The Kato square root problem on vector bundles with generalised bounded geometry

We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive operators over the bundle of finite rank tensors. These results are obtained as a special case of similar estimates on smooth vector bundles satisfying a criterion which we call generalised bounded geometry. We prove this by establishing quadratic estimates for perturbations of Dirac type operators on such bundles under an appropriate set of assumptions.Comment: Slight technical modification of the notion of "GBG constant section" on page 7, and a few technical modifications to Proposition 8.4, 8.6, 8.

On stoichiometry and intermixing at the spinel/perovskite interface in CoFe2O4/BaTiO3 thin films

The performance of complex oxide heterostructures depends primarily on the interfacial coupling of the two component structures. This interface character inherently varies with the synthesis method and conditions used since even small composition variations can alter the electronic, ferroelectric, or magnetic functional properties of the system. The focus of this article is placed on the interface character of a pulsed laser deposited CoFe2O4/BaTiO3 thin film. Using a range of state-of-the-art transmission electron microscopy methodologies, the roles of substrate morphology, interface stoichiometry, and cation intermixing are determined on the atomic level. The results reveal a surprisingly uneven BaTiO3 substrate surface formed after the film deposition and Fe atom incorporation in the top few monolayers inside the unit cell of the BaTiO3 crystal. Towards the CoFe2O4 side, a disordered region extending several nanometers from the interface was revealed and both Ba and Ti from the substrate were found to diffuse into the spinel layer. The analysis also shows that within this somehow incompatible composite interface, a different phase is formed corresponding to the compound Ba2Fe3Ti5O15, which belongs to the ilmenite crystal structure of FeTiO3 type. The results suggest a chemical activity between these two oxides, which could lead to the synthesis of complex engineered interfaces

The Effect of a Needs-Related Caries Preventive Program in Children and Young Adults – Results after 20 Years

The risk for caries development in children varies significantly for different age groups, individuals, teeth, and surfaces. Thus from a cost-effectiveness point of view, caries preventive measures must be integrated and based on predicted risk from age group down to individual tooth surfaces. Based on this philosophy and experiences from continuously ongoing research on evaluating and reevaluating separate and integrated caries preventive measures, as well as methods for prediction of caries risk, a needs-related caries preventive program was introduced for all 0–19-year-olds in the county of Värmland, Sweden, in 1979. The goals for the subjects following the program from birth to the age of 19 years were

Extremely narrow spectrum of GRB110920A: further evidence for localised, subphotospheric dissipation

Much evidence points towards that the photosphere in the relativistic outflow in GRBs plays an important role in shaping the observed MeV spectrum. However, it is unclear whether the spectrum is fully produced by the photosphere or whether a substantial part of the spectrum is added by processes far above the photosphere. Here we make a detailed study of the $\gamma-$ray emission from single pulse GRB110920A which has a spectrum that becomes extremely narrow towards the end of the burst. We show that the emission can be interpreted as Comptonisation of thermal photons by cold electrons in an unmagnetised outflow at an optical depth of $\tau \sim 20$. The electrons receive their energy by a local dissipation occurring close to the saturation radius. The main spectral component of GRB110920A and its evolution is thus, in this interpretation, fully explained by the emission from the photosphere including localised dissipation at high optical depths.Comment: 14 pages, 11 figures, accepted to MNRA

Dynamo effect in parity-invariant flow with large and moderate separation of scales

It is shown that non-helical (more precisely, parity-invariant) flows capable of sustaining a large-scale dynamo by the negative magnetic eddy diffusivity effect are quite common. This conclusion is based on numerical examination of a large number of randomly selected flows. Few outliers with strongly negative eddy diffusivities are also found, and they are interpreted in terms of the closeness of the control parameter to a critical value for generation of a small-scale magnetic field. Furthermore, it is shown that, for parity-invariant flows, a moderate separation of scales between the basic flow and the magnetic field often significantly reduces the critical magnetic Reynolds number for the onset of dynamo action.Comment: 44 pages,11 figures, significantly revised versio

Cold Physiology: Postprandial Blood Flow Dynamics and Metabolism in the Antarctic Fish Pagothenia borchgrevinki

Previous studies on metabolic responses to feeding (i.e. the specific dynamic action, SDA) in Antarctic fishes living at temperatures below zero have reported long-lasting increases and small peak responses. We therefore hypothesized that the postprandial hyperemia also would be limited in the Antarctic fish Pagothenia borchgrevinki. The proportion of cardiac output directed to the splanchnic circulation in unfed fish was 18%, which is similar to temperate fish species. Contrary to our prediction, however, gastrointestinal blood flow had increased by 88% at twenty four hours after feeding due to a significant increase in cardiac output and a significant decrease in gastrointestinal vascular resistance. While gastric evacuation time appeared to be longer than in comparable temperate species, digestion had clearly commenced twenty four hours after feeding as judged by a reduction in mass of the administered feed. Even so, oxygen consumption did not increase suggesting an unusually slowly developing SDA. Adrenaline and angiotensin II was injected into unfed fish to investigate neuro-humoral control mechanisms of gastrointestinal blood flow. Both agonists increased gastrointestinal vascular resistance and arterial blood pressure, while systemic vascular resistance was largely unaffected. The hypertension was mainly due to increased cardiac output revealing that the heart and the gastrointestinal vasculature, but not the somatic vasculature, are important targets for these agonists. It is suggested that the apparently reduced SDA in P. borchgrevinki is due to a depressant effect of the low temperature on protein assimilation processes occurring outside of the gastrointestinal tract, while the gastrointestinal blood flow responses to feeding and vasoactive substances resemble those previously observed in temperate species