On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model

We investigate the quantum Jaynes-Cummings model - a particular case of the Gaudin model with one of the spins being infinite. Starting from the Bethe equations we derive Baxter's equation and from it a closed set of equations for the eigenvalues of the commuting Hamiltonians. A scalar product in the separated variables representation is found for which the commuting Hamiltonians are Hermitian. In the semi classical limit the Bethe roots accumulate on very specific curves in the complex plane. We give the equation of these curves. They build up a system of cuts modeling the spectral curve as a two sheeted cover of the complex plane. Finally, we extend some of these results to the XXX Heisenberg spin chain.Comment: 16 page

Validation of a physically-based solid oxide fuel cell anode model combining 3D tomography and impedance spectroscopy

This study presents a physically-based model for the simulation of impedance spectra in solid oxide fuel cell (SOFC) composite anodes. The model takes into account the charge transport and the charge-transfer reaction at the three-phase boundary distributed along the anode thickness, as well as the phenomena at the electrode/electrolyte interface and the multicomponent gas diffusion in the test rig. The model is calibrated with experimental impedance spectra of cermet anodes made of nickel and scandia-stabilized zirconia and satisfactorily validated in electrodes with different microstructural properties, quantified through focused ion beam SEM tomography. Besides providing the material-specific kinetic parameters of the electrochemical hydrogen oxidation, this study shows that the correlation between electrode microstructure and electrochemical performance can be successfully addressed by combining physically-based modelling, impedance spectroscopy and 3D tomography. This approach overcomes the limits of phenomenological equivalent circuits and is suitable for the interpretation of experimental data and for the optimisation of the electrode microstructure

Hypertension Guideline 2003 Update

Outcomes. Extensive data from many randomised controlled trials have shown the benefit of treating hypertension. The target blood pressure (BP) for antihypertensive management should be systolic BP < 140 mmHg, diastolic < 90 mmHg, with minimal or no drug side-effects. However, a lesser reduction will elicit benefit although this is not optimal. The reduction of BP in the elderly and in those with severe hypertension should be achieved gradually over 6 months. Stricter BP control is required for patients with end organ damage, co-existing risk factors and co-morbidity, e.g. diabetes mellitus. Co-existent risk factors should also be controlled.Benefits. Reduction in risk of stroke, cardiac failure, renal insufficiency and probably coronary artery disease. The major precautions and contraindications to each antihypertensive drug recommended are listed.Recommendations. Correct BP measurement procedure is described. Evaluation of cardiovascular risk factors and recommendations for antihypertensive therapy are stipulated. The total cardiovascular disease risk profile should be determined for all patients and this should inform management strategies. 'Lifestyle modification and patient education plays an essential role in the management strategy. Drug therapy: First line -low dose thiazide-like diuretics; second line -add one of the following: reserpine or β-blockers or ACE inhibitors or calcium channel blockers; third line - add another second line drug or hydralazine or α-blocker. The guideline includes management of specific situations, i.e. hypertensive emergency and urgency, severe hypertension with target organ damage and refractory hypertension (BP >160/95 mmHg on triple therapy), hypertension in diabetes mellitus, etc.Validity. Developed by the Working Groups established by the Executive Committee of the Southern African Hypertension Society with broader consensus meeting endorsement. The 2001 version was endorsed by the South African Medical Association Guideline Committee. The 2003 revisions were endorsed by the Executive Committee and a wider Working Group

Soliton Solutions for ABS Lattice Equations II: Casoratians and Bilinearization

In Part I [arXiv:0902.4873 [nlin.SI]] soliton solutions to the ABS list of multi-dimensionally consistent difference equations (except Q4) were derived using connection between the Q3 equation and the NQC equations, and then by reductions. In that work central role was played by a Cauchy matrix. In this work we use a different approach, we derive the $N$-soliton solutions following Hirota's direct and constructive method. This leads to Casoratians and bilinear difference equations. We give here details for the H-series of equations and for Q1; the results for Q3 have been given earlier.Comment: 36 page

On the precision of chiral-dispersive calculations of ππ\pi\pi scattering

We calculate the combination $2a_0^{(0)}-5a_0^{(2)}$ (the Olsson sum rule) and the scattering lengths and effective ranges $a_1$, $a_2^{(I)}$ and $b_1$, $b_2^{(I)}$ dispersively (with the Froissart--Gribov representation) using, at low energy, the phase shifts for $\pi\pi$ scattering obtained by Colangelo, Gasser and Leutwyler (CGL) from the Roy equations and chiral perturbation theory, plus experiment and Regge behaviour at high energy, or directly, using the CGL parameters for $a$s and $b$s. We find mismatch, both among the CGL phases themselves and with the results obtained from the pion form factor. This reaches the level of several (2 to 5) standard deviations, and is essentially independent of the details of the intermediate energy region ($0.82\leq E\leq 1.42$ GeV) and, in some cases, of the high energy behaviour assumed. We discuss possible reasons for this mismatch, in particular in connection with an alternate set of phase shifts.Comment: Version to appear in Phys. Rev. D. Graphs and sum rule added. Plain TeX fil

A multidimensionally consistent version of Hirota's discrete KdV equation

A multidimensionally consistent generalisation of Hirota's discrete KdV equation is proposed, it is a quad equation defined by a polynomial that is quadratic in each variable. Soliton solutions and interpretation of the model as superposition principle are given. It is discussed how an important property of the defining polynomial, a factorisation of discriminants, appears also in the few other known discrete integrable multi-quadratic models.Comment: 11 pages, 2 figure

Fast atom diffraction inside a molecular beam epitaxy chamber, a rich combination

Two aspects of the contribution of grazing incidence fast atom diffraction (GIFAD) to molecular beam epitaxy (MBE) are reviewed here: the ability of GIFAD to provide \emph{in-situ} a precise description of the atomic-scale surface topology, and its ability to follow larger-scale changes in surface roughness during layer-by-layer growth. Recent experimental and theoretical results obtained for the He atom beam incident along the highly corrugated $[ 1\bar{1}0 ]$ direction of the $\beta_{2}$(2$\times$4) reconstructed GaAs(001) surface are summarized and complemented by the measurements and calculations for the beam incidence along the weakly corrugated [010] direction where a periodicity twice smaller as expected is observed. The combination of the experiment, quantum scattering matrix calculations, and semiclassical analysis allows in this case to reveal structural characteristics of the surface. For the in situ measurements of GIFAD during molecular beam epitaxy of GaAs on GaAs surface we analyse the change in elastic and inelastic contributions in the scattered beam, and the variation of the diffraction pattern in polar angle scattering. This analysis outlines the robustness, the simplicity and the richness of the GIFAD as a technique to monitor the layer-by-layer epitaxial growth

Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory

Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schr\"odinger and Dirac particles. A central issue that should be carefully analyzed when functional series are applied is their convergence. In the present paper, we study the properties of the eigenfunction expansions appearing in nonrelativistic and relativistic $R$-matrix theories. In particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13, 491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761 (1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular formulation of the R-matrix theory for Dirac particles, the functional series fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical Physics, 21 pages, 1 figur

Morphological characteristics of the sinus node on postmortem tissue

The sinus node is an intensively researched structure in terms of anatomical, histological, electrophysiological, molecular and genetic approach. For postmortem diagnosis it is still difficult to investigate due to a still reduced accessibility. In this study we tried and succeed to apply molecular biology techniques on postmortem tissues in order to widen the range of postmortem forensic investigation and provide information related to the diagnostic of cardiac arrhythmia. We described the stages of this investigation, with dissection, preservation and analysis that included classical histology, immunohistochemistry, confocal microscope, microdissection, RIN testing, mRNA expression obtaining a precise morphofunctional location of the sinus node

An integrable multicomponent quad equation and its Lagrangian formulation

We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg-de Vries equation, and the lattice modified Boussinesq equation. The N-th member in the hierarchy is an N-component system defined on an elementary plaquette in the 2-dimensional lattice. The system is multidimensionally consistent and a Lagrangian which respects this feature, i.e., which has the desirable closure property, is obtained.Comment: 10 page