Efimov effect in quantum magnets

Physics is said to be universal when it emerges regardless of the underlying microscopic details. A prominent example is the Efimov effect, which predicts the emergence of an infinite tower of three-body bound states obeying discrete scale invariance when the particles interact resonantly. Because of its universality and peculiarity, the Efimov effect has been the subject of extensive research in chemical, atomic, nuclear and particle physics for decades. Here we employ an anisotropic Heisenberg model to show that collective excitations in quantum magnets (magnons) also exhibit the Efimov effect. We locate anisotropy-induced two-magnon resonances, compute binding energies of three magnons and find that they fit into the universal scaling law. We propose several approaches to experimentally realize the Efimov effect in quantum magnets, where the emergent Efimov states of magnons can be observed with commonly used spectroscopic measurements. Our study thus opens up new avenues for universal few-body physics in condensed matter systems.Comment: 7 pages, 5 figures; published versio

Utilisation of an operative difficulty grading scale for laparoscopic cholecystectomy

Background A reliable system for grading operative difficulty of laparoscopic cholecystectomy would standardise description of findings and reporting of outcomes. The aim of this study was to validate a difficulty grading system (Nassar scale), testing its applicability and consistency in two large prospective datasets. Methods Patient and disease-related variables and 30-day outcomes were identified in two prospective cholecystectomy databases: the multi-centre prospective cohort of 8820 patients from the recent CholeS Study and the single-surgeon series containing 4089 patients. Operative data and patient outcomes were correlated with Nassar operative difficultly scale, using Kendall’s tau for dichotomous variables, or Jonckheere–Terpstra tests for continuous variables. A ROC curve analysis was performed, to quantify the predictive accuracy of the scale for each outcome, with continuous outcomes dichotomised, prior to analysis. Results A higher operative difficulty grade was consistently associated with worse outcomes for the patients in both the reference and CholeS cohorts. The median length of stay increased from 0 to 4 days, and the 30-day complication rate from 7.6 to 24.4% as the difficulty grade increased from 1 to 4/5 (both p < 0.001). In the CholeS cohort, a higher difficulty grade was found to be most strongly associated with conversion to open and 30-day mortality (AUROC = 0.903, 0.822, respectively). On multivariable analysis, the Nassar operative difficultly scale was found to be a significant independent predictor of operative duration, conversion to open surgery, 30-day complications and 30-day reintervention (all p < 0.001). Conclusion We have shown that an operative difficulty scale can standardise the description of operative findings by multiple grades of surgeons to facilitate audit, training assessment and research. It provides a tool for reporting operative findings, disease severity and technical difficulty and can be utilised in future research to reliably compare outcomes according to case mix and intra-operative difficulty

Population‐based cohort study of outcomes following cholecystectomy for benign gallbladder diseases

Background The aim was to describe the management of benign gallbladder disease and identify characteristics associated with all‐cause 30‐day readmissions and complications in a prospective population‐based cohort. Methods Data were collected on consecutive patients undergoing cholecystectomy in acute UK and Irish hospitals between 1 March and 1 May 2014. Potential explanatory variables influencing all‐cause 30‐day readmissions and complications were analysed by means of multilevel, multivariable logistic regression modelling using a two‐level hierarchical structure with patients (level 1) nested within hospitals (level 2). Results Data were collected on 8909 patients undergoing cholecystectomy from 167 hospitals. Some 1451 cholecystectomies (16·3 per cent) were performed as an emergency, 4165 (46·8 per cent) as elective operations, and 3293 patients (37·0 per cent) had had at least one previous emergency admission, but had surgery on a delayed basis. The readmission and complication rates at 30 days were 7·1 per cent (633 of 8909) and 10·8 per cent (962 of 8909) respectively. Both readmissions and complications were independently associated with increasing ASA fitness grade, duration of surgery, and increasing numbers of emergency admissions with gallbladder disease before cholecystectomy. No identifiable hospital characteristics were linked to readmissions and complications. Conclusion Readmissions and complications following cholecystectomy are common and associated with patient and disease characteristics

Solution of Navier-Stokes equations on nonstaggered grid at all speeds

The present author recently devised a pressure correction algorithm for solution of incompressible Navier-Stokes equations on a nonstaggered grid [6]. This algorithm introduced the notion of smoothing pressure correction to overcome the problem of checkerboard prediction of pressure. In this article, the algorithm is extended to prediction of compressible flows with and without shocks. The predictions show that the algorithm yields results that compare extremely favorably with previous ones [2] obtained using a staggered grid. Accurate shock capturing on coarse grids, however, requires use of total variation diminishing (TVD) discretization of the covective terms coupled with measures for stabilization of the iteration process

Complete pressure correction algorithm for solution of incompressible Navier-Stokes equations on a nonstaggered grid

When Navier-Stokes equations for incompressible flow are solved on a nonstaggered grid, Be problem of checkerboard prediction of pressure is encountered. So far, this problem has been cured either by evaluating the cell face velocities by the momentum interpolated principle [1] or by evaluating an effective pressure gradient in the nodal momentum equations [2]. In this article it is shown that not only are these practices unnecessary, they can lead to spurious results when the true pressure variation departs considerably from linearity. What is required instead is afresh derivation of the pressure correction equation appropriate for a nonstaggered grid. The pressure correction determined from this equation comprises two components: a mass-conserving component and a smoothing component. The former corresponds to the pressure correction predicted by a staggered grid procedure, whereas the latter simply accounts for the difference between the point value of the pressure and the cell-averaged value of the pressure. The new pressure correction equation facilitates (in a significant way) computer coding of programs written for three-dimensional geometries employing body-fitted curvilinear coordinate grids

Solution of transport equations on unstructured meshes with cell-centered colocated variables. Part I: Discretization

This paper describes discretization of transport equations on unstructured meshes with cell-centered colocated variables. The problem of zig-zag pressure prediction is eliminated by introducing smoothing pressure correction derived by Date [A.W. Date, Complete pressure correction algorithm for solution of incompressible Navier-Stokes equations on a non-staggered grid, Numer. Heat Transfer, Part B 29 (1995) 441-458]. The finite-volume discretization is carried out in a structured grid like manner by invoking a special line-structure to evaluate convective-diffusive transport across the cell-faces. (C) 200

A STRONG ENTHALPY FORMULATION FOR THE STEFAN PROBLEM

This paper demonstrates how the condition of constancy with respect to time of the phase-change interface temperature can be incorporated to arrive at a 'strong' enthalpy formulation. The finite-difference solutions obtained with this formulation show that the problem of 'waviness' of the temperature histories encountered with the 'weak' formulation is now removed and accurate solutions are obtained even with a coarse grid irrespective of the time step. The formulation derived requires no 'book-keeping' of the phase-change node, and allows line-by-line integration of the finite-difference equations

High Resolution TVD Schemes for Interface Tracking

A first order upwind difference scheme (UDS) is routinely adopted for representing convection terms in a discretised space. UDS provides stable solutions. However it also introduces false diffusion in situations in which the flow direction is oblique relative to the numerical grid or when the cell-Peclet number is large. In order to predict sharp interface, higher order upwind schemes are preferred because of they reduce numerical dissipation. In interfacial flows, density and viscosity vary sharply in space. Representation of convective terms by Total variation diminishing (TVD) schemes ensures reduced smearing without impairing convergence property. TVD schemes develop formulae for interpolation of a cell-face value of the transported variable. If the interpolated value is bounded by the neighbouring nodal values then the scheme is ‘Bounded’. However, not all TVD schemes possess this property of ‘Boundedness’. The Normalised Variable Diagram (NVD) defines a domain within which the TVD scheme is bounded. Thus by combining the features of both TVD schemes and ensuring that they fall with the defined area of NVD, the convergence as well as the boundedness of a computational scheme can be ensured. In this paper, six different higher order schemes are considered some which are TVD bounded or unbounded, to solve the well known interface tracking problem of Rayleigh-Taylor Instability. To the best of our knowledge, a comparison of combined TVD/NVD principles in the case of interface tracking problems has not been reported in published literature

Fluid dynamical view of pressure checkerboarding problem and smoothing pressure correction on meshes with colocated variables

This paper presents derivation of the pressure correction equation appropriate for colocated grids within the framework of the SIMPLE algorithm. It is shown that checkerboard prediction of pressure can be prevented by employing algebraic smoothing pressure correction [Numer. Heat Transfer, Part B 29 (1996) 441] that is very simple to implement on both the structured as well as unstructured grids. The ability of the smoothing correction (which is shown to be independent of transformations of the system of coordinates) in providing the necessary dissipation is explained and the connection of the former with requirements of the Stokes's laws is established. (C) 200