834 research outputs found

    Legislative Intent

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    Local Box Adjacency Algorithms for Cylindrical Algebraic Decompositions

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    AbstractWe describe new algorithms for determining the adjacencies between zero-dimensional cells and those one-dimensional cells that are sections (not sectors) in cylindrical algebraic decompositions (cad). Such adjacencies constitute a basis for determining all other cell adjacencies. Our new algorithms are local, being applicable to a specified 0D cell and the 1D cells described by specified polynomials. Particularly efficient algorithms are given for the 0D cells in spaces of dimensions two, three and four. Then an algorithm is given for a space of arbitrary dimension. This algorithm may on occasion report failure, but it can then be repeated with a modified isolating interval and a likelihood of success

    Embodied energy data implications for optimal specification of building envelopes

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    Highly insulated building envelopes have become more commonplace as environmental imperatives require reduction of building carbon footprints. Whilst increased insulation levels reduce operational energy demand, the additional embodied energy investment can increase the buildings’ overall environmental impact. The embodied energy consideration can determine whether, and to what extent, additional insulation is justified. The following paper investigates the impact of uncertainties of embodied energy data on the cumulative operational and embodied energy analyses and holistically appraises its implications for different stakeholders involved with the construction sector. Limitations in current life cycle assessment (LCA) calculation methods and high uncertainty of available data are recognized and reflected in the analyses through studying available environmental product declarations of various types of insulation materials and by modelling a typical semi-detached residential building in the UK as the case study. The results of such approach illustrate ‘optimum insulation thicknesses’ beyond which the embodied energy penalty outweighs operational energy savings. These essentially represent idealized levels of building envelope insulation that can inform the development of future standards for low energy/carbon buildings and support the adoption of LCAs as decision-making tools in informing the urgent debate of optimal insulation requirements of buildings

    Gas compression systematically delays the onset of viscous fingering

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    Using gas to drive liquid from a Hele-Shaw cell leads to classical viscous fingering. Strategies for suppressing fingering have received substantial attention. For steady injection of an incompressible gas, the intensity of fingering is controlled by the capillary number Ca. Here, we show that gas compression leads to an unsteady injection rate controlled primarily by a dimensionless compressibility number C. Increasing C systematically delays the onset of fingering at high Ca, highlighting compressibility as an overlooked but fundamental aspect of gas-driven fingering

    Compression-driven viscous fingering in a radial Hele-Shaw cell

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    The displacement of a viscous liquid by a gas within a Hele-Shaw cell is a classical problem. The gas-liquid interface is hydrodynamically unstable, forming striking finger-like patterns that have attracted research interest for decades. Generally, both the gas and liquid phases are taken to be incompressible, with the capillary number being the key parameter that determines the severity of the instability. Here, we consider a radially outward displacement driven by the steady compression of a gas reservoir. The associated gas-injection rate is then unsteady due to the compressibility of the gas. We identify a second nondimensional parameter, the compressibility number, that plays a strong role in the development of the fingering pattern. We use an axisymmetric model to study the impact of compressibility number on the unsteady evolution of injection rate and gas pressure. We use linear stability analysis to show that increasing the compressibility number delays the onset of finger development relative to the corresponding incompressible case. Finally, we present and compare a series of experiments and fully nonlinear simulations over a broad range of capillary and compressibility numbers. These results show that increasing the compressibility number systematically decreases the severity of the fingering pattern at high capillary number. Our results provide an unprecedented comparison of experiments with simulations for viscous fingering, a comprehensive understanding of the role of compressibility in unstable gas-liquid displacement flows, and insight into a new mechanism for controlling the development of fingering patterns

    Do faecal test-based colorectal cancer screening pilots provide data that are reflected in subsequent programmes? Evidence from interval cancer proportions

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    OBJECTIVE: Guidelines on colorectal cancer (CRC) screening with guaiac faecal occult blood tests (gFOBTs) and faecal immunochemical tests (FITs) include the need for a pilot before a programme is introduced. Interval cancers (ICs), cancers arising after a negative screening test result but before the next scheduled invite, are important indicators of programme quality. Our aim was to compare IC in the gFOBT-based Scottish Bowel Screening Programme (SBoSP), a FIT-based pilot, and the FIT-based SBoSP, to assess if the pilot provided data that was reflected in the subsequent programme. DESIGN: The IC proportions (ICPs) data ([IC/(IC + screen detected CRC)] x 100) from the penultimate year of the gFOBT-based SBoSP, the 6-month pilot and the first year of the FIT-based SBoSP were compared. To ensure appropriate comparison, these data were only from the two pilot NHS Boards. RESULTS: For all participants, and females and males, the ICPs were very similar in the gFOBT-based SBoSP and the pilot. The faecal haemoglobin concentration (f-Hb) threshold for the pilot was set at ≥80 μg Hb/g faeces. However, in marked contrast, in the FIT-based SBoSP, at the same threshold, the ICPs were lower. In all three groups, the ICPs were higher in females than in males. CONCLUSIONS: Data on variables in pilots, including ICP, can be informative, but only if variables such as FIT system are held consistent between pilot and programme. Lowering the f-Hb threshold for females to give the same ICP as males might be a strategy to minimise sex inequality
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