Numerical evaluation of three dimensional effects in planar flow birefringence

The influence of three dimensional effects on isochromatic birefringence is evaluated for planar flows by means of numerical simulation. Two fluid models are investigated in channel and abrupt contraction geometries. In practice, the flows are confined by viewing windows, which alter the stresses along the optical path. The observed optical properties differ therefore from their counterpart in an ideal two-dimensional flow. To investigate the influence of these effects, the stress optical rule and the differential propagation Mueller matrix are used. The material parameters are selected so that a retardation of multiple orders is achieved, as is typical for highly birefringent melts. Errors due to three dimensional effects are mainly found on the symmetry plane, and increase significantly with the flow rate. Increasing the geometric aspect ratio improve the accuracy provided that the error on the retardation is less than one order. (C) 2004 Elsevier B.V. All rights reserved.

Numerical simulation of abrupt contraction flows using the Double Convected Pom-Pom model

The Double Convected Pom-Pom model was recently introduced to circumvent some numerical and theological defects found in other formulations of the Pom-Pom concept. It is used here for the simulation of a benchmark problem: the flow in an abrupt planar contraction. The predictions are compared with birefringence measurements and show reasonable quantitative agreement with experimental data. A parametric study is also carried out with the aim of analysing the effect of the branching parameter on vortex dynamics and extrudate swell. The results show that the Double Convected Pom-Pom model (DCPP) model is able to discriminate between branched and linear macromolecular structures in accordance with experimental observations. In that respect, the role of the extensional properties in determining complex flow behaviour is stressed. Also, the ratio of the first normal stress difference to the shear stress appears to play a major role in die swell observation. For the time being, the role of the second normal stress difference appears to be less obvious to evaluate in this complex flow. (C) 2004 Elsevier B.V. All rights reserved.

Analysis of dynamical tunneling experiments with a Bose-Einstein condensate

Dynamical tunneling is a quantum phenomenon where a classically forbidden process occurs that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunneling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three-dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunneling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime.

Dynamic interfacial tension of aqueous solutions of PVAAs and its role in liquid-liquid dispersion stabilization

In liquid-liquid dispersion systems, the dynamic change of the interfacial properties between the two immiscible liquids plays an important role in both the emulsification process and emulsion stabilization. In this paper, experimentally measured dynamic interfacial tensions of 1-chlorobutane in the aqueous solutions of various random copolymers of polyvinyl acetate and polyvinyl alcohol (PVAA) are presented. Theoretical analyses on these results suggest that the adsorption of the polymer molecules is controlled neither by the bulk diffusion process nor the activation energy barrier for the adsorption but the conformation of polymer molecules. Based on the concept of critical concentration of condensation for polymer adsorption, as well as the observation that the rate at which the dynamic interfacial tension changes does not correlate to the PVAA's ability to stabilize a single drop, it is postulated that the main stabilization mechanism for the PVAAs is by steric hindrance, not the Gibbs-Marangoni effect offered by the small molecule surfactants.

Numerical investigation of seawater intrusion at Gooburrum, Bundaberg, Queensland, Australia

Seawater intrusion in coastal agricultural areas due to groundwater abstraction is a major environmental problem along the northeastern coast of Australia. Management options are being explored using numerical modelling, however, questions remain concerning the appropriate level of sophistication in models, choice of seaward boundary conditions, and how to accommodate heterogeneity and data uncertainty. The choice of seaward boundary condition is important since it affects the amount of salt transported into the aquifers and forms the focus of the present study. The impact of this boundary condition is illustrated for the seawater-intrusion problem in the Gooburrum aquifers, which occur within Tertiary sedimentary strata. A two-dimensional variable-density groundwater and solute-transport model was constructed using the computer code 2DFEMFAT (Cheng et al. 1998). The code was tested against an experiment for a steady-state freshwater-saltwater interface and against the Elder (Elder 1967) free-convection problem. Numerical simulations show that the imposition of the commonly-used equivalent hydrostatic freshwater heads, combined with a constant salt concentration at the seaward boundary, results in overestimated seawater intrusion in the lower Gooburrum aquifer. Since the imposition of this boundary condition allows water flow across the boundary, which subsequently takes salt into the aquifer, a careful check is essential to estimate whether too much mass of salt is introduced.

Numerical analysis of capacities for two-qubit unitary operations

We present numerical results on the capacities of two-qubit unitary operations for performing communication and creating entanglement. The capacities for communication considered are based upon the increase in Holevo information of an ensemble. Our results indicate that the capacity may be accurately estimated using ensemble sizes and ancilla dimensions of 4. In addition, the calculated values of these capacities were close to, and in some cases equal to, the similarly defined entangling capacities; this result indicates connections between these capacities.

On multiple solutions of the exterior neumann problem involving critical sobolev exponent

In this paper we consider the exterior Neumann problem involving a critical Sobolev exponent. We establish the existence of two solutions having a prescribed limit at infinity.

Global behavior of positive solutions of nonlinear three-point boundary value problems

We investigate the structure of the positive solution set for nonlinear three-point boundary value problems of the form u('') + h(t) f(u) = 0, u(0) = 0, u(1) = lambdau(eta), where eta epsilon (0, 1) is given lambda epsilon (0, 1/n) is a parameter, f epsilon C ([0, infinity), [0, infinity)) satisfies f (s) > 0 for s > 0, and h epsilon C([0, 1], [0, infinity)) is not identically zero on any subinterval of [0, 1]. Our main results demonstrate the existence of continua of positive solutions of the above problem. (C) 2004 Elsevier Ltd. All rights reserved.

Numerical modeling of 11.1 T MRI of a human head using MoM/FDTD methods

In a recent study, severe distortions in the proton images of an excised, fixed, human brain in an 11.1 Tesla/40 cm MR instrument have been observed, and the effect modeled on phantom images using a finite difference time domain (FDTD) model. in the present study, we extend these simulations to that of a complete human head, employing a hybrid FDTD and method of moments (MoM) approach, which provides a validated method for simulating biological samples in coil structures. The effect of fixative on the image distortions is explored. importantly, temperature distributions within the head are also simulated using a bioheat method based on parameters derived from the electromagnetic simulations. The MoM/FDTD simulations confirm that the transverse magnetic field (B,) from a ReCav resonator exhibits good homogeneity in air but strong inhomogeneity when loaded with the head with or without fixative. The fixative serves to increase the distortions, but they are still significant for the in vivo simulations. The simulated signal intensity (SI) distribution within the sample confirm the distortions in the experimental images are caused by the complex interactions of the incident electromagnetic fields with tissue, which is heterogeneous in terms of conductivity and permittivity. The temperature distribution is likewise heterogeneous, raising concerns regarding hot spot generation in the sample that may exceed acceptable levels in future in vivo studies. As human imaging at 11.1 T is some time away, simulations are important in terms of predicting potential safety issues as well as evaluating practical concerns about the quality of images. Simulation on a whole human head at 11.1 T implies the wave behavior presents significant engineering challenges for ultra-high-field (UHF) MRI. Novel strategies will have to be employed in imaging technique and resonator design for UHF MRI to achieve the theoretical signal-to-noise ratio (SNR) improvements it offers over lower field systems. (C) 2005 Wiley Periodicals, Inc.

Numerical evaluation of the fields induced by body motion in or near high-field MRI scanners

In modern magnetic resonance imaging, both patients and health care workers are exposed to strong. non-uniform static magnetic fields inside and outside of the scanner. In which body movement may be able to induce electric currents in tissues which could be potentially harmful. This paper presents theoretical investigations into the spatial distribution of induced E-fields in a tissue-equivalent human model when moving at various positions around the magnet. The numerical calculations are based on an efficient. quasi-static, finite-difference scheme. Three-dimensional field profiles from an actively shielded 4 T magnet system are used and the body model projected through the field profile with normalized velocity. The simulation shows that it is possible to induce E-fields/currents near the level of physiological significance under some circumstances and provides insight into the spatial characteristics of the induced fields. The methodology presented herein can be extrapolated to very high field strengths for the evaluation of the effects of motion at a variety of field strengths and velocities. (C) 2004 Elsevier Ltd. All rights reserved.

Numerical simulation of magnetite segregation in a dense medium cyclone

Numerical simulations of turbulent driven flow in a dense medium cyclone with magnetite medium have been conducted using Fluent. The predicted air core shape and diameter were found to be close to the experimental results measured by gamma ray tomography. It is possible that the Large eddy simulation (LES) turbulence model with Mixture multi-phase model can be used to predict the air/slurry interface accurately although the LES may need a finer grid. Multi-phase simulations (air/water/medium) are showing appropriate medium segregation effects but are over-predicting the level of segregation compared to that measured by gamma-ray tomography in particular with over prediction of medium concentrations near the wall. Further, investigated the accurate prediction of axial segregation of magnetite using the LES turbulence model together with the multi-phase mixture model and viscosity corrections according to the feed particle loading factor. Addition of lift forces and viscosity correction improved the predictions especially near the wall. Predicted density profiles are very close to gamma ray tomography data showing a clear density drop near the wall. The effect of size distribution of the magnetite has been fully studied. It is interesting to note that the ultra-fine magnetite sizes (i.e. 2 and 7 mu m) are distributed uniformly throughout the cyclone. As the size of magnetite increases, more segregation of magnetite occurs close to the wall. The cut-density (d(50)) of the magnetite segregation is 32 gm, which is expected with superfine magnetite feed size distribution. At higher feed densities the agreement between the [Dungilson, 1999; Wood, J.C., 1990. A performance model for coal-washing dense medium cyclones, Ph.D. Thesis, JKMRC, University of Queensland] correlations and the CFD are reasonably good, but the overflow density is lower than the model predictions. It is believed that the excessive underflow volumetric flow rates are responsible for under prediction of the overflow density. (c) 2006 Elsevier Ltd. All rights reserved.

Dissolution of porcine incisor pulps in sodium hypochlorite solutions of varying compositions and concentrations

Background: The solubility of dental pulp tissue in sodium hypochlorite has been extensively investigated but results have been inconsistent; due most likely to variations in experimental design, the volume and/or rate of replenishment of the solutions used and the nature of the tissues assessed. Traditionally, the sodium hypochlorite solutions used for endodontic irrigation in Australia have been either Milton or commercial bleach, with Milton being the most common. Recently, a range of Therapeutic Goods Administration (TGA) approved proprietary sodium hypochlorite solutions, which contain surfactant, has become available. Some domestic chlorine bleaches now also contain surfactants. The purpose of this study was to perform new solubility assessments, comparing Milton with new TGA approved products, Hypochlor 1% and Hypochlor 4% forte, and with a domestic bleach containing surfactant (White King). Methods: Ten randomly assigned pulp samples of porcine dental pulp of approximately equal dimensions were immersed in the above solutions, as well as representative concentrations of sodium hydroxide. Time to complete dissolution was measured and assessed statistically. Results: White King 4% showed the shortest dissolution time, closely followed by Hypochlor 4% forte. White King 1% and Hypochlor 1% each took around three times as long to completely dissolve the samples of pulp as their respective 4% concentrations, while Milton took nearly 10 times as long. The sodium hydroxide solutions showed no noticeable dissolution of the pulp samples. Conclusions: The composition and content of sodium hypochlorite solutions had a profound effect on the ability of these solutions to dissolve pulp tissue in vitro. Greater concentrations provided more rapid dissolution of tissue. One per cent solutions with added surfactant and which contained higher concentrations of sodium hydroxide were significantly more effective in dissolution of pulp tissue than Milton.

Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.