On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier Inc. All rights reserved.

Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

The numerical simulation of flows of highly elastic fluids has been the subject of intense research over the past decades with important industrial applications. Therefore, many efforts have been made to improve the convergence capabilities of the numerical methods employed to simulate viscoelastic fluid flows. An important contribution for the solution of the High-Weissenberg Number Problem has been presented by Fattal and Kupferman [J. Non-Newton. Fluid. Mech. 123 (2004) 281-285] who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. Its advantage is a better approximation of the large growth of the stress tensor that occur in some regions of the flow and it is doubly beneficial in that it ensures physically correct stress fields, allowing converged computations at high Weissenberg number flows. In this work we investigate the application of the log-conformation tensor to three-dimensional unsteady free surface flows. The log-conformation tensor formulation was applied to solve the Upper-Convected Maxwell (UCM) constitutive equation while the momentum equation was solved using a finite difference Marker-and-Cell type method. The resulting developed code is validated by comparing the log-conformation results with the analytic solution for fully developed pipe flows. To illustrate the stability of the log-conformation tensor approach in solving three-dimensional free surface flows, results from the simulation of the extrudate swell and jet buckling phenomena of UCM fluids at high Weissenberg numbers are presented. (C) 2012 Elsevier B.V. All rights reserved.

A marker-and-cell approach to free surface 2-D multiphase flows

This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the NavierStokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient. Copyright (c) 2012 John Wiley & Sons, Ltd.

Simulation results and applications of an advection bounded scheme to practical flows

This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena.

A continuously differentiable upwinding scheme for the simulation of fluid flow problems

This paper deals with the numerical solution of complex fluid dynamics problems using a new bounded high resolution upwind scheme (called SDPUS-C1 henceforth), for convection term discretization. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite volume/difference methodologies, either into the CLAWPACK software package for compressible flows or in the Freeflow simulation system for incompressible viscous flows. The performance of the proposed upwind non-oscillatory scheme is demonstrated by solving two-dimensional compressible flow problems, such as shock wave propagation and two-dimensional/axisymmetric incompressible moving free surface flows. The numerical results demonstrate that this new cell-interface reconstruction technique works very well in several practical applications. (C) 2012 Elsevier Inc. All rights reserved.

Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

A new enrichment space for the treatment of discontinuous pressures in multi-fluid flows

In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 10191031, 2010) in several problems involving jumps in the viscosity and/or the presence of singular forces at interfaces not conforming with the element edges. The combination of this enrichment space with another enrichment that accommodates discontinuities in the pressure gradient has also been explored, exhibiting excellent results in problems involving jumps in the density or the volume forces. Copyright (c) 2011 John Wiley & Sons, Ltd.

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.

Qualidade de sementes de soja colhidas de forma manual e mecânica com diferentes teores de água

A colheita é uma das principais etapas no processo de produção de sementes de soja. O momento adequado para se efetuar a colheita pode variar em função do tipo de colheita e do grau de umidade das sementes. Neste sentido, o objetivo dessa pesquisa foi determinar as alterações fisiológicas de sementes de soja colhidas de forma manual e mecânica com diferentes teores de água. Para tanto, utilizaram-se sementes das cultivares Embrapa 48 e FTS Águia, que têm diferenças no teor de lignina do tegumento, colhidas de forma manual e mecanicamente com 18,0; 15,0 e 12,0% de água. Após a colheita, as sementes foram submetidas à secagem, e a qualidade das sementes foi avaliada pelos testes de germinação, emergência de plântulas, tetrazólio (viabilidade e vigor), envelhecimento acelerado e índice de velocidade de emergência de plântula. Em seguida, as sementes foram armazenadas (20 °C e 45% UR do ar) e analisadas logo após a colheita e aos seis meses de armazenamento. Os resultados obtidos indicam que o parâmetro fisiológico das sementes de soja, não é afetado, quando: se realiza colheita manual com grau de umidade das sementes de 11,4% a 18,4%; e para sementes colhidas à máquina, com grau de umidade entre 12,0% a 15,9%; mantendo a qualidade fisiológica mesmo após seis meses de armazenamento.

Qualidade física de um latossolo vermelho sob plantio direto submetido à descompactação mecânica e biológica

A escarificação e o uso de plantas de cobertura de inverno têm sido adotados para promover a melhoria dos atributos físicos do solo relacionados à aeração. O objetivo deste trabalho foi verificar o efeito das plantas de cobertura de inverno e escarificação nas propriedades físicas de um Latossolo Vermelho distrófico, textura argilosa, após 16 anos em sistema plantio direto. Os tratamentos foram realizados em maio de 2009 e consistiram de: plantio direto (PD), plantio direto com escarificação mecânica a 0,25 m (PD-E) e plantio direto com descompactação biológica por meio da cultura do nabo forrageiro (PD-B). O delineamento experimental foi em blocos ao acaso com quatro repetições, totalizando 12 unidades experimentais. Dezoito meses após a aplicação dos tratamentos, foram coletadas amostras indeformadas de solo em cada unidade experimental, em cinco camadas: 0,0-0,1; 0,1-0,2; 0,2-0,3; 0,3-0,4; e 0,4-0,5 m. Foram avaliados os atributos físicos do solo: porosidade, densidade do solo (Ds), permeabilidade ao ar (Ka) e índices de continuidade de poros. A Ka foi medida por meio de um permeâmetro de carga constante de ar em nove potenciais mátricos (ψm): -0,5; -1; -2; -3; -5; -7; -10; -50; e -100 kPa. Os resultados indicam que os atributos físicos do solo avaliados não foram alterados pelo uso de plantas de cobertura e escarificação. Por outro lado, houve diferenças entre camadas de solo, principalmente entre 0,0-0,1 e 0,1-0,2 m. Na camada de 0,1-0,2 m, a Ds foi maior e a porosidade total e Ka (ψm = -5 kPa) foram menores do que na camada de 0,0-0,1 m. No PD-E, verificou-se que a macroporosidade foi maior na camada de 0,0-0,1 m em comparação com os outros tratamentos. Os resultados sugerem que o solo estudado submetido aos tratamentos de descompactação, após 18 meses, retornou a valores semelhantes aos da testemunha.

Artroplastia do joelho navegada x mecânica: comparação entre casos iniciais de navegação e convencionais pelo mesmo cirurgião

OBJETIVO: Foram avaliados e comparados os eixos mecânicos pós-operatórios de 36 artroplastias totais de joelho pelos sistemas de alinhamento navegado e mecânico feitos no mesmo período pelo mesmo cirurgião e equipe, iniciantes na técnica navegada e com experiência na técnica mecânica. MÉTODOS: Entre 2008 e 2010, 36 próteses totais de joelho foram executadas e comparadas, 25 navegadas e 11 mecânicas. Qualquer desvio de eixo medido no RX panorâmico pós-operatório foi considerado positivo. RESULTADOS: As próteses navegadas obtiveram média de desvio de eixo de 1,32 graus e desvio padrão de 1,57 graus e as mecânicas, respectivamente, 3,18 e 2,99 graus. Houve um melhor alinhamento com tendência à diferença estatística em favor da técnica navegada. CONCLUSÃO: Os casos com desvio de eixo maior que três graus foram significativamente maiores na técnica mecânica. A técnica por navegação foi incorporada por nossa equipe sem complicações adicionais e, mesmo sem experiência em cirurgia navegada, os primeiros casos obtiveram melhor alinhamento em relação à técnica mecânica e número significativamente menor de casos fora da zona de segurança de três graus em relação ao eixo mecânico.

Abrasividade pendular e a resistência mecânica das rochas

Esse trabalho emprega o método para avaliar a abrasividade proposto por Golovanevskiy e Bearman (2008). Esse método, ensaio de abrasão por impacto deslizante (Gouging Abrasion Test), é realizado em condições de alta tensão/alto impacto de desgaste. O método consiste de uma ponteira cilíndrica com uma ponta cônica de 90º, que, em trajetória pendular, atinge uma amostra de rocha com energia de impacto de 300 J e velocidade da ordem de 5,2 m/s. O Gouging Abrasion Index (Gi) é calculado como sendo a média do diâmetro da ponta cônica, após desgaste, em milímetros e o resultado é multiplicado por 10. Esse trabalho verificou a adequabilidade do Gouging Abrasion Test, para um pequeno número de amostras de rocha, que representam, qualitativamente, os principais tipos de rocha encontrados em trabalhos de corte, perfuração e britagem no Brasil, e a sua correlação com outros ensaios consagrados como a resistência à compressão, o desgaste Amsler e a dureza Knoop. Essa análise mostrou alta correlação entre Gi e a dureza Knoop (R² = 0,94), baixa correlação com o desgaste