Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

0We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.

Timing, magnitude, and location of initial soluble aluminum injuries to mungbean roots

Despite a century's knowledge that soluble aluminum (Al) is associated with acid soils and poor plant growth, it is still uncertain how Al exerts its deleterious effects. Hypotheses include reactions of Al with components of the cell wall, plasmalemma, or cytoplasm of cells close to the root tip, thereby reducing cell expansion and root growth. Digital microscopy was used to determine the initial injuries of soluble Al to mungbean (Vigna radiata L.) roots. Roots of young seedlings were marked with activated carbon particles and grown in 1 mm CaCl2 solution at pH 6 for ca. 100 min (control period), and AlCl3 solution was added to ensure a final concentration of 50 muM Al (pH 4). Further studies were conducted on the effects of pH 4 with and without 50 muM Al. Four distinct, but possibly related, initial detrimental effects of soluble Al were noted. First, there was a 56-75% reduction in the root elongation rate, first evident 18-52 min after the addition of Al, root elongation continuing at a decreased rate for ca. 20 It. Decreasing solution pH from 6 to 4 increased the root elongation rate 4-fold after 5 min, which decreased to close to the original rate after 130 min. The addition of Al during the period of rapid growth at pH 4 reduced the root elongation rate by 71% 14 min after the addition of Al. The activated carbon marks on the roots showed that, during the control period, the zone of maximum root growth occurred at 2,200-5,100 mum from the root tip (i.e. the cell elongation zone). It was there that Al first exerted its detrimental effect and low pH increased root elongation. Second, soluble Al prevented the progress of cells from the transition to the elongation phase, resulting in a considerable reduction of root growth over the longer term. The third type of soluble Al injury occurred after exposure for ca. 4 h to 50 mum Al when a kink developed at 2,370 mum from the root tip. Fourth, ruptures of the root epidermal and cortical cells at 1,900-2,300 mum from the tip occurred greater than or equal to4.3 h after exposure to soluble Al. The timing and location of Al injuries support the contention that Al initially reduces cell elongation, thus decreasing root growth and causing damage to epidermal and cortical cells.

Emulsion strategies in the microencapsulation of cells: Pathways to thin coherent membranes

Microencapsulation of cell spheroids in an immunoselective, highly biocompatible, biomembrane offers a way to create viable implantation options in the treatment of insulin-dependent diabetes mellitus (IDDM). Traditionally the encapsulation process has been achieved through the injection/extrusion of alginate/cell mixtures into a calcium chloride solution to produce calcium alginate capsules around the cells. A novel alternative is explored here through a procedure using an emulsion process to produce thin adherent calcium alginate membranes around cell spheroids. In this study, a thorough investigation has been used to establish the emulsion process parameters that are critical to the formation of a coherent alginate coat both on a model spheroid system and subsequently on cell spheroids. Optical and fluorescence microscopy are used to assess the morphology and coherence of the calcium alginate/ poly-L-ornithine/alginate (APA) capsules produced. (c) 2005 Wiley Periodicals, Inc.

2D strain - a new approach to strain and strain rate: the solution to the angle-dependence of tissue Doppler?

Purpose: Tissue Doppler strain rate imaging (SRI) have been validated and applied in various clinical settings, but the clinical use of this modality is still limited due to time-consuming postprocessing, unfavorable signal to noise ratio and major angle dependency of image acquisition. 2D Strain (2DS) measures strain parameters through automated tissue tracking (Lagrangian strain) rather than tissue velocity regression. We sought to compare the accuracy of this technique with SRI and evaluate whether it overcomes the above limitations. Methods: We assessed 26 patients (13 female, age 60±5yrs) at low risk of CAD and with normal DSE at both baseline and peak stress. End systolic strain (ESS), peak systolic strain rate (SR), and timing parameters were measured by two independent observers using SRI and 2D Strain. Myocardial segments were excluded from the analyses if the insonation angle exceeded 30 degrees or if the segments were not visualized; 417 segments were evaluated. Results: Normal ranges for TVI and CEB approaches were comparable for SR (-0.99 ± 0.39 vs -0.88 ± 0.36, p=NS), ESS (-15.1 ± 6.5 vs -14.9 ± 6.3, p=NS), time to end of systole (174 ± 47 vs 174 ± 53, p=NS) and time to peak SR (TTP; 340 ± 34 vs 375 ± 57). The best correlations between the techniques were for time to end systole (rest r=0.6, p

Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.

Hitting a moving target: Perception and action in the timing of rapid interceptions

Different interceptive tasks and modes of interception (hitting or capturing) do not necessarily involve similar control processes. Control based on preprogramming of movement parameters is possible for actions with brief movement times but is now widely rejected; continuous perceptuomotor control models are preferred for all types of interception. The rejection of preprogrammed control and acceptance of continuous control is evaluated for the timing of rapidly executed, manual hitting actions. It is shown that a preprogrammed control model is capable of providing a convincing account of observed behavior patterns that avoids many of the arguments that have been raised against it. Prominent continuous perceptual control models are analyzed within a common framework and are shown to be interpretable as feedback control strategies. Although these models can explain observations of on-line adjustments to movement, they offer only post hoc explanations for observed behavior patterns in hitting tasks and are not directly supported by data. It is proposed that rapid manual hitting tasks make up a class of interceptions for which a preprogrammed strategy is adopted-a strategy that minimizes the role of visual feedback. Such a strategy is effective when the task demands a high degree of temporal accuracy.

Analytical solution of forced convection in a duct of rectangular cross-section saturated by a porous medium

A theoretical analysis is presented to investigate fully developed (both thermally and hydrodynamically) forced convection in a duct of rectangular cross-section filled with a hyper-porous medium. The Darcy-Brinkman model for flow through porous media was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [1], is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

Canonical Bose gas simulations with stochastic gauges

A technique to simulate the grand canonical ensembles of interacting Bose gases is presented. Results are generated for many temperatures by averaging over energy-weighted stochastic paths, each corresponding to a solution of coupled Gross-Pitaevskii equations with phase noise. The stochastic gauge method used relies on an off-diagonal coherent-state expansion, thus taking into account all quantum correlations. As an example, the second-order spatial correlation function and momentum distribution for an interacting 1D Bose gas are calculated.

Pair correlations in a finite-temperature 1D Bose gas

We calculate the two-particle local correlation for an interacting 1D Bose gas at finite temperature and classify various physical regimes. We present the exact numerical solution by using the Yang-Yang equations and Hellmann-Feynman theorem and develop analytical approaches. Our results draw prospects for identifying the regimes of coherent output of an atom laser, and of finite-temperature “fermionization” through the measurement of the rates of two-body inelastic processes, such as photoassociation.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

A demonstration of artificial dissipation effects in some finite volume solution methods for the Navier-Stokes equations

The artificial dissipation effects in some solutions obtained with a Navier-Stokes flow solver are demonstrated. The solvers were used to calculate the flow of an artificially dissipative fluid, which is a fluid having dissipative properties which arise entirely from the solution method itself. This was done by setting the viscosity and heat conduction coefficients in the Navier-Stokes solvers to zero everywhere inside the flow, while at the same time applying the usual no-slip and thermal conducting boundary conditions at solid boundaries. An artificially dissipative flow solution is found where the dissipation depends entirely on the solver itself. If the difference between the solutions obtained with the viscosity and thermal conductivity set to zero and their correct values is small, it is clear that the artificial dissipation is dominating and the solutions are unreliable.

Solution structure of robustoxin, the lethal neurotoxin from the funnel-web spider Atrax robustus

The solution structure of robustoxin, the lethal neurotoxin from the Sydney funnel-web spider Atrax robustus, has been determined from 2D H-1 NMR data, Robustoxin is a polypeptide of 42 residues cross-linked by four disulphide bonds, the connectivities of which were determined from NMR data and trial structure calculations to be 1-15, 8-20, 14-31 and 16-42 (a 1-4/2-6/3-7/5-8 pattern), The structure consists of a small three-stranded, anti-parallel beta-sheet and a series of interlocking gamma-turns at the C-terminus. It also contains a cystine knot, thus placing it in the inhibitor cystine knot motif family of structures, which includes the omega-conotoxins and a number of plant and animal toxins and protease inhibitors. Robustoxin contains three distinct charged patches on its surface, and an extended loop that includes several aromatic and non-polar residues, Both of these structural features may play a role in its binding to the voltage-gated sodium channel. (C) 1997 Federation of European Biochemical Societies.

Solution structure and proposed binding mechanism of a novel potassium channel toxin kappa-conotoxin PVIIA

Background: kappa-PVIIA is a 27-residue polypeptide isolated from the venom of Conus purpurascens and is the first member of a new class of conotoxins that block potassium channels. By comparison to other ion channels of eukaryotic cell membranes, voltage-sensitive potassium channels are relatively simple and methodology has been developed for mapping their interactions with small-peptide toxins, PVIIA, therefore, is a valuable new probe of potassium channel structure. This study of the solution structure and mode of channel binding of PVIIA forms the basis for mapping the interacting residues at the conotoxin-ion channel interface. Results: The three-dimensional structure of PVIIA resembles the triple-stranded beta sheet/cystine-knot motif formed by a number of toxic and inhibitory peptides. Subtle structural differences, predominantly in loops 2 and 4, are observed between PVIIA and other conotoxins with similar structural frameworks, however. Electrophysiological binding data suggest that PVIIA blocks channel currents by binding in a voltage-sensitive manner to the external vestibule and occluding the pore, Comparison of the electrostatic surface of PVIIA with that of the well-characterised potassium channel blocker charybdotoxin suggests a likely binding orientation for PVIIA, Conclusions: Although the structure of PVIIA is considerably different to that of the alpha K scorpion toxins, it has a similar mechanism of channel blockade. On the basis of a comparison of the structures of PVIIA and charybdotoxin, we suggest that Lys19 of PVIIA is the residue which is responsible for physically occluding the pore of the potassium channel.