New examples of Willmore submanifolds in the unit sphere via isoparametric functions,II

This paper is a continuation of a paper with the same title of the last two authors. In the first part of the present paper, we give a unified geometric proof that both focal submanifolds of every isoparametric hypersurface in spheres with four distinct principal curvatures are Willmore. In the second part, we completely determine which focal submanifolds are Einstein except one case.Comment: 19 pages,to appear in Annals of Global Analysis and Geometr

The critical dimension for a 4th order problem with singular nonlinearity

We study the regularity of the extremal solution of the semilinear biharmonic equation \bi u=\f{\lambda}{(1-u)^2}, which models a simple Micro-Electromechanical System (MEMS) device on a ball B\subset\IR^N, under Dirichlet boundary conditions $u=\partial_\nu u=0$ on $\partial B$. We complete here the results of F.H. Lin and Y.S. Yang \cite{LY} regarding the identification of a "pull-in voltage" \la^*>0 such that a stable classical solution u_\la with 0 exists for \la\in (0,\la^*), while there is none of any kind when \la>\la^*. Our main result asserts that the extremal solution $u_{\lambda^*}$ is regular $(\sup_B u_{\lambda^*} <1)$ provided $N \le 8$ while $u_{\lambda^*}$ is singular ($\sup_B u_{\lambda^*} =1$) for $N \ge 9$, in which case $1-C_0|x|^{4/3}\leq u_{\lambda^*} (x) \leq 1-|x|^{4/3}$ on the unit ball, where $C_0:= (\frac{\lambda^*}{\overline{\lambda}})^{1/3}$ and $\bar{\lambda}:= {8/9} (N-{2/3}) (N- {8/3})$.Comment: 19 pages. This paper completes and replaces a paper (with a similar title) which appeared in arXiv:0810.5380. Updated versions --if any-- of this author's papers can be downloaded at this http://www.birs.ca/~nassif

Inhibition of metal dusting using thermal spray coatings and laser treatment

Alloy 600 and Alloy 800H are susceptible to metal dusting. Both alloys were thermally sprayed with two different corrosion resistant coatings: Ni50Cr and Ni31Cr11Al0.6Y. Laser remelting was used to enhance further the effectiveness of these coatings to resist metal dusting by eliminating interconnected porosity and improving coating adhesion. Uncoated, coated and laser-treated coated samples of Alloy 600 and Alloy 800H were exposed to a mixed gas atmosphere (20% H2, 80% CO at 650°C). Samples were examined in plan and cross-section using optical and scanning electron microscopy, electron probe microanalysis and X-ray diffraction. The extent of carbon deposition was tracked by mass difference measurements at intervals during exposure. The thermally sprayed coatings enhanced metal dusting resistance by acting as physical barriers to carbon ingress. The NiCrAlY coating performed well on both substrates. The NiCr coating itself underwent metal dusting and spalled from Alloy 800H due partly to CTE mis-match stresses. Laser treatment of both coatings successfully eliminated interconnected porosity and hence enhanced metal dusting resistance

Controlling the dissociation of ligands from the adenosine A(2A) receptor through modulation of salt bridge strength

Controlling the Dissociation of Ligands from the Adenosine A2A Receptor through Modulation of Salt Bridge StrengthElena Segala, Dong Guo, Robert K. Y. Cheng, Andrea Bortolato, Francesca Deflorian, Andrew S. Doré, James C. Errey, Laura H. Heitman, Adriaan P. IJzerman, Fiona H. Marshall, and Robert M. CookeHeptares Therapeutics Ltd, Biopark Broadwater Road, Welwyn Garden City AL7 3AX, U.K.Division of Medicinal Chemistry, Leiden Academic Centre for Drug Research (LACDR), Leiden University P.O. Box 9502, 2300 RA Leiden, the NetherlandsAbstractThe association and dissociation kinetics of ligands binding to proteins vary considerably, but the mechanisms behind this variability are poorly understood, limiting their utilization for drug discovery. This is particularly so for G protein-coupled receptors (GPCRs) where high resolution structural information is only beginning to emerge. Engineering the human A2A adenosine receptor has allowed structures to be solved in complex with the reference compound ZM241385 and four related ligands at high resolution. Differences between the structures are limited, with the most pronounced being the interaction of each ligand with a salt bridge on the extracellular side of the receptor. Mutagenesis experiments confirm the role of this salt bridge in controlling the dissociation kinetics of the ligands from the receptor, while molecular dynamics simulations demonstrate the ability of ligands to modulate salt bridge stability. These results shed light on a structural determinant of ligand dissociation kinetics and identify a means by which this property may be optimized.Medicinal Chemistr

Microwave heating, isothermal sintering, and mechanical properties of powder metallurgy titanium and titanium alloys

This article presents a detailed assessment of microwave (MW) heating, isothermal sintering, and the resulting tensile properties of commercially pure Ti (CP-Ti), Ti-6Al-4V, and Ti-10V-2Fe-3Al (wt pct), by comparison with those fabricated by conventional vacuum sintering. The potential of MW sintering for titanium fabrication is evaluated accordingly. Pure MW radiation is capable of heating titanium powder to ≥1573 K (1300 C), but the heating response is erratic and difficult to reproduce. In contrast, the use of SiC MW susceptors ensures rapid, consistent, and controllable MW heating of titanium powder. MW sintering can consolidate CP-Ti and Ti alloys compacted from -100 mesh hydride-dehydride (HDH) Ti powder to ~95.0 pct theoretical density (TD) at 1573 K (1300 C), but no accelerated isothermal sintering has been observed over conventional practice. Significant interstitial contamination occurred from the Al2O3-SiC insulation-susceptor package, despite the high vacuum used (≤4.0 × 10-3 Pa). This leads to erratic mechanical properties including poor tensile ductility. The use of Ti sponge as impurity (O, N, C, and Si) absorbers can effectively eliminate this problem and ensure good-to-excellent tensile properties for MW-sintered CP-Ti, Ti-10V-2Fe-3Al, and Ti-6Al-4V. The mechanisms behind various observations are discussed. The prime benefit of MW sintering of Ti powder is rapid heating. MW sintering of Ti powder is suitable for the fabrication of small titanium parts or titanium preforms for subsequent thermomechanical processing

Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection

Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, including the situations when turbulent reconnection is self-driven, i.e. the turbulence in the system is generated by the reconnection process itself. We show how turbulent reconnection entails the violation of magnetic flux freezing, the conclusion that has really far reaching consequences for many realistically turbulent astrophysical environments. In addition, we consider observational testing of turbulent reconnection as well as numerous implications of the theory. The former includes the Sun and solar wind reconnection, while the latter include the process of reconnection diffusion induced by turbulent reconnection, the acceleration of energetic particles, bursts of turbulent reconnection related to black hole sources as well as gamma ray bursts. Finally, we explain why turbulent reconnection cannot be explained by turbulent resistivity or derived through the mean field approach.Comment: 66 pages, 24 figures, a chapter of the book "Magnetic Reconnection - Concepts and Applications", editors W. Gonzalez, E. N. Parke

What is the Oxygen Isotope Composition of Venus? The Scientific Case for Sample Return from Earth’s “Sister” Planet

Venus is Earth’s closest planetary neighbour and both bodies are of similar size and mass. As a consequence, Venus is often described as Earth’s sister planet. But the two worlds have followed very different evolutionary paths, with Earth having benign surface conditions, whereas Venus has a surface temperature of 464 °C and a surface pressure of 92 bar. These inhospitable surface conditions may partially explain why there has been such a dearth of space missions to Venus in recent years.The oxygen isotope composition of Venus is currently unknown. However, this single measurement (Δ17O) would have first order implications for our understanding of how large terrestrial planets are built. Recent isotopic studies indicate that the Solar System is bimodal in composition, divided into a carbonaceous chondrite (CC) group and a non-carbonaceous (NC) group. The CC group probably originated in the outer Solar System and the NC group in the inner Solar System. Venus comprises 41% by mass of the inner Solar System compared to 50% for Earth and only 5% for Mars. Models for building large terrestrial planets, such as Earth and Venus, would be significantly improved by a determination of the Δ17O composition of a returned sample from Venus. This measurement would help constrain the extent of early inner Solar System isotopic homogenisation and help to identify whether the feeding zones of the terrestrial planets were narrow or wide.Determining the Δ17O composition of Venus would also have significant implications for our understanding of how the Moon formed. Recent lunar formation models invoke a high energy impact between the proto-Earth and an inner Solar System-derived impactor body, Theia. The close isotopic similarity between the Earth and Moon is explained by these models as being a consequence of high-temperature, post-impact mixing. However, if Earth and Venus proved to be isotopic clones with respect to Δ17O, this would favour the classic, lower energy, giant impact scenario.We review the surface geology of Venus with the aim of identifying potential terrains that could be targeted by a robotic sample return mission. While the potentially ancient tessera terrains would be of great scientific interest, the need to minimise the influence of venusian weathering favours the sampling of young basaltic plains. In terms of a nominal sample mass, 10 g would be sufficient to undertake a full range of geochemical, isotopic and dating studies. However, it is important that additional material is collected as a legacy sample. As a consequence, a returned sample mass of at least 100 g should be recovered.Two scenarios for robotic sample return missions from Venus are presented, based on previous mission proposals. The most cost effective approach involves a “Grab and Go” strategy, either using a lander and separate orbiter, or possibly just a stand-alone lander. Sample return could also be achieved as part of a more ambitious, extended mission to study the venusian atmosphere. In both scenarios it is critical to obtain a surface atmospheric sample to define the extent of atmosphere-lithosphere oxygen isotopic disequilibrium. Surface sampling would be carried out by multiple techniques (drill, scoop, “vacuum-cleaner” device) to ensure success. Surface operations would take no longer than one hour.Analysis of returned samples would provide a firm basis for assessing similarities and differences between the evolution of Venus, Earth, Mars and smaller bodies such as Vesta. The Solar System provides an important case study in how two almost identical bodies, Earth and Venus, could have had such a divergent evolution. Finally, Venus, with its runaway greenhouse atmosphere, may provide data relevant to the understanding of similar less extreme processes on Earth. Venus is Earth’s planetary twin and deserves to be better studied and understood. In a wider context, analysis of returned samples from Venus would provide data relevant to the study of exoplanetary systems

Mapping subnational HIV mortality in six Latin American countries with incomplete vital registration systems

BackgroundHuman immunodeficiency virus (HIV) remains a public health priority in Latin America. While the burden of HIV is historically concentrated in urban areas and high-risk groups, subnational estimates that cover multiple countries and years are missing. This paucity is partially due to incomplete vital registration (VR) systems and statistical challenges related to estimating mortality rates in areas with low numbers of HIV deaths. In this analysis, we address this gap and provide novel estimates of the HIV mortality rate and the number of HIV deaths by age group, sex, and municipality in Brazil, Colombia, Costa Rica, Ecuador, Guatemala, and Mexico.MethodsWe performed an ecological study using VR data ranging from 2000 to 2017, dependent on individual country data availability. We modeled HIV mortality using a Bayesian spatially explicit mixed-effects regression model that incorporates prior information on VR completeness. We calibrated our results to the Global Burden of Disease Study 2017.ResultsAll countries displayed over a 40-fold difference in HIV mortality between municipalities with the highest and lowest age-standardized HIV mortality rate in the last year of study for men, and over a 20-fold difference for women. Despite decreases in national HIV mortality in all countries-apart from Ecuador-across the period of study, we found broad variation in relative changes in HIV mortality at the municipality level and increasing relative inequality over time in all countries. In all six countries included in this analysis, 50% or more HIV deaths were concentrated in fewer than 10% of municipalities in the latest year of study. In addition, national age patterns reflected shifts in mortality to older age groups-the median age group among decedents ranged from 30 to 45years of age at the municipality level in Brazil, Colombia, and Mexico in 2017.ConclusionsOur subnational estimates of HIV mortality revealed significant spatial variation and diverging local trends in HIV mortality over time and by age. This analysis provides a framework for incorporating data and uncertainty from incomplete VR systems and can help guide more geographically precise public health intervention to support HIV-related care and reduce HIV-related deaths.Peer reviewe