Stochastic transport in the presence of spatial disorder: fluctuation-induced corrections to homogenization

Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent random variables. We assume particles are removed from the system via first-order kinetics. We analyse the system using a hierarchy of approaches when the sinks are sparsely distributed, including a stochastic homogenization approximation that yields explicit predictions for the extrinsic disorder in the stationary state due to sink strength fluctuations. The extrinsic noise induces long-range spatial correlations in the particle concentration, unlike fluctuations due to the intrinsic noise alone. Additionally, the mean concentration profile, averaged over both intrinsic and extrinsic noise, is elevated compared with the corresponding profile from a uniform sink distribution, showing that the classical homogenization approximation can be a biased estimator of the true mean.Comment: 16 pages, 8 figure

Infrared interferometry to spatially and spectrally resolve jets in X-ray binaries

Infrared interferometry is a new frontier for precision ground based observing, with new instrumentation achieving milliarcsecond (mas) spatial resolutions for faint sources, along with astrometry on the order of 10 microarcseconds. This technique has already led to breakthroughs in the observations of the supermassive black hole at the Galactic centre and its orbiting stars, AGN, and exo-planets, and can be employed for studying X-ray binaries (XRBs), microquasars in particular. Beyond constraining the orbital parameters of the system using the centroid wobble and spatially resolving jet discrete ejections on mas scales, we also propose a novel method to discern between the various components contributing to the infrared bands: accretion disk, jets and companion star. We demonstrate that the GRAVITY instrument on the Very Large Telescope Interferometer (VLTI) should be able to detect a centroid shift in a number of sources, opening a new avenue of exploration for the myriad of transients expected to be discovered in the coming decade of radio all-sky surveys. We also present the first proof-of-concept GRAVITY observation of a low-mass X-ray binary transient, MAXI J1820+070, to search for extended jets on mas scales. We place the tightest constraints yet via direct imaging on the size of the infrared emitting region of the compact jet in a hard state XRB.Comment: 12 Pages, 3 figures, accepted for publication in MNRA

Estimating the effects of preventive and weight-management interventions on the prevalence of childhood obesity in England: a modelling study

BACKGROUND: The effects of the systematic delivery of treatments for obesity are unknown. We aimed to estimate the potential effects on the prevalence of childhood obesity of systematically offering preventive and treatment interventions to eligible children in England, based on weight or health status. METHODS: For this modelling study, we developed a cross-sectional simulation model of the child and young adult population in England using data from multiple years of the Health Survey of England conducted between Jan 1, 2010, and Dec 31, 2019. Individuals were assessed for eligibility via age, BMI, and medical complications. Weight status was defined based on clinical criteria used by the UK National Institute of Health and Care Excellence. Published systematic reviews were used to estimate effect sizes for treatments, uptake, and completion for each weight-management tier. We used all available evidence, including evidence from studies that showed an unfavourable effect. We estimated the effects of two systematic approaches: a staged approach, in which children and young people were simultaneously given the most intensive treatment for which they were eligible, and a stepped approach, in which each management tier was applied sequentially, with additive effects. The primary outcomes were estimated prevalence of clinical obesity, defined as a BMI ≥98th centile on the UK90 growth chart, and difference in comparison with the estimated baseline prevalence. FINDINGS: 18 080 children and young people were included in the analytical sample. Baseline prevalence of clinical obesity was estimated to be 11·2% (95% CI 10·5 to 11·8) for children and young people aged 2-18 years. In modelling, we estimated absolute decreases in the prevalence of obesity of 0·9% (95% CI 0·1 to 1·8) for universal, preventive interventions; 0·2% (0·1 to 0·4) for interventions within a primary-care setting; 1·0% (0·1 to 2·1) for community and lifestyle interventions; 0·2% (0·0 to 0·4) for pharmaceutical interventions; and 0·4% (0·1 to 0·7) for surgical interventions. Staged care was estimated to result in an absolute decrease in the prevalence of obesity of 1·3% (-0·3 to 2·4) and stepped care was estimated to lead to an absolute decrease of 2·4% (0·1 to 4·8). INTERPRETATION: Although individual effect sizes for prevention and treatment interventions were small, when delivered at scale across England, these interventions have the potential to meaningfully contribute to reducing the prevalence of childhood obesity. FUNDING: UK National Institute for Health and Care Research

Equivalence of Edge Bicolored Graphs on Surfaces

Consider the collection of edge bicolorings of a graph that are cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colorings under two relations: reversing colors around a face and reversing colors around a vertex. In the case of the plane, this is well studied, but for other surfaces, the computation is more subtle. While this question can be stated purely graph theoretically, it has interesting applications in knot theory

Damping and Mass Sensitivity of Laterally Vibrating Resonant Microcantilevers in Viscous Liquid Media

The effect of liquid viscosity and density on the characteristics of laterally excited microcantilevers is investigated and compared to transversely excited microcantilevers. When immersed into a viscous liquid medium such as water from air, the resonant frequency of laterally (in-plane) vibrating microcantilevers is shown to decrease by only 5-10% as compared to ~50% reduction for transversely (out-of-plane) vibrating microcantilevers. Furthermore, as the viscosity of the medium increases the resonant frequency of a laterally vibrating beam is shown to decrease at a slower rate than that of a transversely vibrating beam. The decreased viscous damping also leads to increases in the quality factor of the system by a factor of 4-5 compared to beams vibrating transversely. The mass sensitivities of laterally vibrating beams are also theoretically predicted to be roughly two orders of magnitude larger in water for some cantilever geometries. The increase in the quality factor and mass sensitivity indicate that operating in the in-plane flexural mode (lateral vibration) will decrease the limit of detection compared to operating in the more common out-of-plane flexural mode (transverse vibration). These improvements in device characteristics indicate that microcantilevers excited laterally are more suited for operating in media of high viscosities