Realistic computable error bounds for three dimensional finite element analyses in linear elasticity

We obtain a computable estimator for the energy norm of the error in piecewise affine and piecewise quadratic finite element approximations of linear elasticity in three dimensions. We show that the estimator provides guaranteed upper bounds on the energy norm of the error as well as (up to a constant and data oscillation terms) local lower bounds

The synthesis and adsorption properties of some carbohydrate-terminated dendrimer wedges

A range of dendritic molecules that are designed to bind to a cotton surface has been synthesised. The architecture of the molecules allows the location of various functional, property modifying units at the focus and the attachment of recognition groups at the periphery of a dendritic molecule with wedge topology. The synthesis and characterisation of dendrimer wedges up to the second-generation using a divergent approach has been performed. These wedges are readily built up using a simple and efficient stepwise pathway from the central core, and surface recognising species are subsequently attached to the molecule utilising procedures developed in conjunction with Unilever Research Laboratories. Work has been carried out to assess their adsorption onto a cotton surface and the postulated adsorption mechanism is discussed

Animal derived antibodies should be considered alongside convalescent human plasma to deliver treatments for COVID-19

Published data on the first 5,000 coronavirus patients to receive plasma shows promise in the United States. However, delivering convalescent plasma therapies in low- and even middle-income countries is both difficult and costly. Here we discuss the advantages and disadvantages of antisera raised in animals that ma

Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes

We obtain fully computable constant free a posteriori error bounds on the broken energy seminorm and the discontinuous Galerkin (DG) norm of the error for nonuniform polynomial order symmetric interior penalty Galerkin, nonsymmetric interior penalty Galerkin and incomplete interior penalty Galerkin finite-element approximations of a linear second-order elliptic problem on meshes containing hanging nodes and comprised of triangular elements. The estimators are completely free of unknown constants and provide guaranteed numerical bounds on the broken energy seminorm and the DG norm of the error. These estimators are also shown to provide a lower bound for the broken energy seminorm and the DG norm of the error up to a constant and higher-order data oscillation terms

Molecular dynamics simulations of bio-active phosphate-based glass surfaces

Classical molecular dynamics (MD) simulations were used to study the structural changes in the surfaces of biocompatible phosphate glasses with compositions (P2O5)0.45(CaO)x(Na2O)0.55 − x (x = 30, 35, 40) to evaluate their effect on the solubility of the material. Direct comparison of the data for the three compositions highlighted the critical role that an enhancement in Na+ concentration plays in the hydrolysis of the material, which is responsible for the release of network components into solution. The calculations also confirm that the most soluble material is (P2O5)0.45(CaO)0.30(Na2O)0.25, has the lowest calcium coordination number, thereby causing fewer cross links to phosphate chains