment. Each room is associated with a metric local map and, consequently, with an edge of the topo-logical map. During the mapping procedure, the robot may use recent metric information of the environment to improve its global or relative pose

Análise da magnetohidrodinâmica com transferência de calor em canais de placas paralelas via transformação integral

The main goal of the present work is related to the dynamics of the steady state, incompressible, laminar flow with heat transfer, of an electrically conducting and Newtonian fluid inside a flat parallel-plate channel under the action of an external and uniform magnetic field. For solution of the governing equations, written in the parabolic boundary layer and stream-function formulation, it was employed the hybrid, numericalanalytical, approach known as Generalized Integral Transform Technique (GITT). The flow is sustained by a pressure gradient and the magnetic field is applied in the direction normal to the flow and is assumed that normal magnetic field is kept uniform, remaining larger than any other fields generated in other directions. In order to evaluate the influence of the applied magnetic field on both entrance regions, thermal and hydrodynamic, for this forced convection problem, as well as for validating purposes of the adopted solution methodology, two kinds of channel entry conditions for the velocity field were used: an uniform and an non-MHD parabolic profile. On the other hand, for the thermal problem only an uniform temperature profile at the channel inlet was employed as boundary condition. Along the channel wall, plates are maintained at constant temperature, either equal to or different from each other. Results for the velocity and temperature fields as well as for the main related potentials are produced and compared, for validation purposes, to results reported on literature as function of the main dimensionless governing parameters as Reynolds and Hartman numbers, for typical situations. Finally, in order to illustrate the consistency of the integral transform method, convergence analyses are also effectuated and presented

Image registration and image interpolation in volume rendering of cross sections

We outline a method for registration of images of cross sections using the concepts of The Generalized Hough Transform (GHT). The approach may be useful in situations where automation should be a concern. To overcome known problems of noise of traditional GHT we have implemented a slight modified version of the basic algorithm. The modification consists of eliminating points of no interest in the process before the application of the accumulation step of the algorithm. This procedure minimizes the amount of accumulation points while reducing the probability of appearing of spurious peaks. Also, we apply image warping techniques to interpolate images among cross sections. This is needed where the distance of samples between sections is too large. Then it is suggested that the step of registration with GHT can help the interpolation automation by simplifying the correspondence between points of images. Some results are shown.

Analytical/numerical hybrid solution for one-dimensional ablation problem

Ablation is a thermal protection process with several applications in engineering, mainly in the field of airspace industry. The use of conventional materials must be quite restricted, because they would suffer catastrophic flaws due to thermal degradation of their structures. However, the same materials can be quite suitable once being protected by well-known ablative materials. The process that involves the ablative phenomena is complex, could involve the whole or partial loss of material that is sacrificed for absorption of energy. The analysis of the ablative process in a blunt body with revolution geometry will be made on the stagnation point area that can be simplified as a one-dimensional plane plate problem, hi this work the Generalized Integral Transform Technique (GITT) is employed for the solution of the non-linear system of coupled partial differential equations that model the phenomena. The solution of the problem is obtained by transforming the non-linear partial differential equation system to a system of coupled first order ordinary differential equations and then solving it by using well-established numerical routines. The results of interest such as the temperature field, the depth and the rate of removal of the ablative material are presented and compared with those ones available in the open literature.

Aplicação da transformada integral generalizada no escoamento potencial em contrações

Pós-graduação em Engenharia Mecânica - FEIS

Estudo analítico/numérico do problema de ablação em corpos rombudos com simetria axial

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Laplace transform approach to the quantum harmonic oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Oscilador harmônico unidimensional via transformada unilateral de Fourier e mapeamento do potencial de morse unidimensional nos potenciais pseudo-harmônico e de kratzer tridimensionais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Oscilador harmônico unidimensional via transformada unilateral de Fourier e mapeamento do potencial de morse unidimensional nos potenciais pseudo-harmônico e de kratzer tridimensionais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Hilbert transform

The Hilbert transform is an important tool in both pure and applied mathematics. It is largely used in the field of signal processing. Lately has been used in mathematical finance as the fast Hilbert transform method is an efficient and accurate algorithm for pricing discretely monitored barrier and Bermudan style options. The purpose of this report is to show the basic properties of the Hilbert transform and to check the domain of definition of this operator.

Un método de diferencias finitas generalizadas para simular la actividad eléctrica de un tejido cardiaco

Una evolución del método de diferencias finitas ha sido el desarrollo del método de diferencias finitas generalizadas (MDFG) que se puede aplicar a mallas irregulares o nubes de puntos. En este método se emplea una expansión en serie de Taylor junto con una aproximación por mínimos cuadrados móviles (MCM). De ese modo, las fórmulas explícitas de diferencias para nubes irregulares de puntos se pueden obtener fácilmente usando el método de Cholesky. El MDFG-MCM es un método sin malla que emplea únicamente puntos. Una contribución de esta Tesis es la aplicación del MDFG-MCM al caso de la modelización de problemas anisótropos elípticos de conductividad eléctrica incluyendo el caso de tejidos reales cuando la dirección de las fibras no es fija, sino que varía a lo largo del tejido. En esta Tesis también se muestra la extensión del método de diferencias finitas generalizadas a la solución explícita de ecuaciones parabólicas anisótropas. El método explícito incluye la formulación de un límite de estabilidad para el caso de nubes irregulares de nodos que es fácilmente calculable. Además se presenta una nueva solución analítica para una ecuación parabólica anisótropa y el MDFG-MCM explícito se aplica al caso de problemas parabólicos anisótropos de conductividad eléctrica. La evidente dificultad de realizar mediciones directas en electrocardiología ha motivado un gran interés en la simulación numérica de modelos cardiacos. La contribución más importante de esta Tesis es la aplicación de un esquema explícito con el MDFG-MCM al caso de la modelización monodominio de problemas de conductividad eléctrica. En esta Tesis presentamos un algoritmo altamente eficiente, exacto y condicionalmente estable para resolver el modelo monodominio, que describe la actividad eléctrica del corazón. El modelo consiste en una ecuación en derivadas parciales parabólica anisótropa (EDP) que está acoplada con un sistema de ecuaciones diferenciales ordinarias (EDOs) que describen las reacciones electroquímicas en las células cardiacas. El sistema resultante es difícil de resolver numéricamente debido a su complejidad. Proponemos un método basado en una separación de operadores y un método sin malla para resolver la EDP junto a un método de Runge-Kutta para resolver el sistema de EDOs de la membrana y las corrientes iónicas. ABSTRACT An evolution of the method of finite differences has been the development of generalized finite difference (GFD) method that can be applied to irregular grids or clouds of points. In this method a Taylor series expansion is used together with a moving least squares (MLS) approximation. Then, the explicit difference formulae for irregular clouds of points can be easily obtained using a simple Cholesky method. The MLS-GFD is a mesh-free method using only points. A contribution of this Thesis is the application of the MLS-GFDM to the case of modelling elliptic anisotropic electrical conductivity problems including the case of real tissues when the fiber direction is not fixed, but varies throughout the tissue. In this Thesis the extension of the generalized finite difference method to the explicit solution of parabolic anisotropic equations is also given. The explicit method includes a stability limit formulated for the case of irregular clouds of nodes that can be easily calculated. Also a new analytical solution for homogeneous parabolic anisotropic equation has been presented and an explicit MLS- GFDM has been applied to the case of parabolic anisotropic electrical conductivity problems. The obvious difficulty of performing direct measurements in electrocardiology has motivated wide interest in the numerical simulation of cardiac models. The main contribution of this Thesis is the application of an explicit scheme based in the MLS-GFDM to the case of modelling monodomain electrical conductivity problems using operator splitting including the case of anisotropic real tissues. In this Thesis we present a highly efficient, accurate and conditionally stable algorithm to solve a monodomain model, which describes the electrical activity in the heart. The model consists of a parabolic anisotropic partial differential equation (PDE), which is coupled to systems of ordinary differential equations (ODEs) describing electrochemical reactions in the cardiac cells. The resulting system is challenging to solve numerically, because of its complexity. We propose a method based on operator splitting and a meshless method for solving the PDE together with a Runge-Kutta method for solving the system of ODE’s for the membrane and ionic currents.