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.

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.

Isolation and characterization of novel cyclotides from Viola hederaceae - Solution structure and anti-HIV activity of vhl-1, a leaf-specific expressed cyclotide

Based on a newly established sequencing strategy featured by its efficiency, simplicity, and easy manipulation, the sequences of four novel cyclotides (macrocyclic knotted proteins) isolated from an Australian plant Viola hederaceae were determined. The three-dimensional solution structure of V. hederaceae leaf cyclotide-1 ( vhl-1), a leaf-specific expressed 31-residue cyclotide, has been determined using two-dimensional H-1 NMR spectroscopy. vhl-1 adopts a compact and well defined structure including a distorted triple-stranded β- sheet, a short 310 helical segment and several turns. It is stabilized by three disulfide bonds, which, together with backbone segments, form a cyclic cystine knot motif. The three-disulfide bonds are almost completely buried into the protein core, and the six cysteines contribute only 3.8% to the molecular surface. A pH titration experiment revealed that the folding of vhl-1 shows little pH dependence and allowed the pK(a) of 3.0 for Glu(3) and &SIM; 5.0 for Glu(14) to be determined. Met(7) was found to be oxidized in the native form, consistent with the fact that its side chain protrudes into the solvent, occupying 7.5% of the molecular surface. vhl-1 shows anti-HIV activity with an EC50 value of 0.87 μ m.

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.

Structure-activity relationships for a new family of sulfonylurea herbicides

Acetohydroxyacid synthase (AHAS; EC 2.2.1.6) catalyzes the first common step in branched-chain amino acid biosynthesis. The enzyme is inhibited by several chemical classes of compounds and this inhibition is the basis of action of the sulfonylurea and imidazolinone herbicides. The commercial sulfonylureas contain a pyrimidine or a triazine ring that is substituted at both meta positions, thus obeying the initial rules proposed by Levitt. Here we assess the activity of 69 monosubstituted sulfonylurea analogs and related compounds as inhibitors of pure recombinant Arabidopsis thaliana AHAS and show that disubstitution is not absolutely essential as exemplified by our novel herbicide, monosulfuron (2-nitro-N-(4'-methyl-pyrimidin-2'-yl) phenyl-sulfonylurea), which has a pyrimidine ring with a single meta substituent. A subset of these compounds was tested for herbicidal activity and it was shown that their effect in vivo correlates well with their potency in vitro as AHAS inhibitors. Three-dimensional quantitative structure-activity relationships were developed using comparative molecular field analysis and comparative molecular similarity indices analysis. For the latter, the best result was obtained when steric, electrostatic, hydrophobic and H-bond acceptor factors were taken into consideration. The resulting fields were mapped on to the published crystal structure of the yeast enzyme and it was shown that the steric and hydrophobic fields are in good agreement with sulfonylurea-AHAS interaction geometry.

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.

Flow focusing in microchannels

A volume-of-fluid numerical method is used to predict the dynamics of drop formation in an axi-symmetric microfluidic flow-focusing geometry for a liquid-liquid system. The Reynolds numbers and Weber numbers approximate those of a three-dimensional flow in recently published experiments. We compare the predicted drop formation with the experimental results at various flow rates, and discuss the mechanisms of drop formation in this context. Despite the differences in geometry, we find qualitative correspondence between the numerical and experimental results. Both end-pinching and capillary-wave instability are important for droplet break-up at the higher flow rates.

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.

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.

Comparison between real-time three-dimensional echocardiography, T1-201 single photon emission computed tomography and cardiac magnetic resonance imaging in the quantitative assessment of left ventricular volumes

Left ventricular (LV) volumes have important prognostic implications in patients with chronic ischemic heart disease. We sought to examine the accuracy and reproducibility of real-time 3D echo (RT-3DE) compared to TI-201 single photon emission computed tomography (SPECT) and cardiac magnetic resonance imaging (MRI). Thirty (n = 30) patients (age 62±9 years, 23 men) with chronic ischemic heart disease underwent LV volume assessment with RT-3DE, SPECT, and MRI. Ano vel semi-automated border detection algorithmwas used by RT-3DE. End diastolic volumes (EDV) and end systolic volumes (ESV) measured by RT3DE and SPECT were compared to MRI as the standard of reference. RT-3DE and SPECT volumes showed excellent correlation with MRI (Table). Both RT- 3DE and SPECT underestimated LV volumes compared to MRI (ESV, SPECT 74±58 ml versus RT-3DE 95±48 ml versus MRI 96±54 ml); (EDV, SPECT 121±61 ml versus RT-3DE 169±61 ml versus MRI 179±56 ml). The degree of ESV underestimation with RT-3DE was not significant.