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.

Three-dimensional solitons in coupled atomic-molecular Bose-Einstein condensates

We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BECs). The soliton solutions to the mean-field equations are obtained in an approximate analytical form by means of a variational approach. We investigate soliton stability within the parameter space described by the atom-molecule conversion coupling, the atom-atom s-wave scattering, and the bare formation energy of the molecular species. In terms of ordinary optics, this is analogous to the process of sub- or second-harmonic generation in a quadratic nonlinear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatiotemporal solitons in pure quadratic media has been theoretically demonstrated previously, here we extend this prediction to matter-wave interactions in BEC systems where higher-order nonlinear processes due to interparticle collisions are unavoidable and may not be neglected. The stability of the solitons predicted for repulsive atom-atom interactions is investigated by direct numerical simulations of the equations of motion in a full 3D lattice. Our analysis also leads to a possible technique for demonstrating the ground state of the Schrodinger-Newton and related equations that describe Bose-Einstein condensates with nonlocal interparticle forces.

Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones.

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented three-dimensional fault zone has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system. (C) 2004 Published by Elsevier B.V.

Three-dimensional simulation of the rolling of a saturated fibro-porous media

This paper describes recent advances made in computational modelling of the sugar cane liquid extraction process. The saturated fibro-porous material is rolled between circumferentially grooved rolls, which enhance frictional grip and provide a low-resistance path for liquid flow during the extraction process. Previously reported two-dimensional (2D) computational models, account for the large deformation of the porous material by solving the fully coupled governing fibre stress and fluid-flow equations using finite element techniques. While the 2D simulations provide much insight into the overarching cause-effect relationships, predictions of mechanical quantities such as roll separating force and particularly torque as a function of roll speed and degree of compression are not satisfactory for industrial use. It is considered that the unsatisfactory response in roll torque prediction may be due to the stress levels that exist between the groove tips and roots which have been largely neglected in the geometrically simplified 2D model. This paper gives results for both two- and three-dimensional finite element models and highlights their strengths and weaknesses in predicting key milling parameters. (c) 2005 Elsevier B.V. All rights reserved.

Use of real-time three-dimensional echocardiography to measure left atrial volume: Comparison with other echocardiographic techniques

Objectives: Left atrial (LA) volume (LAV) is a prognostically important biomarker for diastolic dysfunction, but its reproducibility on repeated testing is not well defined. LA assessment with 3-dimensional. (3D) echocardiography (3DE) has been validated against magnetic resonance imaging, and we sought to assess whether this was superior to existing measurements for sequential echocardiographic follow-up. Methods: Patients (n = 100; 81 men; age 56 +/- 14 years) presenting for LA evaluation were studied with M-mode (MM) echocardiography, 2-dimensional (2D) echocardiography, and 3DE. Test-retest variation was performed by a complete restudy by a separate sonographer within 1 hour without alteration of hemodynamics or therapy. In all, 20 patients were studied for interobserver and intraobserver variation. LAVs were calculated by using M-mode diameter and planimetered atrial area in the apical. 4-chamber view to calculate an assumed sphere, as were prolate ellipsoid, Simpson's biplane, and biplane area-length methods. All were compared with 3DE. Results: The average LAV was 72 +/- 27 mL by 3DE. There was significant underestimation of LAV by M-mode (35 +/- 20 mL, r = 0.66, P < .01). The 3DE and various 2D echocardiographic techniques were well correlated: LA planimetry (85 +/- 38 mL, r = 0.77, P < .01), prolate ellipsoid (73 +/- 36 mL, r = 0.73, P = .04), area-length (64 +/- 30 mL, r = 0.74, P < .01), and Simpson's biplane (69 +/- 31 mL, r = 0.78, P = .06). Test-retest variation for 3DE was most favorable (r = 0.98, P < .01), with the prolate ellipsoid method showing most variation. Interobserver agreement between measurements was best for 3DE (r = 0.99, P < .01), with M-mode the worst (r = 0.89, P < .01). Intraobserver results were similar to interobserver, the best correlation for 3DE (r = 0.99, P < .01), with LA planimetry the worst (r = 0.91, P < .01). Conclusions. The 2D measurements correlate closely with 3DE. Follow-up assessment in daily practice appears feasible and reliable with both 2D and 3D approaches.

Changes in three dimensional lumbo-pelvic kinematics and trunk muscle activity with speed and mode of locomotion

Background Control of the trunk is critical for locomotor efficiency. However, investigations of trunk muscle activity and three-dimensional lumbo-pelvic kinematics during walking and running remain scarce. Methods. Gait parameters and three-dimensional lumbo-pelvic kinematics were recorded in seven subjects. Electromyography recordings of abdominal and paraspinal muscles were made using fine-wire and surface electrodes as subjects walked on a treadmill at 1 and 2 ms(-1) and ran at 2, 3, 4 and 5 ms(-1). Findings. Kinematic data indicate that the amplitude but not timing of lumbo-pelvic motion changes with locomotor speed. Conversely, a change in locomotor mode is associated with temporal but not spatial adaptation in neuromotor strategy. That is, peak transverse plane lumbo-pelvic rotation occurs at foot strike during walking but prior to foot strike during running. Despite this temporal change, there is a strong correlation between the amplitude of transverse plane lumbo-pelvic rotation and stride length during walking and running. In addition, Jumbo-pelvic motion was asymmetrical during all locomotor tasks. Trunk muscle electromyography occurred biphasically in association with foot strike. Transversus abdominis was tonically active with biphasic modulation. Consistent with the kinematic data, electromyography activity of the abdominal muscles and the superficial fibres of multifidus increased with locomotor speed, and timing of peak activity of superficial multifidus and obliquus externus abdominis was modified in association with the temporal adaptation in lumbo-pelvic motion with changes in locomotor mode. Interpretation. These data provide evidence of the association between lumbo-pelvic motion and trunk muscle activity during locomotion at different speeds and modes. (c) 2005 Elsevier Ltd. All rights reserved.

Method for the generation and cultivation of functional three-dimensional mammary constructs without exogenous extracellular matrix

During puberty, pregnancy, lactation and postlactation, breast tissue undergoes extensive remodelling and the disruption of these events can lead to cancer. In vitro studies of mammary tissue and its malignant transformation regularly employ mammary epithelial cells cultivated on matrigel or floating collagen rafts. In these cultures, mammary epithelial cells assemble into three-dimensional structures resembling in vivo acini. We present a novel technique for generating functional mammary constructs without the use of matrix substitutes.

Three-dimensional analysis of eutectic grains in hypoeutectic Al-Si alloys

An approach to the qualitative analysis of quenched microstructures in three dimensions is presented and demonstrated on unmodified and Sr-modified Al-10% Si samples. The samples were repeatedly polished to obtain a series of digital images through the depth of the microstructure. A three-dimensional reconstruction of the microstructure was obtained by assembling the images of the serial sections. Reconstructions were made of unmodified and Sr-modified Al-Si eutectic grains that were quenched during eutectic solidification. The three-dimensional reconstructions show that strontium modification changes the size and morphology of the Al-Si eutectic grains. Sr-modified eutectic grains are large approximately spherical grains and grow with a high interface velocity. In the unmodified alloy, many small eutectic grains grow from the dendrite arm tips. The unmodified eutectic grains appear to grow from the dendrite tips into the undercooled liquid, rather than back-filling the dendrite envelope, possibly continuing to grow in the same manner as the equiaxed dendrites. (C) 2004 Elsevier B.V. All rights reserved.

Analysis of cardiac ventricular wall motion based on a three-dimensional electromechanical biventricular model

This paper describes a biventricular model, which couples the electrical and mechanical properties of the heart, and computer simulations of ventricular wall motion and deformation by means of a biventricular model. In the constructed electromechanical model, the mechanical analysis was based on composite material theory and the finite-element method; the propagation of electrical excitation was simulated using an electrical heart model, and the resulting active forces were used to calculate ventricular wall motion. Regional deformation and Lagrangian strain tensors were calculated during the systole phase. Displacements, minimum principal strains and torsion angle were used to describe the motion of the two ventricles. The simulations showed that during the period of systole, (1) the right ventricular free wall moves towards the septum, and at the same time, the base and middle of the free wall move towards the apex, which reduces the volume of the right ventricle; the minimum principle strain (E3) is largest at the apex, then at the middle of the free wall and its direction is in the approximate direction of the epicardial muscle fibres; (2) the base and middle of the left ventricular free wall move towards the apex and the apex remains almost static; the torsion angle is largest at the apex; the minimum principle strain E3 is largest at the apex and its direction on the surface of the middle wall of the left ventricle is roughly in the fibre orientation. These results are in good accordance with results obtained from MR tagging images reported in the literature. This study suggests that such an electromechanical biventricular model has the potential to be used to assess the mechanical function of the two ventricles, and also could improve the accuracy ECG simulation when it is used in heart torso model-based body surface potential simulation studies.

The influence of architecture on degradation and tissue ingrowth into three-dimensional poly(lactic-co-glycolic acid) scaffolds in vitro and in vivo

The in vitro and in vivo degradation properties of poly(lactic-co-glycolic acid) (PLGA) scaffolds produced by two different technologies-therm ally induced phase separation (TIPS), and solvent casting and particulate leaching (SCPL) were compared. Over 6 weeks, in vitro degradation produced changes in SCPL scaffold dimension, mass, internal architecture and mechanical properties. TIPS scaffolds produced far less changes in these parameters providing significant advantages over SCPL. In vivo results were based on a microsurgically created arteriovenous (AV) loop sandwiched between two TIPS scaffolds placed in a polycarbonate chamber under rat groin skin. Histologically, a predominant foreign body giant cell response and reduced vascularity was evident in tissue ingrowth between 2 and 8 weeks in TIPS scaffolds. Tissue death occurred at 8 weeks in the smallest pores. Morphometric comparison of TIPS and SCPL scaffolds indicated slightly better tissue ingrowth but greater loss of scaffold structure in SCPL scaffolds. Although advantageous in vitro, large surface area:volume ratios and varying pore sizes in PLGA TIPS scaffolds mean that effective in vivo (AV loop) utilization will only be achieved if the foreign body response can be significantly reduced so as to allow successful vascularisation, and hence sustained tissue growth, in pores less than 300 mu m. (C) 2005 Elsevier Ltd. All rights reserved.

Using two dimensional sectional distributions to infer three dimensional volumetric distributions - Validation using tomography

The critical process parameter for mineral separation is the degree of mineral liberation achieved by comminution. The degree of liberation provides an upper limit of efficiency for any physical separation process. The standard approach to measuring mineral liberation uses mineralogical analysis based two-dimensional sections of particles which may be acquired using a scanning electron microscope and back-scatter electron analysis or from an analysis of an image acquired using an optical microscope. Over the last 100 years, mathematical techniques have been developed to use this two dimensional information to infer three-dimensional information about the particles. For mineral processing, a particle that contains more than one mineral (a composite particle) may appear to be liberated (contain only one mineral) when analysed using only its revealed particle section. The mathematical techniques used to interpret three-dimensional information belong, to a branch of mathematics called stereology. However methods to obtain the full mineral liberation distribution of particles from particle sections are relatively new. To verify these adjustment methods, we require an experimental method which can accurately measure both sectional and three dimensional properties. Micro Cone Beam Tomography provides such a method for suitable particles and hence, provides a way to validate methods used to convert two-dimensional measurements to three dimensional estimates. For this study ore particles from a well-characterised sample were subjected to conventional mineralogical analysis (using particle sections) to estimate three-dimensional properties of the particles. A subset of these particles was analysed using a micro-cone beam tomograph. This paper presents a comparison of the three-dimensional properties predicted from measured two-dimensional sections with the measured three-dimensional properties.

A method for screening the temperature dependence of three-dimensional crystal formation

Temperature is an important parameter controlling protein crystal growth. A new temperature-screening system (Thermo-screen) is described consisting of a gradient thermocycler fitted with a special crystallization-plate adapter onto which a 192-well sitting-drop crystallization plate can be mounted (temperature range 277-372 K; maximum temperature gradient 20 K; interval precision 0.3 K). The system allows 16 different conditions to be monitored simultaneously over a range of 12 temperatures and is well suited to conduct wide (similar to 20 K) and fine (similar to 3 K) temperature-optimization screens. It can potentially aid in the determination of temperature phase diagrams and run more complex temperature-cycling experiments for seeding and crystal growth.

Simulation of Brugada syndrome using cellular and three-dimensional whole-heart modeling approaches

Brugada syndrome (BS) is a genetic disease identified by an abnormal electrocardiogram ( ECG) ( mainly abnormal ECGs associated with right bundle branch block and ST-elevation in right precordial leads). BS can lead to increased risk of sudden cardiac death. Experimental studies on human ventricular myocardium with BS have been limited due to difficulties in obtaining data. Thus, the use of computer simulation is an important alternative. Most previous BS simulations were based on animal heart cell models. However, due to species differences, the use of human heart cell models, especially a model with three-dimensional whole-heart anatomical structure, is needed. In this study, we developed a model of the human ventricular action potential (AP) based on refining the ten Tusscher et al (2004 Am. J. Physiol. Heart Circ. Physiol. 286 H1573 - 89) model to incorporate newly available experimental data of some major ionic currents of human ventricular myocytes. These modified channels include the L-type calcium current (ICaL), fast sodium current (I-Na), transient outward potassium current (I-to), rapidly and slowly delayed rectifier potassium currents (I-Kr and I-Ks) and inward rectifier potassium current (I-Ki). Transmural heterogeneity of APs for epicardial, endocardial and mid-myocardial (M) cells was simulated by varying the maximum conductance of IKs and Ito. The modified AP models were then used to simulate the effects of BS on cellular AP and body surface potentials using a three-dimensional dynamic heart - torso model. Our main findings are as follows. (1) BS has little effect on the AP of endocardial or mid-myocardial cells, but has a large impact on the AP of epicardial cells. (2) A likely region of BS with abnormal cell AP is near the right ventricular outflow track, and the resulting ST-segment elevation is located in the median precordium area. These simulation results are consistent with experimental findings reported in the literature. The model can reproduce a variety of electrophysiological behaviors and provides a good basis for understanding the genesis of abnormal ECG under the condition of BS disease.

The displacement and strain field of three-dimensional rheologic model of earthquake preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.