Exact Quantum Solutions of Extraordinary N-body Problems

The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in 3 dimensions. For the harmonic case that function is linear in r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) = \zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2 M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the solution is given in terms of the one or two body problem with potential U(r) in 3 dimensions. The degeneracies of the levels are derived for distinguishable particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter involve significant combinatorial analysis which may have application to the shell model of atomic nuclei. For large N the Fermionic ground state gives the binding energy of a degenerate white dwarf star treated as a giant atom with an N-body wave function. The N-body forces involved in these extraordinary N-body problems are not the usual sums of two body interactions, but nor are forces between quarks or molecules. Bose-Einstein condensation of particles in 3 dimensions interacting via these strange potentials can be treated by this method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal Societ

Automated flow rate calculation based on digital analysis of flow convergence proximal to regurgitant orifice

AbstractObjectives. The purpose of the study was to develop and validate an automated method for calculating regurgitant flow rate using color Doppler echocardiography.Background. The proximal flow convergence method is a promising approach to quantitate valvular regurgitation noninvasively because it allows one to calculate regurgitant flow rate and regurgitant orifice area; however, defining the location of the regurgitant orifice is often difficult and can lead to significant error in the calculated flow rates. To overcome this problem we developed an automated algorithm to locate the orifice and calculate flow rate based on the digital Doppler velocity map.Methods. This algorithm compares the observed velocities with the anticipated relative velocities, cos ϑ/μt2. The orifice is localized as the point with maximal correlation between predicted and observed velocity, whereas flow rate is specified as the slope of the regression line. We validated this algorithm in an in vitro model for flow through circular orifices with planar surroundings and a porcine bioprosthesis.Results. For flow through circular orifices, flow rates calculated on individual Doppler maps and on an average of eight velocity maps showed excellent agreement with true flow, with r = 0.977 and ΔQ = −3.7 ± 15.8 cm3/s and r = 0.991 and ΔQ = −4.3 ± 8.5 cm3/s, respectively. Calculated flow rates through the bioprosthesis correlated well but underestimated true flow, with r = 0.97, ΔQ = −10.9 ± 12.5 cm3/s, suggesting flow convergence over an >2π. This systematic underestimation was corrected by assuming an effective convergence angle of 212 δ.Conclusions. This algorithm accurately locates the regurgitant orifice and calculates regurgitant flow rate for circular orifices with planar surroundings. Automated analysis of the proximal flow field is also applicable to more physiologic surfaces surrounding the regurgitant orifice; however, the convergence angle should be adjusted. This automated algorithm should make quantification of regurgitant flow rate and regurgitant orifice area more reproducible and readily available in clinical cardiology practice

Reprocessing the Hipparcos data for evolved giant stars II. Absolute magnitudes for the R-type carbon stars

The Hipparcos Intermediate Astrometric Data for carbon stars have been reprocessed using an algorithm which provides an objective criterion for rejecting anomalous data points and constrains the parallax to be positive. New parallax solutions have been derived for 317 cool carbon stars, mostly of types R and N. In this paper we discuss the results for the R stars. The most important result is that the early R stars (i.e., R0 - R3) have absolute magnitudes and V-K colors locating them among red clump giants in the Hertzsprung-Russell diagram. Stars with subtypes R4 - R9 tend to be cooler and have similar luminosity to the N-type carbon stars, as confirmed by their position in the (J-H, H-K) color-color diagram. The sample of early R-type stars selected from the Hipparcos Catalogue appears to be approximately complete to magnitude K_0 ~ 7, translating into a completeness distance of 600 pc if all R stars had M_K= -2 (400 pc if M_K= -1). With about 30 early R-type stars in that volume, they comprise about 0.04% (0.14% for M_K= -1) of the red clump stars in the solar neighborhood. Identification with the red clump locates these stars at the helium core burning stage of stellar evolution, while the N stars are on the asymptotic giant branch, where helium shell burning occurs. The present analysis suggests that for a small fraction of the helium core burning stars (far lower than the fraction of helium shell-burning stars), carbon produced in the interior is mixed to the atmosphere in sufficient quantities to form a carbon star.Comment: 11 pages, 6 figures, A&A Latex. To appear in A&

Scaling of the Equilibrium Magnetization in the Mixed State of Type-II Superconductors

We discuss the analysis of mixed-state magnetization data of type-II superconductors using a recently developed scaling procedure. It is based on the fact that, if the Ginzburg-Landau parameter kappa does not depend on temperature, the magnetic susceptibility is a universal function of H/H_c2(T), leading to a simple relation between magnetizations at different temperatures. Although this scaling procedure does not provide absolute values of the upper critical fieldH_c2(T), its temperature variation can be established rather accurately. This provides an opportunity to validate theoretical models that are usually employed for the evaluation of H_c2(T) from equilibrium magnetization data. In the second part of the paper we apply this scaling procedure for a discussion of the notorious first order phase transition in the mixed state of high temperature superconductors. Our analysis, based on experimental magnetization data available in the literature, shows that the shift of the magnetization accross the transition may adopt either sign, depending on the particular chosen sample. We argue that this observation is inconsistent with the interpretation that this transition always represents the melting transition of the vortex lattice.Comment: 18 pages, 12 figure

Multiscale and multicycle instrumented indentation to determine mechanical properties: Application to the BK7 crown borosilicate

In this work, nano, micro, and macro-indentation tests under standard or multicycle loading conditions were performed for studying the mechanical behavior of a crown borosilicate glass sample with the objective to study the scale effect in indentation and the influence of cracks formation on the assessment of mechanical properties. When no cracks were initiated during the indenter penetration, especially for low indentation loads, the mechanical properties were deduced by applying different methodologies, (i) Standard (or monocyclic) loading, (ii) Continuous Stiffness Measurement mode, (iii) Constant and progressive multicycle loading, and (iv) Dynamic hardness computation. It has been found independently of the loading conditions, Martens hardness and elastic modulus are approximately 3.3 and 70 GPa, respectively. However, when cracking and chipping are produced during the indentation test, two damage parameters related to hardness and elastic modulus can be used for representing the decrease of the mechanical properties as a function of the relative penetration depth

Mapping stationary axisymmetric phase-space distribution functions by orbit libraries

This is the first of a series of papers dedicated to unveil the mass composition and dynamical structure of a sample of flattened early type galaxies in the Coma cluster. We describe our modifications to the Schwarzschild code of Richstone et al. (in preparation). Applying a Voronoi tessellation in the surface of section we are able to assign accurate phase-space volumes to individual orbits and to reconstruct the full three-integral phase-space distribution function (DF) of any axisymmetric orbit library. Two types of tests have been performed to check the accuracy with which DFs can be represented by appropriate orbit libraries. First, by mapping DFs of spherical gamma-models and flattened Plummer models on to the library we show that the resulting line-of-sight velocity distributions and internal velocity moments of the library match those directly derived from the DF to a precision better than that of present day observational errors. Second, by fitting libraries to the projected kinematics of the same DFs we show that the distribution function reconstructed from the fitted library matches the input DF to a rms of about 15 per cent over a region in phase-space covering 90 per cent of the mass of the library. The achieved accuracy allows us to implement effective entropy-based regularisation to fit real, noisy and spatially incomplete data.Comment: 15 pages, 13 figures, accepted for publication in MNRA

Predictors of complications after endoscopic retrograde cholangiopancreatography: a prognostic model for early discharge

Background: Several studies have evaluated predictors for complications of endoscopic retrograde cholangiopancreatography (ERCP), but their relative importance is unknown. In addition, currently used blood tests to detect post-ERCP pancreatitis are inconsistent. The aim of this study was to determine predictors of post-ERCP complications that could discriminate between patients at highest and lowest risk of post-ERCP complications and to develop a model that is able to identify patients that can safely be discharged shortly after ERCP. Methods: In a single-center, retrospective analysis over the period 2002-2007, predictors of post-ERCP complications were evaluated in a multivariable analysis and compared with those identified from a literature review. A prognostic model was developed based on these risk factors, which was further evaluated in a prospective patient population. Results: From our retrospective analysis and literature review, we selected the eight most important risk factors for post-ERCP pancreatitis and cholangitis. In the prognostic model, the risk factors (precut) sphincterotomy, sphincter of Oddi dysfunction, younger age, female gender, history of pancreatitis, p