Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology, which postulates that the bulk friction coefficient $\unicode[STIX]{x1D707}$ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction $\unicode[STIX]{x1D719}$ are functions of the inertial number $I$ only. Although the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology that does not suffer from such defects is proposed. In the framework of compressible $I$ -dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established $\unicode[STIX]{x1D707}(I)$ and $\unicode[STIX]{x1D6F7}(I)$ relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations.

Objectives: Patient production losses occur when individuals’ capacities to work, whether paid or unpaid, are impaired by illness, treatment, disability, or death. There is controversy about whether and how to include patient production losses in economic evaluations in health care. Patient production losses have not previously been considered when evaluating medications for reimbursement under the U.K. National Health Service. Proposals for value-based assessment of health technologies in the United Kingdom created renewed interest in whether and how to include costs from a wider societal perspective, such as patient production losses, within economic evaluation of healthcare interventions.

Methods: A narrative review was undertaken of theoretical, ethical, and policy issues that might inform decisions that involve the normative question of whether or not to include patient production losses in economic evaluation.

Results: It seems difficult to reconcile the implications of including patient production losses with the objectives of a healthcare system dedicated to providing universal healthcare coverage without regard to patients’ ability to pay.

Conclusions: Tax payer funded healthcare systems may legitimately adopt maximands other than health gain, but these will be at the opportunity cost of less than maximum health gains.

The Galway Astronomical Stokes Polarimeter (GASP) is a high time resolution, full-Stokes imaging polarimeter which utilises a Fresnel rhomb prism as a beam-splitter and quarter wave retarder. The ability to perform optical photometry and polarimetry at high frame rates enables more detailed studies of a multitude of compact objects including; optical pulsars, magnetars and Active Galactic Nuclei (AGN). We present a brief discussion of the instruments’ current capabilities and hardware design. GASP is currently configured with two Electron Multiplying Charge-Coupled Devices (EMCCDs), which offer sub-millisecond frame readout speeds over a defined region of interest on the sensor. We will report results from an observational campaign at the William Herschel Telescope (WHT) in December, 2015. During this campaign GASP was used to study the Crab Pulsar, V404 Cygni and polarisation standards. As a subset of our analysis we have identified a significant contribution from the Interstellar Medium (ISM) and the interaction of a varying polarised source with the ISM, the subsequent conversion of linearly polarised light to circular, and its dependence on the angle of the source emission electric field orientation. Further to the presentation of results we will discuss future observational work, which is planned for September 2017 and subsequent improvements to increase the temporal resolution of the detectors.

Despite the early optical detection of the Crab pulsar in 1969, optical pulsars have become the poor cousin of the neutron star family. Only five normal pulsars have been observed to pulse in the optical waveband. A further three magnetars/SGRs have been detected in the optical/near IR. Optical pulsars are intrinsically faint with a first order luminosity, predicted by Pacini, to be proportional to P−10, where P is the pulsar’s period. Consequently they require both large telescopes, generally over-subscribed, and long exposure times, generally difficult to get. However optical observations have the benefit that polarisation and spectral observations are possible compared to X-ray and gamma-ray observations where polarisation measurements are limited. Over the next decade the number of optical pulsars should increase as optical detectors approach 100% quantum efficiency and as we move into the era of extremely large telescopes where limiting fluxes will be 30 to 100 times fainter compared to existing optical telescopes.

On a sufficiently soft substrate, a resting fluid droplet will cause significant deformation of the substrate. This deformation is driven by a combination of capillary forces at the contact line and the fluid pressure at the solid surface. These forces are balanced at the surface by the solid traction stress induced by the substrate deformation. Young's Law, which predicts the equilibrium contact angle of the droplet, also indicates an a priori radial force balance for rigid substrates, but not necessarily for soft substrates that deform under loading. It remains an open question whether the contact line transmits a non-zero force tangent to the substrate surface in addition to the conventional normal (vertical) force. We present an analytic Fourier transform solution technique that includes general interfacial energy conditions, which govern the contact angle of a 2D droplet. This includes evaluating the effect of gravity on the droplet shape in order to determine the correct fluid pressure at the substrate surface for larger droplets. Importantly, we find that in order to avoid a strain singularity at the contact line under a non-zero tangential contact line force, it is necessary to include a previously neglected horizontal traction boundary condition. To quantify the effects of the contact line and identify key quantities that will be experimentally accessible for testing the model, we evaluate solutions for the substrate surface displacement field as a function of Poisson's ratio and zero/non-zero tangential contact line forces.