A multilayer method for the hydrostatic Navier-Stokes equations: A particular weak solution

In this work we present a multilayer approach to the solution of non-stationary 3D Navier-Stokes equations. We use piecewise smooth weak solutions. We approximate the velocity by a piecewise constant (in z) horizontal velocity and a linear (in z) vertical velocity in each layer, possibly discontinuous across layer interfaces. The multilayer approach is deduced by using the variational formulation and by considering a reduced family of test functions. The procedure naturally provides the mass and momentum interfaces conditions. The mass and momentum conservation across interfaces is formulated via normal flux jump conditions. The jump conditions associated to momentum conservation are formulated by means of an approximation of the vertical derivative of the velocity that appears in the stress tensor. We approximate the multilayer model for hydrostatic pressure, by using a polynomial viscosity matrix finite volume scheme and we present some numerical tests that show the main advantages of the model: it improves the approximation of the vertical velocity, provides good predictions for viscous effects and simulates re-circulations behind solid obstacles

Some Remarks on Avalanches Modelling: An Introduction to Shallow Flows Models

International audienceThe main goal of these notes is to present several depth-averaged models with application in granular avalanches. We begin by recalling the classical Saint-Venant or Shallow Water equations and present some extensions like the Saint-Venant-Exner model for bedload sediment transport. The first part is devoted to the derivation of several avalanche models of Savage-Hutter type, using a depth-averaging procedure of the 3D momentum and mass equations. First, the Savage-Hutter model for aerial avalanches is presented. Two other models for partially fluidized avalanches are then described: one in which the velocities of both the fluid and the solid phases are assumed to be equal, and another one in which both velocities are unknowns of the system. Finally, a Savage-Hutter model for submarine avalanches is derived. The second part is devoted to non-newtonian models, namely viscoplastic fluids. Indeed, a one-phase viscoplastic model can also be used to simulate fluidized avalanches. A brief introduction to Rheology and plasticity is presented in order to explain the Herschel-Bulkley constitutive law. We finally present the derivation of a shallow Herschel-Bulkley model

Correction to: Is diet partly responsible for differences in COVID-19 death rates between and within countries? (Clinical and Translational Allergy, (2020), 10, 1, (16), 10.1186/s13601-020-00323-0)

Following publication of the original article [1], the authors identified an error in the affiliation list. The affiliation of author G. Walter Canonica should have been split up into two affiliations: • Personalized Medicine, Asthma and Allergy – Humanitas Clinical and Research Center – IRCCS, Rozzano (MI), Italy • Department of Biomedical Sciences, Humanitas University, Pieve Emanuele (MI), Italy The corrected affiliation list is reflected in this Correction. © 2020, The Author(s)

Body mass index and complications following major gastrointestinal surgery: A prospective, international cohort study and meta-analysis

Aim Previous studies reported conflicting evidence on the effects of obesity on outcomes after gastrointestinal surgery. The aims of this study were to explore the relationship of obesity with major postoperative complications in an international cohort and to present a metaanalysis of all available prospective data. Methods This prospective, multicentre study included adults undergoing both elective and emergency gastrointestinal resection, reversal of stoma or formation of stoma. The primary end-point was 30-day major complications (Clavien–Dindo Grades III–V). A systematic search was undertaken for studies assessing the relationship between obesity and major complications after gastrointestinal surgery. Individual patient meta-analysis was used to analyse pooled results. Results This study included 2519 patients across 127 centres, of whom 560 (22.2%) were obese. Unadjusted major complication rates were lower in obese vs normal weight patients (13.0% vs 16.2%, respectively), but this did not reach statistical significance (P = 0.863) on multivariate analysis for patients having surgery for either malignant or benign conditions. Individual patient meta-analysis demonstrated that obese patients undergoing surgery formalignancy were at increased risk of major complications (OR 2.10, 95% CI 1.49–2.96, P < 0.001), whereas obese patients undergoing surgery for benign indications were at decreased risk (OR 0.59, 95% CI 0.46–0.75, P < 0.001) compared to normal weight patients. Conclusions In our international data, obesity was not found to be associated with major complications following gastrointestinal surgery. Meta-analysis of available prospective data made a novel finding of obesity being associated with different outcomes depending on whether patients were undergoing surgery for benign or malignant disease

Safety of hospital discharge before return of bowel function after elective colorectal surgery

Background: Ileus is common after colorectal surgery and is associated with an increased risk of postoperative complications. Identifying features of normal bowel recovery and the appropriateness for hospital discharge is challenging. This study explored the safety of hospital discharge before the return of bowel function. Methods: A prospective, multicentre cohort study was undertaken across an international collaborative network. Adult patients undergoing elective colorectal resection between January and April 2018 were included. The main outcome of interest was readmission to hospital within 30 days of surgery. The impact of discharge timing according to the return of bowel function was explored using multivariable regression analysis. Other outcomes were postoperative complications within 30 days of surgery, measured using the Clavien\u2013Dindo classification system. Results: A total of 3288 patients were included in the analysis, of whom 301 (9\ub72 per cent) were discharged before the return of bowel function. The median duration of hospital stay for patients discharged before and after return of bowel function was 5 (i.q.r. 4\u20137) and 7 (6\u20138) days respectively (P &lt; 0\ub7001). There were no significant differences in rates of readmission between these groups (6\ub76 versus 8\ub70 per cent; P = 0\ub7499), and this remained the case after multivariable adjustment for baseline differences (odds ratio 0\ub790, 95 per cent c.i. 0\ub755 to 1\ub746; P = 0\ub7659). Rates of postoperative complications were also similar in those discharged before versus after return of bowel function (minor: 34\ub77 versus 39\ub75 per cent; major 3\ub73 versus 3\ub74 per cent; P = 0\ub7110). Conclusion: Discharge before return of bowel function after elective colorectal surgery appears to be safe in appropriately selected patients