Numerical solution of a class of random boundary value problems

AbstractThis paper deals with the nonlinear two point boundary value problem y″ = f(x, y, y′, R1,…, Rn), x0 < x < xf S1y(x0) + S2 y′(x0) = S3, S4 y(xf) + S5 y′(xf) = S6 where R1,…, Rn, S1,…, S6 are bounded continuous random variables. An approximate probability distribution function for y(x) is constructed by numerical integration of a set of related deterministic problems. Two distinct methods are described, and in each case convergence of the approximate distribution function to the actual distribution function is established. Primary attention is placed on problems with two random variables, but various generalizations are noted. As an example, a nonlinear one-dimensional heat conduction problem containing one or two random variables is studied in some detail

Mantle sources and magma evolution in Europe's largest rare earth element belt (Gardar Province, SW Greenland) : new insights from sulfur isotopes

This work is a contribution to the HiTech AlkCarb project and was funded by the European Union's Horizon 2020 research and innovation programme under grant agreement No. 689909. W.H. also acknowledges support from a UKRI Future Leaders Fellowship (MR/S033505/1). A.J.B. is funded by the NERC National Environment Isotope Facility award (NE/S011587/1) and the Scottish Universities Environmental Research Centre.Alkaline igneous complexes are often rich in rare earth elements (REE) and other metals essential for modern technologies. Although a variety of magmatic and hydrothermal processes explain the occurrence of individual deposits, one common feature identified in almost all studies, is a REE-enriched parental melt sourced from the lithospheric mantle. Fundamental questions remain about the origin and importance of the mantle source in the genesis of REE-rich magmas. In particular, it is often unclear whether localized enrichments within an alkaline province reflect heterogeneity in the mantle source lithology (caused by prior subduction or plume activity) or variations in the degree of partial melting and differentiation of a largely homogeneous source. Sulfur isotopes offer a means of testing these hypotheses because they are unaffected by high temperature partial melting processes and can fingerprint different mantle sources. Although one must be careful to rule out subsequent isotope fractionation during magma ascent, degassing and crustal interactions. Here, we present new S concentration and isotope (δ34S) measurements, as well as a compilation of major and trace element data, for a suite of alkaline magmatic units and crustal lithologies from the Mesoproterozoic Gardar Province. Samples span all phases of Gardar magmatism (1330–1140 Ma) and include regional dykes, rift lavas and the alkaline complexes Motzfeldt and Ilímaussaq, which represent two of Europe's largest REE deposits. We show that the vast majority of our 115 samples have S contents >100 ppm and δ34S of −1 to 5‰. Only 8 samples (with low S contents, <100 ppm) show evidence for crustal interactions, implying that the vast majority of Gardar melts preserve the S isotopic signature of their magma source. Importantly, samples from across the Gardar Province δ34S have above the canonical mantle range (≤−1.4‰) and therefore require recycled surface S in their mantle source. Elevated values are explained by a period of Andean-style subduction and mantle metasomatism which took place ∼500 Ma before rift onset and are also supported by trace elements signatures (e.g. Ba/La) which match modern subduction zones. Comparing the various generations of Gardar magmas, we find that δ34S  values, large ion lithophile elements (K, Ba, P) and selective incompatible elements (Nb and light REE) are particularly enriched in the Late Gardar dykes, alkaline complexes and clusters of silica-undersaturated dykes spatially associated with the alkaline complexes. These data indicate that subduction-related metasomatism of the Gardar mantle was spatially heterogeneous, and that alkaline complexes are sourced from localized mantle domains highly enriched in 34S, REE, alkalis and volatiles (particularly, F). Since alkalis and volatiles play an essential role in driving extreme differentiation of alkaline melts and fluids, we suggest the co-location of these species plus incompatible metals at high concentrations in the lithospheric mantle is a critical first-step in the genesis of a world-class alkaline REE deposit. S isotopes are powerful tools for identifying enriched mantle domains and the sources of mineralized alkaline igneous bodies.Publisher PDFPeer reviewe

Adding evidence type representation to DIDEO

Abstract-In this poster we present novel development and extension of the Drug-drug Interaction and Drug-drug Interaction Evidence Ontology (DIDEO). We demonstrate how reasoning over this extension of DIDEO can a) automatically create a multi-level hierarchy of evidence types from descriptions of the underlying scientific observations and b) automatically subsume individual evidence items under the correct evidence type. Thus DIDEO will enable evidence items added manually by curators to be automatically categorized into a drug-drug interaction framework with precision and minimal effort from curators. As with all previous DIDEO development this extension is consistent with OBO Foundry principles

The Ethical Triage and Management Guidelines of the Entrapped and Mangled Extremity in Resource Scarce Environments: A Systematic Literature Review.

ABSTRACTObjective:A systematic literature review (SLR) was performed to elucidate the current triage and treatment of an entrapped or mangled extremity in resource scarce environments (RSEs).Methods:A lead researcher followed the search strategy following inclusion and exclusion criteria. A first reviewer (FR) was randomly assigned sources. One of the 2 lead researchers was the second reviewer (SR). Each determined the level of evidence (LOE) and quality of evidence (QE) from each source. Any differing opinions between the FR and SR were discussed between them, and if differing opinions remained, then a third reviewer (the other lead researcher) discussed the article until a consensus was reached. The final opinion of each article was entered for analysis.Results:Fifty-eight (58) articles were entered into the final study. There was 1 study determined to be LOE 1, 29 LOE 2, and 28 LOE 3, with 15 determined to achieve QE 1, 37 QE 2, and 6 QE 3.Conclusion:This SLR showed that there is a lack of studies producing strong evidence to support the triage and treatment of the mangled extremity in RSE. Therefore, a Delphi process is suggested to adapt and modify current civilian and military triage and treatment guidelines to the RSE

Speech Communication

Contains reports on three research projects.National Institutes of Health (Grant 2 ROI NS04332)National Institutes of Health (Training Grant 5 T32 NS07040)C. J. LeBel FellowshipsNational Institutes of Health (Grant 5 RO1 NS13028)National Science Foundation (Grant BNS76-80278)National Science Foundation (Grant BNS77-26871

Practical Approach to Surge and Surge Control Systems

TutorialPg. 147-174This paper addresses the area of compressor stability, surge and surge control and relates to the practical aspects involved. An emphasis is placed on the physical understanding of surge phenomena and on the practical limitations of surge control systems. Topics discussed are physical interpretation of instability, causative factors, types of stall, machine and process design factors, surge effects and characteristics, control system types and practical application aspects. Some case studies also are presented. The discussion primarily relates to centrifugal compressors, but several aspects pertain to axial flow compressors as well. The paper is split into three sections: Section A consists of an introduction to surge and a discussion of centrifugal compressor design and process factors that affect operating stability. Section B discusses the various types of control schemes and surge protection devices. Several examples and common pitfalls are addressed. Section C addresses the important design tool, surge system simulation. Several references are provided to enable the reader to pursue this topic in greater detail

Localized precipitation and runoff on Mars

We use the Mars Regional Atmospheric Modeling System (MRAMS) to simulate lake storms on Mars, finding that intense localized precipitation will occur for lake size >=10^3 km^2. Mars has a low-density atmosphere, so deep convection can be triggered by small amounts of latent heat release. In our reference simulation, the buoyant plume lifts vapor above condensation level, forming a 20km-high optically-thick cloud. Ice grains grow to 200 microns radius and fall near (or in) the lake at mean rates up to 1.5 mm/hr water equivalent (maximum rates up to 6 mm/hr water equivalent). Because atmospheric temperatures outside the surface layer are always well below 273K, supersaturation and condensation begin at low altitudes above lakes on Mars. In contrast to Earth lake-effect storms, lake storms on Mars involve continuous precipitation, and their vertical velocities and plume heights exceed those of tropical thunderstorms on Earth. Convection does not reach above the planetary boundary layer for lakes O(10^2) mbar. Instead, vapor is advected downwind with little cloud formation. Precipitation occurs as snow, and the daytime radiative forcing at the land surface due to plume vapor and storm clouds is too small to melt snow directly (<+10 W/m^2). However, if orbital conditions are favorable, then the snow may be seasonally unstable to melting and produce runoff to form channels. We calculate the probability of melting by running thermal models over all possible orbital conditions and weighting their outcomes by probabilities given by Laskar et al., 2004. We determine that for an equatorial vapor source, sunlight 15% fainter than at present, and snowpack with albedo 0.28 (0.35), melting may occur with 4%(0.1%) probability. This rises to 56%(12%) if the ancient greenhouse effect was modestly (6K) greater than today.Comment: Submitted to JGR Planet

Speech Communication

Contains reports on two research projects.National Institutes of Health (Grant 2 ROl1 NS04332)National Institutes of Health (Training Grant 5 T32 NS07040)C.J. LeBel FellowshipsNational Science Foundation (Grant BNS77-26871

The Astropy Problem

The Astropy Project (http://astropy.org) is, in its own words, "a community effort to develop a single core package for Astronomy in Python and foster interoperability between Python astronomy packages." For five years this project has been managed, written, and operated as a grassroots, self-organized, almost entirely volunteer effort while the software is used by the majority of the astronomical community. Despite this, the project has always been and remains to this day effectively unfunded. Further, contributors receive little or no formal recognition for creating and supporting what is now critical software. This paper explores the problem in detail, outlines possible solutions to correct this, and presents a few suggestions on how to address the sustainability of general purpose astronomical software