Neste trabalho, desenvolve-se um método de fronteira imersa para o estudo de escoamento compressível modelado pelas equações de Euler bidimensionais. O método de discretização de diferenças finitas é empregado, usando o método de Steger-Warming de ordem dois para discretizar as variáveis espaciais e o esquema de Runge-Kutta de ordem quatro para discretizar as variáveis temporais. O método da fronteira imersa foi empregado para o estudo de aeroelasticidade computacional em uma seção típica de aerofólio bidimensional com dois movimentos prescritos: torsional e vertical, com o objetivo de se verifcar a eficiência do método e sua aplicabilidade para problemas em aeroelasticidade computacional. Neste estudo desenvolveu-se também um programa de computador para simular escoamentos compressíveis de fluido invíscido utilizando a metodologia proposta. A verificação do código gerado foi feita utilizando o método das soluções manufaturadas e o problema de reflexão de choque oblíquo. A validação foi realizada comparando-se os resultados obtidos para o escoamento ao redor de uma seção circular e de uma seção de aerofólio NACA 0012 com os resultados experimentais, para cada caso. / In this work, an immersed boundary method is developed to study compressible flow modeled by the two-dimensional Euler equations. The finite difference method is employed, using the second order Steger-Warming method to discretizate the space variables and the fourth order Runge-Kutta method to discretizate the time variables. The immersed boundary method was employed to study computational aeroelasticity on a typical two-dimensional airfoil section with two prescribed motion: pitching and plunging, in order to verify the efficiency of the numerical method and its applicability in computational aeroelasticity problems. In this work, a computer program was developed to simulate compressible flows for inviscid fluids using the methodology proposed. The verification of the computational code was performed using the method of manufactured solutions and the oblique shock wave reflection problem. The validation was performed comparing the obtained results for flows around a circular section and a NACA 0012 airfoil section with the experimental results, for each case.

abstract: Rabies is an infectious viral disease. It is usually fatal if a victim reaches the rabid stage, which starts after the appearance of disease symptoms. The disease virus attacks the central nervous system, and then it migrates from peripheral nerves to the spinal cord and brain. At the time when the rabies virus reaches the brain, the incubation period is over and the symptoms of clinical disease appear on the victim. From the brain, the virus travels via nerves to the salivary glands and saliva. A mathematical model is developed for the spread of rabies in a spatially distributed fox population to model the spread of the rabies epizootic through middle Europe that occurred in the second half of the 20th century. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. Since the model assumes these two kinds of rabid foxes, it is a system of both partial differential and integral equations (with integration over space and, occasionally, also over time). To study the spreading speeds of the rabies epidemic, the model is reduced to a scalar Volterra-Hammerstein integral equation, and space-time Laplace transform of the integral equation is used to derive implicit formulas for the spreading speed. The spreading speeds are discussed and implicit formulas are given for latent periods of fixed length, exponentially distributed length, Gamma distributed length, and log-normally distributed length. A number of analytic and numerical results are shown pertaining to the spreading speeds. Further, a numerical algorithm is described for the simulation of the spread of rabies in a spatially distributed fox population on a bounded domain with Dirichlet boundary conditions. I propose the following methods for the numerical approximation of solutions. The partial differential and integral equations are discretized in the space variable by central differences of second order and by the composite trapezoidal rule. Next, the ordinary or delay differential equations that are obtained this way are discretized in time by explicit continuous Runge-Kutta methods of fourth order for ordinary and delay differential systems. My particular interest is in how the partition of rabid foxes into territorial and diffusing rabid foxes influences the spreading speed, a question that can be answered by purely analytic means only for small basic reproduction numbers. I will restrict the numerical analysis to latent periods of fixed length and to exponentially distributed latent periods. The results of the numerical calculations are compared for latent periods of fixed and exponentially distributed length and for various proportions of territorial and wandering rabid foxes. The speeds of spread observed in the simulations are compared to spreading speeds obtained by numerically solving the analytic formulas and to observed speeds of epizootic frontlines in the European rabies outbreak 1940 to 1980. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2018

The validity of transfer matrix method (TMM) employed in a nonlinear gear cam system is studied in this thesis. The nonlinear dynamic responses of each part in the nonlinear system are estimated by applying the 4th-order Runge-Kutta method. A high speed gear cam drive automatic die cutter was analyzed in this study. A 25 horsepower AC induction motor is designed to drive the system. To complete the cutting work, a sequential process of the harmonic motion and the intermittent motion are generated by the elbow mechanism and the gear cam mechanism, respectively. A simplified branched multi-rotor system is modeled to approximate the motion of the system. The variation of the dynamic parameters of the system in a loading cycle is estimated under a branched torsional system. The Holzer¡¦s transfer matrix method is used to study the variation of the system parameters during the intermittent movement. Moreover, the effect of time-varied speed introduced from the torque variation of the induction motor and gear cam mechanism on the nonlinear dynamic response of the system has also been investigated. To explore the dynamic effect of different cam designs, three different cam motion curves and seven operating rates have been analyzed in this work. The residual vibration of the last sprocket has also been discussed. Numerical results indicate that the proposed model is available to simulate the dynamic responses of a nonlinear gear cam drive system.

Neste trabalho, desenvolve-se um método de fronteira imersa para o estudo de escoamento compressível modelado pelas equações de Euler bidimensionais. O método de discretização de diferenças finitas é empregado, usando o método de Steger-Warming de ordem dois para discretizar as variáveis espaciais e o esquema de Runge-Kutta de ordem quatro para discretizar as variáveis temporais. O método da fronteira imersa foi empregado para o estudo de aeroelasticidade computacional em uma seção típica de aerofólio bidimensional com dois movimentos prescritos: torsional e vertical, com o objetivo de se verifcar a eficiência do método e sua aplicabilidade para problemas em aeroelasticidade computacional. Neste estudo desenvolveu-se também um programa de computador para simular escoamentos compressíveis de fluido invíscido utilizando a metodologia proposta. A verificação do código gerado foi feita utilizando o método das soluções manufaturadas e o problema de reflexão de choque oblíquo. A validação foi realizada comparando-se os resultados obtidos para o escoamento ao redor de uma seção circular e de uma seção de aerofólio NACA 0012 com os resultados experimentais, para cada caso. / In this work, an immersed boundary method is developed to study compressible flow modeled by the two-dimensional Euler equations. The finite difference method is employed, using the second order Steger-Warming method to discretizate the space variables and the fourth order Runge-Kutta method to discretizate the time variables. The immersed boundary method was employed to study computational aeroelasticity on a typical two-dimensional airfoil section with two prescribed motion: pitching and plunging, in order to verify the efficiency of the numerical method and its applicability in computational aeroelasticity problems. In this work, a computer program was developed to simulate compressible flows for inviscid fluids using the methodology proposed. The verification of the computational code was performed using the method of manufactured solutions and the oblique shock wave reflection problem. The validation was performed comparing the obtained results for flows around a circular section and a NACA 0012 airfoil section with the experimental results, for each case.

Neste trabalho efetuamos uma análise quantitativa das forças que atuam entre partículas coloidais. Para isto integramos a Equação de Poisson-Boltzmann não linearizada levando em consideração o tamanho finito dos íons. Os resultados são aplicados a sistemas formados por esferas de poliestireno em dispersão aquosa. Concluímos que as forças repulsivas são dominantes nestes sistemas permitindo-nos negligenciar as forças atrativas. Também efetuamos algumas comparações dos mesmos resultados com dados experimentais / We present a quantitative analisis of the forces acting in colloidal particles. For this purpose we integrated the non linerized Poisson- Boltzmann Equation by a numerical method. We took in accont the finite size of the ions and applied the results to systems formed by polystirene spheres in aqueous dispersion. We were able to conclude that the attractive forces can be neglicted in front of the repulsive forces. We also were able to perform same comparasion com experimental data

Made available in DSpace on 2014-10-09T12:51:51Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:06:32Z (GMT). No. of bitstreams: 0 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP / FAPESP:00/11446-0

Neste trabalho efetuamos uma análise quantitativa das forças que atuam entre partículas coloidais. Para isto integramos a Equação de Poisson-Boltzmann não linearizada levando em consideração o tamanho finito dos íons. Os resultados são aplicados a sistemas formados por esferas de poliestireno em dispersão aquosa. Concluímos que as forças repulsivas são dominantes nestes sistemas permitindo-nos negligenciar as forças atrativas. Também efetuamos algumas comparações dos mesmos resultados com dados experimentais / We present a quantitative analisis of the forces acting in colloidal particles. For this purpose we integrated the non linerized Poisson- Boltzmann Equation by a numerical method. We took in accont the finite size of the ions and applied the results to systems formed by polystirene spheres in aqueous dispersion. We were able to conclude that the attractive forces can be neglicted in front of the repulsive forces. We also were able to perform same comparasion com experimental data

Made available in DSpace on 2014-10-09T12:51:51Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:06:32Z (GMT). No. of bitstreams: 0 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Foram estudados os processos de transferência de energia (TE) dos níveis 4I13/2 ; 4I11/2 do Er3+ e 5I7 ; 5I6 do Ho3+ no LiYF4 (YLF) e no ZBLAN, para os íons desativadores Nd3+, Tb3+ ou Eu3+. Os microparâmetros de interação dessas TE foram obtidos utilizandose o método da integral de sobreposição e os resultados indicaram que o íon de Eu3+ é o melhor desativador do primeiro estado excitado do Ho3+ no YLF e o Nd3+ é o mais eficiente desativador do Er3+ no YLF e ZBLAN. A dependência temporal das fluorescências do Er3+ em 1,5 ; 2,7 m e do Ho3+ em 2,1 ; 2,9 m foram medidas utilizandose excitações laser pulsadas provenientes do Nd-YAG+2 +OPO sintonizável. Foi proposto um critério geral para a discriminação dos processos de TE assistidos pela migração da excitação entre doadores (difusão ou saltos). Verificou-se que o modelo de migração por difusão ajusta melhor os processos de TE do segundo estado excitado do doador (Er3+ or Ho3+) independentemente da razão CD-D / CD-A, enquanto que o modelo de migração por saltos aplica-se ao primeiro estado excitado do doador. Foi proposta uma modificação no modelo de saltos que descreve os resultados experimentais para sistemas com CD-D / CD-A> 10. Utilizando-se os parâmetros de TE verificamos que os melhores sistemas para a ação laser em 3µm são: Ho:Eu:YLF, Ho:Nd:YLF e Er:Nd:YLF. Por outro lado, verifica-se que os sistemas com baixas concentrações (1,5mol%) de Er:Nd; Er:Tb e Er:Eu no ZBLAN não apresentaram potencial de inversão de população para a ação laser em 2,8 m. Os processos de conversão ascendente no sistema Er:YLF foram estudados em função da concentração de Er3+, sendo que os processos de absorção de estado excitado (ESA) e de conversão ascendente por transferência de energia (ETU) foram discriminados utilizando as curvas de decaimento resolvidas no tempo. Observou-se que o comprimento de onda de excitação em 980nm é o mais adequado para o bombeamento do sistema Er:YLF para a emissão laser quase contínua (cw) em 2,8 m. A técnica de pump-probe foi utilizada a fim de serem investigados os efeitos nos tempos de vida do sistema Er:YLF, sendo verificada uma diminuição da contribuição da migração da excitação nos tempos de vida do primeiro e segundo estados excitados do Er3+ no YLF com o aumento da potência de bombeamento cw ( pump ). As taxas experimentais de TE, determinadas para os melhores sistemas por meio do parâmetro RN, foram utilizadas no sistema de equações de taxa e, resolvendo-as pelo método numérico de Runge-Kutta de 4a ordem, pudemos avaliar a densidade de população invertida para as emissões em 2,8 m do Er3+ e 2,9 m do Ho3+ em função das taxas de bombeamento e das concentrações dos íons ativador e desativador. A melhor concentração do sistema Er:YLF foi de 20mol% e no sistema Er:Nd:YLF foi de 4mol% de Er3+ e 1,5mol% de Nd3+. Verificou-se que o sistema Er(4mol%):Nd(1.5mol%):YLF favorece o aumento da freqüência máxima de operação de 14Hz no Er:YLF para 391Hz baseando-se na medida do tempo de vida do nível laser inferior (4I13/2) do Er3+. O sistema Ho3+ no YLF é otimizado utilizando-se 0,6mol% de Ho3+ e 1,5mol% de Nd3+ ou pelo sistema Ho(3mol%):Eu(1,2mol%):YLF, sendo que a densidade de população invertida observada no sistema Ho(3mol%):Eu(1,2mol%) é 2,4 vezes maior que no sistema Ho(0,6mol%):Nd(1,5mol%). / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP / FAPESP:00/11446-0

This work addresses the question of the efficient numerical solution of time-domain boundary integral equations with retarded potentials arising in the problems of acoustic and electromagnetic scattering. The convolutional form of the time-domain boundary operators allows to discretize them with the help of Runge-Kutta convolution quadrature. This method combines Laplace-transform and time-stepping approaches and requires the explicit form of the fundamental solution only in the Laplace domain to be known. Recent numerical and analytical studies revealed excellent properties of Runge-Kutta convolution quadrature, e.g. high convergence order, stability, low dissipation and dispersion. As a model problem, we consider the wave scattering in three dimensions. The convolution quadrature discretization of the indirect formulation for the three-dimensional wave equation leads to the lower triangular Toeplitz system of equations. Each entry of this system is a boundary integral operator with a kernel defined by convolution quadrature. In this work we develop an efficient method of almost linear complexity for the solution of this system based on the existing recursive algorithm. The latter requires the construction of many discretizations of the Helmholtz boundary single layer operator for a wide range of complex wavenumbers. This leads to two main problems: the need to construct many dense matrices and to evaluate many singular and near-singular integrals. The first problem is overcome by the use of data-sparse techniques, namely, the high-frequency fast multipole method (HF FMM) and H-matrices. The applicability of both techniques for the discretization of the Helmholtz boundary single-layer operators with complex wavenumbers is analyzed. It is shown that the presence of decay can favorably affect the length of the fast multipole expansions and thus reduce the matrix-vector multiplication times. The performance of H-matrices and the HF FMM is compared for a range of complex wavenumbers, and the strategy to choose between two techniques is suggested. The second problem, namely, the assembly of many singular and nearly-singular integrals, is solved by the use of the Huygens principle. In this work we prove that kernels of the boundary integral operators $w_n^h(d)$ ($h$ is the time step and $t_n=nh$ is the time) exhibit exponential decay outside of the neighborhood of $d=nh$ (this is the consequence of the Huygens principle). The size of the support of these kernels for fixed $h$ increases with $n$ as $n^a,a<1$, where $a$ depends on the order of the Runge-Kutta method and is (typically) smaller for Runge-Kutta methods of higher order. Numerical experiments demonstrate that theoretically predicted values of $a$ are quite close to optimal. In the work it is shown how this property can be used in the recursive algorithm to construct only a few matrices with the near-field, while for the rest of the matrices the far-field only is assembled. The resulting method allows to solve the three-dimensional wave scattering problem with asymptotically almost linear complexity. The efficiency of the approach is confirmed by extensive numerical experiments.

Ce document traite premièrement des diverses tentatives de modélisation et de simulation de la nage anguilliforme puis élabore une nouvelle technique, basée sur la méthode de la frontière immergée généralisée et la théorie des poutres de Reissner-Simo. Cette dernière, comme les équations des fluides polaires, est dérivée de la mécanique des milieux continus puis les équations obtenues sont discrétisées afin de les amener à une résolution numérique. Pour la première fois, la théorie des schémas de Runge-Kutta additifs est combinée à celle des schémas de Runge-Kutta-Munthe-Kaas pour engendrer une méthode d’ordre de convergence formel arbitraire. De plus, les opérations d’interpolation et d’étalement sont traitées d’un nouveau point de vue qui suggère l’usage des splines interpolatoires nodales en lieu et place des fonctions d’étalement traditionnelles. Enfin, de nombreuses vérifications numériques sont faites avant de considérer les simulations de la nage. / This paper first discusses various attempts at modeling and simulating anguilliform swimming, then we develop a new technique, based on a method of generalized immersed boundary and the beam theory of Reissner-Simo. Subsequent to the derivation of the equations of polar fluids, the beam theory is derived from continuum mechanics and the resulting equations are then discretized, allowing a numerical solution. For the first time, the theory of additive Runge-Kutta schemes are combined with the Runge-Kutta-Munthe-Kaas method to generate schemes of arbitrarily high formal order of convergence. Moreover, the interpolation and spreading operations are handled from a new point of view that suggests the use of interpolatory nodal splines instead of spreading traditional functions. Finally, many numerical verifications are done before considering simulations of swimming.