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.

Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

This study investigates the numerical simulation of three-dimensional time-dependent viscoelastic free surface flows using the Upper-Convected Maxwell (UCM) constitutive equation and an algebraic explicit model. This investigation was carried out to develop a simplified approach that can be applied to the extrudate swell problem. The relevant physics of this flow phenomenon is discussed in the paper and an algebraic model to predict the extrudate swell problem is presented. It is based on an explicit algebraic representation of the non-Newtonian extra-stress through a kinematic tensor formed with the scaled dyadic product of the velocity field. The elasticity of the fluid is governed by a single transport equation for a scalar quantity which has dimension of strain rate. Mass and momentum conservations, and the constitutive equation (UCM and algebraic model) were solved by a three-dimensional time-dependent finite difference method. The free surface of the fluid was modeled using a marker-and-cell approach. The algebraic model was validated by comparing the numerical predictions with analytic solutions for pipe flow. In comparison with the classical UCM model, one advantage of this approach is that computational workload is substantially reduced: the UCM model employs six differential equations while the algebraic model uses only one. The results showed stable flows with very large extrudate growths beyond those usually obtained with standard differential viscoelastic models. (C) 2010 Elsevier Ltd. All rights reserved.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.

PL spectroscopy of Fermi electrons in regime of the quantum Hall effect

The influence of the interlayer coupling on formation of the quantized Hall phase at the filling factor v = 2 was studied in the multilayer GaAs/AlGaAs heterostructures The disorder broaden Gaussian photoluminescence line due to the localized electrons was found in the quantized Hall phase of the isolated multi-quantum well structure On the other hand. the quantized Hall phase of the weakly-coupled multilayers emitted an asymmetrical line similar to that one observed in the metallic electron systems. We demonstrated that the observed asymmetry indicates a formation of the Fermi Surface in the quantized Hall phase of the multilayer electron system due to the interlayer peicolation. A sharp decrease of the single-particle scattering time associated with the extended states oil the Fermi surface was observed at the filling factor v = 2. (C) 2009 Elsevier B.V All rights reserved

Magnetic structures of quaternary intermetallic borocarbides RCo(2)B(2)C (R = Dy, Ho, Er)

The magnetic structures of the title compounds have been studied by neutron diffraction. In contrast to the isomorphous RNi(2)B(2)C compounds, wherein a variety of exotic incommensurate modulated structures has been observed, the magnetic structure of ErCo(2)B(2)C is found to be a collinear antiferromagnet with k = (12, 0, 12) while those of HoCo(2)B(2)C and DyCo(2)B(2)C are observed to be simple ferromagnets. For all studied compounds, the moments are found to be confined within the basal plane and their magnitudes are comparable to the values obtained from the low-temperature isothermal magnetization measurements. The absence of modulated magnetic structures in the RCo(2)B(2)C series (for ErCo(2)B(2)C, verified down to 50 mK) is attributed to the quenching of the Fermi surface nesting features.

SURFACE ALFVEN WAVE DAMPING IN A THREE-DIMENSIONAL SIMULATION OF THE SOLAR WIND

Here we investigate the contribution of surface Alfven wave damping to the heating of the solar wind in minima conditions. These waves are present in the regions of strong inhomogeneities in density or magnetic field (e.g., the border between open and closed magnetic field lines). Using a three-dimensional (3D) magnetohydrodynamics (MHD) model, we calculate the surface Alfven wave damping contribution between 1 and 4 R(circle dot) (solar radii), the region of interest for both acceleration and coronal heating. We consider waves with frequencies lower than those that are damped in the chromosphere and on the order of those dominating the heliosphere: 3 x 10(-6) to 10(-1) Hz. In the region between open and closed field lines, within a few R(circle dot) of the surface, no other major source of damping has been suggested for the low frequency waves we consider here. This work is the first to study surface Alfven waves in a 3D environment without assuming a priori a geometry of field lines or magnetic and density profiles. We demonstrate that projection effects from the plane of the sky to 3D are significant in the calculation of field line expansion. We determine that waves with frequencies >2.8 x 10(-4) Hz are damped between 1 and 4 R(circle dot). In quiet-Sun regions, surface Alfven waves are damped at further distances compared to active regions, thus carrying additional wave energy into the corona. We compare the surface Alfven wave contribution to the heating by a variable polytropic index and find it as an order of magnitude larger than needed for quiet-Sun regions. For active regions, the contribution to the heating is 20%. As it has been argued that a variable gamma acts as turbulence, our results indicate that surface Alfven wave damping is comparable to turbulence in the lower corona. This damping mechanism should be included self-consistently as an energy driver for the wind in global MHD models.

In Vitro Evaluation of Acellular Dermal Matrix as a Three-Dimensional Scaffold for Gingival Fibroblasts Seeding

Background: Tissue engineering principles could improve the incorporation of acellular dermal matrix (ADM). The aim of this study is to verify if ADM is a suitable three-dimensional matrix for gingival fibroblasts and cancerous cells ingrowth, and also if cultured medium conditioned in ADM affect cellular behavior. Methods: Canine gingival fibroblasts (CGF), human gingival fibroblasts (HGF), and murine melanoma cell line (B16F10) were seeded on ADM for up to 14 days. The following parameters were assessed: morphology and distribution of CGF, HGF, and B16F10; CGF and HGF viability; and the effect of ADM conditioned medium (CM) on CGF viability. Results: Epifluorescence revealed that CGF were unevenly distributed on the ADM surface, showing no increase in cell number over the periods of study; HGF formed a monolayer on the ADM surface in a higher number at 14 days (P<0.05); B16F10 exhibited an increase in cell number within 7 days (P<0.05), and were mainly arranged in cell aggregates on the ADM, forming a continuous layer at 14 days. A higher percentage of cells on the ADM surface (P<0.05) compared to inside was observed for all cell types. 3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyl tetrazolium bromide (MU) values indicated higher cell viability in samples cultured with HGF compared to CGF (P=0.024). A significantly lower cell viability for CGF grown in CM compared to cells grown in non-CM was observed at 48 and 72 hours (P<0.05). Conclusions: ADM is not suitable as a three-dimensional matrix for gingival fibroblasts ingrowth. Gingival fibroblasts and highly proliferative cells as B16F10 can only be superficially located on ADM, and CGF are negatively affected by culture medium conditioned in ADM, reducing its viability. J Periodontol 2011;82:293-301.

STUDY OF THE EQUATORIAL ATLANTIC OCEAN MIXING LAYER USING A ONE-DIMENSIONAL TURBULENCE MODEL

The General Ocean Turbulence Model (GOTM) is applied to the diagnostic turbulence field of the mixing layer (ML) over the equatorial region of the Atlantic Ocean. Two situations were investigated: rainy and dry seasons, defined, respectively, by the presence of the intertropical convergence zone and by its northward displacement. Simulations were carried out using data from a PIRATA buoy located on the equator at 23 degrees W to compute surface turbulent fluxes and from the NASA/GEWEX Surface Radiation Budget Project to close the surface radiation balance. A data assimilation scheme was used as a surrogate for the physical effects not present in the one-dimensional model. In the rainy season, results show that the ML is shallower due to the weaker surface stress and stronger stable stratification; the maximum ML depth reached during this season is around 15 m, with an averaged diurnal variation of 7 m depth. In the dry season, the stronger surface stress and the enhanced surface heat balance components enable higher mechanical production of turbulent kinetic energy and, at night, the buoyancy acts also enhancing turbulence in the first meters of depth, characterizing a deeper ML, reaching around 60 m and presenting an average diurnal variation of 30 m.

MAGNETOHYDRODYNAMIC SIMULATIONS OF RECONNECTION AND PARTICLE ACCELERATION: THREE-DIMENSIONAL EFFECTS

Magnetic fields can change their topology through a process known as magnetic reconnection. This process in not only important for understanding the origin and evolution of the large-scale magnetic field, but is seen as a possibly efficient particle accelerator producing cosmic rays mainly through the first-order Fermi process. In this work we study the properties of particle acceleration inserted in reconnection zones and show that the velocity component parallel to the magnetic field of test particles inserted in magnetohydrodynamic (MHD) domains of reconnection without including kinetic effects, such as pressure anisotropy, the Hall term, or anomalous effects, increases exponentially. Also, the acceleration of the perpendicular component is always possible in such models. We find that within contracting magnetic islands or current sheets the particles accelerate predominantly through the first-order Fermi process, as previously described, while outside the current sheets and islands the particles experience mostly drift acceleration due to magnetic field gradients. Considering two-dimensional MHD models without a guide field, we find that the parallel acceleration stops at some level. This saturation effect is, however, removed in the presence of an out-of-plane guide field or in three-dimensional models. Therefore, we stress the importance of the guide field and fully three-dimensional studies for a complete understanding of the process of particle acceleration in astrophysical reconnection environments.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

A numerical method for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field

A finite difference technique, based on a projection method, is developed for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field. The governing equations in this situation are derived using primitive variables and are solved using the ideas behind the GENSMAC methodology (Tome and McKee [32]; Tome et al. [34]). The resulting numerical technique is then validated by comparing the numerical solution against an analytic solution for steady three-dimensional flow between two-parallel plates subject to a strong magnetic field. The validated code is then employed to solve channel flow for which there is no analytic solution. (C) 2009 Elsevier B.V. All rights reserved.

Electrochemical Control of the Time-Dependent Intensity Fluctuations in Surface-Enhanced Raman Scattering (SERS)

Time-dependent fluctuations in surface-enhanced Raman scattering (SERS) intensities were recorded from a roughened silver electrode immersed in diluted solutions of rhodamine 6G (R6G) and congo red (CR). These fluctuations were attributed to a small number of SERS-active molecules probing regions of extremely high electromagnetic field (hot spots) at the nanostructured surface. The time-dependent distribution of SERS intensities followed a tailed statistics at certain applied potentials, which has been linked to single-molecule dynamics. The shape of the distribution was reversibly tuned by the applied voltage. Mixtures of both dyes, R6G and CR, at low concentrations were also investigated. Since R6G is a cationic dye and CR is an anionic dye, the statistics of the SERS intensity distribution of either dye in a mixture were independently controlled by adjusting the applied potential. The potential-controlled distribution of SERS intensities was interpreted by considering the modulation of the surface coverage of the adsorbed dye by the interfacial electric field. This interpretation was supported by a two-dimensional Monte Carlo simulation that took into account the time evolution of the surface configuration of the adsorbed species and their probability to populate a hypothetical hot spot. The potential-controlled SERS dynamics reported here is a first step toward the spectroelectrochemical investigation of redox processes at the single-molecule level by SERS.