A direct solver with O(N) complexity for variable coefficient elliptic PDEs discretized via a high-order composite spectral collocation method

A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite spectral approximations and is designed for problems with smooth solutions. The resulting system of linear equations is solved using a direct (as opposed to iterative) solver that has optimal O(N) complexity for all stages of the computation when applied to problems with non-oscillatory solutions such as the Laplace and the Stokes equations. Numerical examples demonstrate that the scheme is capable of computing solutions with relative accuracy of $10^{-10}$ or better, even for challenging problems such as highly oscillatory Helmholtz problems and convection-dominated convection diffusion equations. In terms of speed, it is demonstrated that a problem with a non-oscillatory solution that was discretized using $10^{8}$ nodes was solved in 115 minutes on a personal work-station with two quad-core 3.3GHz CPUs. Since the solver is direct, and the "solution operator" fits in RAM, any solves beyond the first are very fast. In the example with $10^{8}$ unknowns, solves require only 30 seconds.Comment: arXiv admin note: text overlap with arXiv:1302.599

Development of a special purpose spacecraft interior coating, phase 3

A variety of intumescent coatings based on a fluorocarbon latex resin modified with either an acrylic resin or an epoxy resin were prepared. Several intumescent systems were used for these studies including some based on ammonium polyphosphate and others based on sulfanilamide. The best coatings developed had a high concentration (60-70% by wt.) of intumescent additives and had to be applied thick, approximately 100 mils, in order to have adequate intumescent/fire protection properties

Developing a multi-pollutant conceptual framework for the selection and targeting of interventions in water industry catchment management schemes

In recent years water companies have started to adopt catchment management to reduce diffuse pollution in drinking water supply areas. The heterogeneity of catchments and the range of pollutants that must be removed to meet the EU Drinking Water Directive (98/83/EC) limits make it difficult to prioritise areas of a catchment for intervention. Thus conceptual frameworks are required that can disaggregate the components of pollutant risk and help water companies make decisions about where to target interventions in their catchments to maximum effect. This paper demonstrates the concept of generalising pollutants in the same framework by reviewing key pollutant processes within a source-mobilisation-delivery context. From this, criteria are developed (with input from water industry professionals involved in catchment management) which highlights the need for a new water industry specific conceptual framework. The new CaRPoW (Catchment Risk to Potable Water) framework uses the Source-Mobilisation-Delivery concept as modular components of risk that work at two scales, source and mobilisation at the field scale and delivery at the catchment scale. Disaggregating pollutant processes permits the main components of risk to be ascertained so that appropriate interventions can be selected. The generic structure also allows for the outputs from different pollutants to be compared so that potential multiple benefits can be identified. CaRPow provides a transferable framework that can be used by water companies to cost-effectively target interventions under current conditions or under scenarios of land use or climate change

Combining Reinforcement Learning and Tensor Networks, with an Application to Dynamical Large Deviations

We present a framework to integrate tensor network (TN) methods with reinforcement learning (RL) for solving dynamical optimisation tasks. We consider the RL actor-critic method, a model-free approach for solving RL problems, and introduce TNs as the approximators for its policy and value functions. Our "actor-critic with tensor networks" (ACTeN) method is especially well suited to problems with large and factorisable state and action spaces. As an illustration of the applicability of ACTeN we solve the exponentially hard task of sampling rare trajectories in two paradigmatic stochastic models, the East model of glasses and the asymmetric simple exclusion process (ASEP), the latter being particularly challenging to other methods due to the absence of detailed balance. With substantial potential for further integration with the vast array of existing RL methods, the approach introduced here is promising both for applications in physics and to multi-agent RL problems more generally.Comment: [v1]: Combined main text of 6 pages, 3 figures and supplemental materials of 7 pages, 1 figure. [v2]: Accepted version, Phys. Rev. Lett. Combined main text of 8 pages, 4 figures and supplemental materials of 5 page

Hybrid Pixel Detector Development for the Linear Collider Vertex Tracker

In order to fully exploit the physics potential of the future high energy e+e- linear collider, a Vertex Tracker able to provide particle track extrapolation with very high resolution is needed. Hybrid Si pixel sensors are an attractive technology due to their fast read-out capabilities and radiation hardness. A novel pixel detector layout with interleaved cells has been developed to improve the single point resolution. Results of the characterisation of the first processed prototypes by electrostatic measurements and charge collection studies are discussed.Comment: 5 pages, 1 figure, to appear in the Proceedings of the 9th Int. Workshop on Vertex Detectors, Lake Michigan MI (USA), September~200

A cross sectional study of the prevalence and associated risks for bursitis in 6250 weaner, grower and finisher pigs from 103 British pig farms

A cross-sectional study of 93 farms in England was carried out to estimate the prevalence and associated risk factors for bursitis. A total of 6250 pigs aged 6–22 weeks were examined for presence and severity of bursitis. Details of pen construction, pen quality and farm management were recorded including floor type, presence of bedding, condition of the floor and floor materials. The prevalence of bursitis was 41.2% and increased with each week of age (OR 1.1). Two-level logistic regression models were developed with the outcome as the proportion of pigs affected with bursitis in a pen. Pigs kept on soil floors with straw bedding were used as the reference level. In comparison with these soil floors, bursitis increased on concrete floors where the bedding was deep throughout (OR 4.6), deep in part (OR 3.7), and sparse throughout (OR 9.0), part slatted floors (OR 8.0), and fully slatted floors (OR 18.8). Slip or skid marks in the dunging area (OR 1.5), pigs observed slipping during the examination of the pen (OR 1.3) and wet floors (OR 3.6) were also associated with an increased risk of bursitis. The results indicate that bursitis is a common condition of growing pigs and that the associated risk factors for bursitis were a lack of bedding in the lying area, presence of voids and pen conditions which increased the likelihood of injury