Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions. (C) 2011 Elsevier Inc. All rights reserved.

Cell activation state influences the modulation of HLA-DR surface expression on human monocytes/macrophages by parenteral fish oil lipid emulsion

Abnormal surface expression of HLA-DR by leukocytes is associated with a poor prognosis in critical care patients. Critical care patients often receive total parenteral nutrition with lipid emulsion (LE). In this study we evaluated the influence of fish oil LE (FO) on human monocyte/macrophage (M phi) expression of surface HLA-DR under distinct activation states. Mononuclear leukocytes from the peripheral blood of healthy volunteers (n = 18) were cultured for 24 hours without LE (control) or with 3 different concentrations (0.1, 0.25, and 0.5%) of the follow LE: a) pure FO b) FO in association (1:1 v/v) with LE composed of 50% medium-chain trygliceride and 50% soybean oil (MCTSO), and c) pure MCTSO. The leukocytes were also submitted to different cell activation states, as determinate by INF-gamma addition time: no INF-gamma addition, 18 hours before, or at the time of LE addition. HLA-DR expression on M phi surface was evaluated by flow cytometry using specific monoclonal antibodies. In relation to controls (for 0.1%, 0.25%, and 0.5%: 100) FO decreased the expression of HLA-DR when added alone [in simultaneously-activated M phi, for 0.1%: 70 (59 +/- 73); for 0.25%: 51 (48 +/- 56); and for 0.5%: 52.5(50 +/- 58)] or in association with MCTSO [in simultaneously-activated M phi, for 0.1%: 50.5 (47 +/- 61); for 25%: 49 (45 +/- 52); and for 05 %: 51 (44 +/- 54) and in previously-activated M phi, for 1.0 % : 63 (44 +/- 88); for 0.25%: 70 (41 +/- 88); and for 0.5%: 59.5 (39 +/- 79)] in culture medium (Friedman p<0.05). In relation to controls (for 0.1%, 0.25%, and 0.5%: 100), FO did not influence the expression of these molecules on non-activated M phi [for 0.1 % : 87.5 (75 +/- 93); for 0.25%: 111 (98 +/- 118); and for 0.5%: 101.5 (84 +/- 113)]. Results show that parenteral FO modulates the expression of HLA-DR on human M phi surface accordingly to leukocyte activation state. Further clinical studies evaluating the ideal moment of fish oil LE infusion to modulate leukocyte functions may contribute to a better understanding of its immune modulatory properties.

Fiedler trees for multiscale surface analysis

In this work we introduce a new hierarchical surface decomposition method for multiscale analysis of surface meshes. In contrast to other multiresolution methods, our approach relies on spectral properties of the surface to build a binary hierarchical decomposition. Namely, we utilize the first nontrivial eigenfunction of the Laplace-Beltrami operator to recursively decompose the surface. For this reason we coin our surface decomposition the Fiedler tree. Using the Fiedler tree ensures a number of attractive properties, including: mesh-independent decomposition, well-formed and nearly equi-areal surface patches, and noise robustness. We show how the evenly distributed patches can be exploited for generating multiresolution high quality uniform meshes. Additionally, our decomposition permits a natural means for carrying out wavelet methods, resulting in an intuitive method for producing feature-sensitive meshes at multiple scales. Published by Elsevier Ltd.

Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

This work deals with the development of a numerical technique for simulating three-dimensional viscoelastic free surface flows using the PTT (Phan-Thien-Tanner) nonlinear constitutive equation. In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method, which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work flow predictions for fully developed pipe flow are compared with an analytic solution from the literature. Then, results of complex free surface flows using the FIT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters epsilon and xi on the extrudate swell and jet buckling problems is reported. (C) 2010 Elsevier B.V. All rights reserved.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

The Stern-Gerlach Phenomenon According to Classical Electrodynamics

We present a description of the Stem-Gerlach type experiments using only the concepts of classical electrodynamics and the Newton`s equations of motion. The quantization of the projections of the spin (or the projections of the magnetic dipole) is not introduced in our calculations. The main characteristic of our approach is a quantitative analysis of the motion of the magnetic atoms at the entrance of the magnetic field region. This study reveals a mechanism which modifies continuously the orientation of the magnetic dipole of the atom in a very short time interval, at the entrance of the magnetic field region. The mechanism is based on the conservation of the total energy associated with a magnetic dipole which moves in a non uniform magnetic field generated by an electromagnet. A detailed quantitative comparison with the (1922) Stem-Gerlach experiment and the didactical (1967) experiment by J.R. Zacharias is presented. We conclude, contrary to the original Stern-Gerlach statement, that the classical explanations are not ruled out by the experimental data.

Concentric characterization and classification of complex network nodes: Application to an institutional collaboration network

Differently from theoretical scale-free networks, most real networks present multi-scale behavior, with nodes structured in different types of functional groups and communities. While the majority of approaches for classification of nodes in a complex network has relied on local measurements of the topology/connectivity around each node, valuable information about node functionality can be obtained by concentric (or hierarchical) measurements. This paper extends previous methodologies based on concentric measurements, by studying the possibility of using agglomerative clustering methods, in order to obtain a set of functional groups of nodes, considering particular institutional collaboration network nodes, including various known communities (departments of the University of Sao Paulo). Among the interesting obtained findings, we emphasize the scale-free nature of the network obtained, as well as identification of different patterns of authorship emerging from different areas (e.g. human and exact sciences). Another interesting result concerns the relatively uniform distribution of hubs along concentric levels, contrariwise to the non-uniform pattern found in theoretical scale-free networks such as the BA model. (C) 2008 Elsevier B.V. All rights reserved.

Absorption and emission properties of LBL PPV films deposited on ITO electrodes

In this work we studied the properties of absorption and emission line shape of layer-by-layer (LBL) poly(p-phenylene vinylene) (PPV) on indium-tin oxide (ITO) electrode. To minimize the PPV thermal conversion effects during the polymer processing, we used a less aggressive leaving group in the precursor polymer; minimizing electrode degradation. LBL ITO/PPV films showed the same absorption and emission line shape compared with LBL PPV films deposited on non-metallic substrates (glass). With this analysis we indirectly observe the decrease in the ITO degradation. Atomic force microscopy (AFM) technique was used to analyze quantitatively the microscopic morphology of the film surface. Results indicated that the substrate topology is not affected, to a large extent, by the use of dodecylbenzensulfonate (DBS) ion. (C) 2008 Elsevier B.V. All rights reserved.