An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

Critical discontinuous phase transition in the threshold contact process

We analyze a threshold contact process on a square lattice in which particles are created on empty sites with at least two neighboring particles and are annihilated spontaneously. We show by means of Monte Carlo simulations that the process undergoes a discontinuous phase transition at a definite value of the annihilation parameter, in accordance with the Gibbs phase rule, and that the discontinuous transition exhibits critical behavior. The simulations were performed by using boundary conditions in which the sites of the border of the lattice are permanently occupied by particles.

Computational aspects of harmonic wavelet Galerkin methods and an application to a precipitation front propagation model

This article is dedicated to harmonic wavelet Galerkin methods for the solution of partial differential equations. Several variants of the method are proposed and analyzed, using the Burgers equation as a test model. The computational complexity can be reduced when the localization properties of the wavelets and restricted interactions between different scales are exploited. The resulting variants of the method have computational complexities ranging from O(N(3)) to O(N) (N being the space dimension) per time step. A pseudo-spectral wavelet scheme is also described and compared to the methods based on connection coefficients. The harmonic wavelet Galerkin scheme is applied to a nonlinear model for the propagation of precipitation fronts, with the front locations being exposed in the sizes of the localized wavelet coefficients. (C) 2011 Elsevier Ltd. All rights reserved.

Estimativas do erro nas aproximações de Galerkin para as equações de Navier-Stokes

Neste trabalho são provadas algumas estimativas de erro em espaços para as aproximações de Galerkin para a solução do sistema de equações de Navier-Stokes. Mostra-se que o erro decresce em proporção inversa aos autovalores do operador de Stokes.

Aproximação de Petrov-Galerkin para o escoamento de sangue em anastomoses sistêmico-pulmonares do tipo Blalock-Taussig modificada

A anastomose sistêmico-pulmonar é um excelente procedimento paliativo para crianças e recém-nascidos portadores de cardiopatias congênitas cianóticas com diminuição da circulação pulmonar. Neste artigo, as aproximações “Streamline Upwind/Petrov-Galerkin – SUPG” foram utilizadas na simulação de escoamento de sangue em uma anastomose sistêmico pulmonar. A Anastomose estudada neste artigo é conhecido como Blalock-Taussig modificada no qual um enxerto de tubo sintético (prótese) é interposto entre a artéria subclávia esquerda e a artéria pulmonar com o objetivo de desviar parte do fluxo sistêmico ao pulmonar. A metodologia de elementos finitos utilizada, conhecida como método SUPG, supera as dificuldades enfrentadas pelo método de Galerkin clássico em altos números de Reynolds, que são compatibilizar os subespaços de velocidade e pressão – satisfazendo deste modo a condição denominada de Babuška-Brezzi e evitar oscilações espúrias devido à natureza assimétrica da aceleração advectiva de equação de momentum – adicionando termos malha-dependentes para a formulação de Galerkin clássica. Estes termos adicionais são construídos para aumentar a estabilidade da formulação de Galerkin original sem prejudicar sua consistência. Um modelo tridimensional parametrizado, utilizando o elemento lagrangeano trilinear, foi criado a partir de medições obtidas durante procedimento cirúrgico para avaliar os efeitos dos parametros geométricos envolvidos na cirurgia (diâmetro e ângulo do enxerto e a pulsatilidade do escoamento) Os resultados apresentam que o ângulo da anastomose proximal tem sensível influência na quantidade de fluxo desviada pelo enxerto e enorme influência na porcentagem de fluxo direcionado para cada um dos pulmões. Quanto ao diâmetro do enxerto conclui-se que este é o regulador principal da porcentagem de fluxo desviada. A partir das simulações realizadas determinou-se correlações para o fator de atrito e porcentagem de fluxo sangüíneo desviado pelo enxerto.

Aproximações de Galerkin clássico e Galerkin/mínimos quadrados de escoamentos viscosos incompressíveis : aplicação à medição de fluxos

Desde a antigüidade a medição do escoamento dos fluidos tem sido uma marca de nossa civilização, ajudando a predizer a fertilidade das terras e o consumo d’água em fontes e aquedutos. Nos nossos dias, a área de medição de fluxo está bem estabelecida e ainda desperta grande interesse nas linhas de pesquisa da mecânica dos fluidos experimental e computacional. Em particular, o estudo da medição de fluxo com elementos intrusivos, tais como placas de orifício, é de grande interesse dado o preço baixo do medidor, e sua boa precisão quando comparada à sua simplicidade de instalação e manutenção. Esta dissertação tem como objetivo o estudo da aplicação de elementos finitos aos escoamentos de fluidos viscosos - via aproximação clássica de Galerkin e Galerkin/mínimos-quadrados (GLS) – com particular ênfase na aproximação das equações de Navier-Stokes incompressível no escoamento newtoniano através de um canal obstruído por uma placa de orifício. Inicialmente, são apresentadas as dificuldades do método de Galerkin clássico na aproximação de escoamentos incompressíveis; ou seja, através da simulação de escoamentos viscosos bem conhecidos - como o escoamento no interior de uma cavidade e através de uma expansão súbita - fica evidenciada a restrição imposta pela condição de Babuška-Brezzi quando da escolha dos subespaços aproximantes do campo de velocidade e pressão Como alternativa às patologias do método de Galerkin clássico, esta dissertação emprega a metodologia de Galerkin/mínimos-quadrados na simulação acima mencionada da placa de orifício, a qual permite o uso de elementos de igual-ordem para aproximar velocidade e pressão e capturar de maneira estável escoamentos sujeitos a altos números de Reynolds. Os testes computacionais realizados se apresentaram fisicamente realistas quando comparados com a literatura e dados experimentais, sendo todos desenvolvidos no Laboratório de Mecânica dos Fluidos Aplicada e Computacional (LAMAC) do Departamento de Engenharia Mecânica da Universidade Federal do Rio Grande do Sul.

Study of the innovation management process in the development of a discontinuous product case: Motorola RAZR V3

This study will collaborate by bringing some detailed analysis and findings on a special case study of a discontinuous product development process, trying to answer how the discontinuous product development process takes place and the main factors that influence this process. Additionally, it tried to explore some explanations for the difficulties generally faced by the companies to sustain innovation. The case is about the Motorola cell phone RAZR V3, launched in 2004. RAZR V3 was noted by industry experts as game-changing feat of design and engineering, selling more than 110 million units by end of 2008 and recognized as one of the fastest selling products in the industry. The study uses a single case methodology, which is appropriate given the access to a phenomenon that happened inside corporate dominium and it is not easily accessed for academic studies, besides being a rare case of success in the cellular phone industry. In order to magnify the understanding of the phenomenon, the exploration was extended to contrast the RAZR development process and the standard product development process in Motorola. Additionally, it was integrated a longitudinal reflection of the company product development evolution until the next breakthrough product hitting the cellular phone industry. The result of the analysis shows that discontinuous products do not fit well traditional product development process (in this case, stage-gate). This result reinforces the results obtained on previous studies of discontinuous product development conducted by other authors. Therefore, it is clear that the dynamics of discontinuous product development are different from the continuous product development, requiring different treatment to succeed. Moreover, this study highlighted the importance of the management influence in all the phases of the process as one of the most important factors, suggesting a key component to be carefully observed in future researches. Some other findings of the study that were considered very important for a discontinuous product development process: have champions (who believe and protect the project) and not only one champion; create a right atmosphere to make flow the creative process; question paradigms to create discontinuous products; simple guiding light to focus the team; company culture that accepts and knows how to deal with risks; and undoubtedly, have a company strategy that understands the different dynamics of continuous and discontinuous product development processes and treat them accordingly.

Solução de uma classe de equações diferenciais parciais em espaços de Niko'skii através do método de Galerkin

Neste trabalho apresenta-se uma solu c~ao para um problema abstrato de Cauchy. Basicamente, d a-se uma formula c~ao abstrata para certos tipos de equa c~oes diferenciais parciais n~ao lineares de evolu c~ao em espa cos de Nikol'skii, tais espa cos possuem boas propriedades de regularidade e resultados de imers~ao compacta, num certo sentido s~ao intermedi arios entre os espa cos de Holder e os espa cos de Sobolev. Aplicando o m etodo de Galerkin, prova-se resultados de exist^encia global de solu c~oes fracas, como tamb em a exist^encia de solu c~oes fracas com a propriedade de reprodu c~ao. E impondo mais hip oteses sobre os operadores envolvidos demonstra-se unicidade de solu c~oes fracas.

Effects of discontinuous Percoll gradient centrifugation on the quality of bovine spermatozoa evaluated with computer-assisted semen analysis and fluorescent probes association

The objective of this study was to evaluate the quality of bovine frozen-thawed sperm cells after Percoll gradient centrifugation. Frozen semen doses were obtained from six bulls of different breeds, including three taurine and three Zebu animals. Four ejaculates per bull were evaluated before and after discontinuous Percoll gradient centrifugation. Sperm motility was assessed by computer-assisted semen analysis and the integrity of the plasma and acrosomal membranes, as well as mitochondrial function, were evaluated using a combination of fluorescent probes propidium iodide, fluorescein isothiocyanate-conjugated Pisum sativum agglutinin and 5,5',6,6'-tetrachloro-1,1',3,3'-tetraethylbenzimidazolcarbocyanine iodide. The procedure of Percoll gradient centrifugation increased the percentage of total and progressive sperm motility, beat frequency, rectilinear motility, linearity and rapidly moving cells. In addition, the percentage of cells with intact plasma membrane and mitochondrial membrane potential was increased in post-centrifugation samples. However, the percentage of sperm cells with intact acrosomal membrane was markedly reduced. The method used selected the motile cells with intact plasma membrane and higher mitochondrial functionality in frozen-thawed bull semen, but processing, centrifugation and/or the Percoll medium caused damage to the acrosomal membrane.

LIMIT CYCLES of DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

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

Experimental pathogenicity of Candida albicans and Candida dubliniensis with continuous and discontinuous fringes morphotypes

A possible correlation between the presence of discontinuous fringes and high virulence has been previously suggested. The aim of this study was to compare the pathogenicity of Candida albicans and Candida dubliniensis with continuous and discontinuous fringes morphotypes on mice. For C. albicans, two discontinuous fringe morphotype isolates (PN 69, PN 74), two continuous fringe morphotype isolates (N 60, N 33) and one reference strain were used. For C. dubliniensis, three discontinuous fringe morphotype isolates (97487, 97464, 97519), two continuous fringe morphotype isolates (97040, 98026) and one reference strain were used. Swiss male mice were inoculated with a standardised suspension of the microorganisms and observed for 35 days. The pathogenicity of the isolates was analysed according to parameters proposed previously. Three isolates were considered pathogenic: PN 74, N 60 and 98026. Strain N 60 killed the highest amount of mice (80%). Animals inoculated with C. albicans did not show differences on survival estimate. Candida dubliniensis 98026 was more pathogenic than samples 97464 and 97519. on the other hand, the sample 97487 showed a higher pathogenicity when compared with 97040 (Kaplan-Meier test, P = 0.008). Strains with continuous fringe morphotypes were also associated with Candida sp. virulence in vivo.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier B.V. All rights reserved.

An application of the Element Free Galerkin Method to the analysis of quantum well structures

In order to obtain the quantum-mechanical properties of layered semicondutor structures (quantum well and superlattice structures, for instance), solutions of the Schrodinger equation should be obtained for arbitrary potential profiles. In this paper, it is shown that such problems may be also studied by the Element Free Galerkin Method.

A singular approach to discontinuous vector fields on the plane

In this paper we deal with discontinuous vector fields on R-2 and we prove that the analysis of their local behavior around a typical singularity can be treated via singular perturbation. The regularization process developed by Sotomayor and Teixeira is crucial for the development of this work. (c) 2006 Elsevier B.V. All rights reserved.

Regularization of discontinuous vector fields on R-3 via singular perturbation

Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of' sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields.