Flux-balance laws in scalar self-force theory

The motion of a radiating point particle can be represented by a series of geodesics whose "constants" of motion evolve slowly with time. The evolution of these constants of motion can be determined directly from the self-force equations of motion. In the presence of spacetime symmetries, the situation simplifies: there exist not only constants of motion conjugate to these symmetries, but also conserved currents whose fluxes can be used to determine their evolution. Such a relationship between point-particle motion and fluxes of conserved currents is a flux-balance law. However, there exist constants of motion that are not related to spacetime symmetries, the most notable example of which is the Carter constant in the Kerr spacetime. In this paper, we first present a new approach to flux-balance laws for spacetime symmetries, using the techniques of symplectic currents and symmetry operators, which can also generate more general conserved currents. We then derive flux-balance laws for all constants of motion in the Kerr spacetime, using the fact that the background, geodesic motion is integrable. For simplicity, we restrict derivations in this paper to the scalar self-force problem. While generalizing the discussion in this paper to the gravitational case will be straightforward, there will be additional complications in turning these results into a practical flux-balance law in this case.Comment: 15+3 pages, 1 figure; v2: corrected typos and added appendix and figure, "matches" published versio

Exercise dose and all-cause mortality within extended cardiac rehabilitation: a cohort study.

AIMS: To investigate the relationship between exercise participation, exercise 'dose' expressed as metabolic equivalent (MET) hours (h) per week, and prognosis in individuals attending an extended, community-based exercise rehabilitation programme. METHODS: Cohort study of 435 participants undertaking exercise-based cardiac rehabilitation (CR) in Leeds, West Yorkshire, UK between 1994 and 2006, followed up to 1 November 2013. MET intensity of supervised exercise was estimated utilising serial submaximal exercise test results and corresponding exercise prescriptions. Programme participation was routinely monitored. Cox regression analysis including time-varying and propensity score adjustment was applied to identify predictors of long-term, all-cause mortality across exercise dose and programme duration groups. RESULTS: There were 133 events (31%) during a median follow-up of 14 years (range, 1.2 to 18.9 years). The significant univariate association between exercise dose and all-cause mortality was attenuated following multivariable adjustment for other predictors, including duration in the programme. Longer-term adherence to supervised exercise training (>36 months) was associated with a 33% lower mortality risk (multivariate-adjusted HR: 0.67; 95% CI: 0.47 to 0.97; p=0.033) compared with all lesser durations of CR (3, 12, 36 months), even after adjustment for baseline fitness, comorbidities and survivor bias. CONCLUSION: Exercise dose (MET-h per week) appears less important than long-term adherence to supervised exercise for the reduction of long-term mortality risk. Extended, supervised CR programmes within the community may play a key role in promoting long-term exercise maintenance and other secondary prevention therapies for survival benefit

Submaximal fitness and mortality risk reduction in coronary heart disease: a retrospective cohort study of community-based exercise rehabilitation.

To examine the association between submaximal cardiorespiratory fitness (sCRF) and all-cause mortality in a cardiac rehabilitation (CR) cohort.Retrospective cohort study of participants entering CR between 26 May 1993 and 16 October 2006, followed up to 1 November 2013 (median 14 years, range 1.2-19.4 years).A community-based CR exercise programme in Leeds, West Yorkshire, UK.A cohort of 534 men (76%) and 136 women with a clinical diagnosis of coronary heart disease (CHD), aged 22-82 years, attending CR were evaluated for the association between baseline sCRF and all-cause mortality. 416 participants with an exercise test following CR (median 14 weeks) were examined for changes in sCRF and all-cause mortality.All-cause mortality and change in sCRF expressed in estimated metabolic equivalents (METs).Baseline sCRF was a strong predictor of all-cause mortality; compared to the lowest sCRF group (<5 METs for women and <6 METs for men), mortality risk was 41% lower in those with moderate sCRF (HR 0.59; 95% CI 0.42 to 0.83) and 60% lower (HR 0.40; 95% CI 0.25 to 0.64) in those with higher sCRF levels (≥7 METs women and ≥8 METs for men). Although improvement in sCRF at 14 weeks was not associated with a significant mortality risk reduction (HR 0.91; 95% CI 0.79 to 1.06) for the whole cohort, in those with the lowest sCRF (and highest all-cause mortality) at baseline, each 1-MET improvement was associated with a 27% age-adjusted reduction in mortality risk (HR 0.73; 95% CI 0.57 to 0.94).Higher baseline sCRF is associated with a reduced risk of all-cause mortality over 14 years in adults with CHD. Improving fitness through exercise-based CR is associated with significant risk reduction for the least fit

Characteristics, accuracy and reverification of robotised articulated arm CMMs

VDI article 2617 specifies characteristics to describe the accuracy of articulated arm coordinate measuring machines (AACMMs) and outlines procedures for checking them. However the VDI prescription was written with a former generation of machines in mind: manual arms exploiting traditional touch probe technologies. Recent advances in metrology have given rise to noncontact laser scanning tools and robotic automation of articulated arms – technologies which are not adequately characterised using the VDI specification. In this paper we examine the “guidelines” presented in VDI 2617, finding many of them to be ambiguous and open to interpretation, with some tests appearing even to be optional. The engineer is left significant flexibility in the execution of the test procedures and the manufacturer is free to specify many of the test parameters. Such flexibility renders the VDI tests of limited value and the results can be misleading. We illustrate, with examples using the Nikon RCA, how a liberal interpretation of the VDI guidelines can significantly improve accuracy characterisation and suggest ways in which to mitigate this problem. We propose a series of stringent tests and revised definitions, in the same vein as VDI 2617 and similar US standards, to clarify the accuracy characterisation process. The revised methodology includes modified acceptance and reverification tests which aim to accommodate emerging technologies, laser scanning devices in particular, while maintaining the spirit of the existing and established standards. We seek to supply robust re-definitions for the accepted terms “zero point” and “useful arm length”, pre-supposing nothing about the geometry of the measuring device. We also identify a source of error unique to robotised AACMMs employing laser scanners – the forward-reverse pass error. We show how eliminating this error significantly improves the repeatability of a device and propose a novel approach to the testing of probing error based on statistical uncertainty

Atmospheric extinction coefficients in the Ic\mathrm{I_c} band for several major international observatories: Results from the BiSON telescopes, 1984 to 2016

Over 30 years of solar data have been acquired by the Birmingham Solar Oscillations Network (BiSON), an international network of telescopes used to study oscillations of the Sun. Five of the six BiSON telescopes are located at major observatories. The observational sites are, in order of increasing longitude: Mount Wilson (Hale) Observatory (MWO), California, USA; Las Campanas Observatory (LCO), Chile; Observatorio del Teide, Iza\~{n}a, Tenerife, Canary Islands; the South African Astronomical Observatory (SAAO), Sutherland, South Africa; Carnarvon, Western Australia; and the Paul Wild Observatory, Narrabri, New South Wales, Australia. The BiSON data may be used to measure atmospheric extinction coefficients in the $\mathrm{I_c}$ band (approximately 700-900 nm), and presented here are the derived atmospheric extinction coefficients from each site over the years 1984 to 2016.Comment: 15 pages, 10 figures, 4 tables. Accepted by Astronomical Journal: 2017 July 2

Improving Gravitational Wave Extraction Using Weyl Characteristic Fields

We present a detailed methodology for extracting the full set of Newman-Penrose Weyl scalars from numerically generated spacetimes without requiring a tetrad that is completely orthonormal or perfectly aligned to the principal null directions. We also describe an extrapolation technique for computing the Weyl scalars' contribution at asymptotic null infinity in post-processing. These methods have continued to be used to produce $\Psi_4$ and $h$ waveforms for the Simulating eXtreme Spacetimes Waveform Catalog and now have been expanded to produce the entire set of Weyl scalars. These new waveform quantities are critical for the future of gravitational wave astronomy in order to understand the finite-amplitude gauge differences that can occur in numerical waveforms. We also present a new analysis of the accuracy of waveforms produced by the Spectral Einstein Code. While ultimately we expect Cauchy Characteristic Extraction to yield more accurate waveforms, the extraction techniques described here are far easier to implement and have already proven to be a viable way to produce production-level waveforms that can meet the demands of current gravitational-wave detectors

Ultrasonography of the prostate gland and testes in dogs

Ultrasonographic imaging is an important diagnostic tool because it allows assessment of the shape, size, position, margination and internal architecture of organs, as well as facilitating the study of vascular supply and vascularisation. Recently, there has been considerable development of B-mode, Doppler and contrast-enhanced ultrasonography for examination of the reproductive tract of dogs, both for studying normal physiology and in the clinical setting. This article describes the practical examination of the canine prostate gland and testes using a variety of ultrasound techniques, and details the normal appearance and blood flow of these organs as well as changes that may be observed with common reproductive disorders

3D bioprinting of an intervertebral disc tissue analogue with a highly aligned annulus fibrosus via suspended layer additive manufacture

Intervertebral disc (IVD) function is achieved through integration of its two component regions: the nucleus pulposus (NP) and the annulus fibrosus (AF). The NP is soft (0.3–5 kPa), gelatinous and populated by spherical NP cells in a polysaccharide-rich extracellular matrix (ECM). The AF is much stiffer (∼100 kPa) and contains layers of elongated AF cells in an aligned, fibrous ECM. Degeneration of the disc is a common problem with age being a major risk factor. Progression of IVD degeneration leads to chronic pain and can result in permanent disability. The development of therapeutic solutions for IVD degeneration is impaired by a lack of in vitro models of the disc that are capable of replicating the fundamental structure and biology of the tissue. This study aims to investigate if a newly developed suspended hydrogel bioprinting system (termed SLAM) could be employed to fabricate IVD analogues with integrated structural and compositional features similar to native tissue. Bioprinted IVD analogues were fabricated to recapitulate structural, morphological and biological components present in the native tissue. The constructs replicated key structural components of native tissue with the presence of a central, polysaccharide-rich NP surrounded by organised, aligned collagen fibres in the AF. Cell tracking, actin and matrix staining demonstrated that embedded NP and AF cells exhibited morphologies and phenotypes analogous to what is observed in vivo with elongated, aligned AF cells and spherical NP cells that deposited HA into the surrounding environment. Critically, it was also observed that the NP and AF regions contained a defined cellular and material interface and segregated regions of the two cell types, thus mimicking the highly regulated structure of the IVD

Strongly Bound Surface Water Affects the Shape Evolution of Cerium Oxide Nanoparticles

The surface structure and composition of functional materials are well-known to be critically important factors controlling the surface reactivity. However, when doped the surface composition will change, and the challenge is to identify its impact on important surface processes and nanoparticle morphologies. We have begun to address this by using a combination of density functional theory and potential-based methods to investigate the effect of surface dopants on water adsorption and morphology of the technologically important material, CeO$_2$, which finds application as electrolyte in SOFCs, catalyst in soot combustion, and enzyme mimetic agents in biomedicine. We show that by mapping CeO$_2$ surface phase diagrams we can predict nanoparticle morphologies as a function of dopant, temperature, and water partial pressure. Our results show that low-temperature, undoped CeO$_2$ nanocubes with active {100} surface sites are thermodynamically stable, but at the typical high temperature, operating conditions favor polyhedra where {100} surfaces are replaced by less active {111} surfaces by surface ion migration. However, doping with trivalent cations, such as Gd$^{3+}$, will increase binding of water on the {100} surfaces and hence act to preserve the cuboidal architecture by capping the active surfaces. As surfaces tend to be decorated by impurities and dopants it is clear that their role should receive more attention and the approach we describe can be routinely applied to nanomaterials, morphologies, and associated active/inactive surfaces