Intergranular diffusion rates from the analysis of garnet surfaces: implications for metamorphic equilibration

Novel approaches to garnet analysis have been used to assess rates of intergranular diffusion between different matrix phases and garnet porphyroblasts in a regionally metamorphosed staurolite-mica-schist from the Barrovian-type area in Scotland. X-ray maps and chemical traverses of planar porphyroblast surfaces reveal chemical heterogeneity of the garnet grain boundary linked to the nature of the adjacent matrix phase. The garnet preserves evidence of low temperature retrograde exchange with matrix minerals and diffusion profiles documenting cation movement along the garnet boundaries. Garnet–quartz and garnet–plagioclase boundaries preserve evidence of sluggish Mg, Mn and Fe diffusion at comparable rates to volume diffusion in garnet, whereas diffusion along garnet–biotite interfaces is much more effective. Evidence of particularly slow Al transport, probably coupled to Fe3+ exchange, is locally preserved on garnet surfaces adjacent to Fe-oxide phases. The Ca distribution on the garnet surface shows the most complex behaviour, with long-wavelength heterogeneities apparently unrelated to the matrix grain boundaries. This implies that the Ca content of garnet is controlled by local availability and is thought likely to reflect disequilibrium established during garnet growth. Geochemical anomalies on the garnet surfaces are also linked to the location of triple junctions between the porphyroblasts and the matrix phases, and imply enhanced transport along these channels. The slow rates of intergranular diffusion and the characteristics of different boundary types may explain many features associated with the prograde growth of garnet porphyroblasts. Thus, minerals such as quartz, Fe-oxides and plagioclase whose boundaries with garnet are characterized by slow intergranular diffusion rates appear to be preferentially trapped as inclusions within porphyroblasts. As such grain boundary diffusion rates may be a significant kinetic impediment to metamorphic equilibrium and garnet may struggle to maintain chemical and textural equilibrium during growth in pelites

Effective crustal permeability controls fault evolution: An integrated structural, mineralogical and isotopic study in granitic gneiss, Monte Rosa, Northern Italy

Two dextral faults within granitic gneiss in the Monte Rosa nappe, northern Italy reveal key differences in their evolution controlled by evolving permeability and water/rock reactions. The comparison reveals that identical host rock lithologies develop radically different mineralogies within the fault zones, resulting in fundamentally different deformation histories. Oxygen and hydrogen isotope analyses coupled to microstructural characterisation show that infiltration of meteoric water occurred into both fault zones. The smaller Virgin Fault shows evidence of periodic closed system behaviour, which promoted the growth of hydrothermal K-feldspar, whilst the more open system behaviour of the adjacent Ciao Ciao Fault generated a weaker muscovite-rich fault core, which promoted a step change in fault evolution. Effective crustal permeability is a vital control on fault evolution and, coupled to the temperature (i.e. depth) at which key mineral transformations occur, is probably a more significant factor than host rock strength in controlling fault development. The study suggests that whether a fault in granitic basement grows into a large structure may be largely controlled by the initial hydrological properties of the host rocks. Small faults exposed at the surface may therefore be evolutionary “dead-ends” that typically do not represent the early stages in the development of larger faults

Designing a Belief Function-Based Accessibility Indicator to Improve Web Browsing for Disabled People

The purpose of this study is to provide an accessibility measure of web-pages, in order to draw disabled users to the pages that have been designed to be ac-cessible to them. Our approach is based on the theory of belief functions, using data which are supplied by reports produced by automatic web content assessors that test the validity of criteria defined by the WCAG 2.0 guidelines proposed by the World Wide Web Consortium (W3C) organization. These tools detect errors with gradual degrees of certainty and their results do not always converge. For these reasons, to fuse information coming from the reports, we choose to use an information fusion framework which can take into account the uncertainty and imprecision of infor-mation as well as divergences between sources. Our accessibility indicator covers four categories of deficiencies. To validate the theoretical approach in this context, we propose an evaluation completed on a corpus of 100 most visited French news websites, and 2 evaluation tools. The results obtained illustrate the interest of our accessibility indicator

2-(1,4-Dioxo-1,4-dihydro-2-naphthyl)-2-methylpropanoic acid

The sterically crowded title compound, C₁₄H₁₂O₄, crystallizes as centrosymmetric hydrogen-bonded dimers involving the carboxyl groups. The naphthoquinone ring system is folded by 11.5 (1)° about a vector joining the 1,4-C atoms, and the quinone O atoms are displaced from the ring plane, presumably because of steric interactions with the bulky substituent

Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background

Power spectrum estimation and evaluation of associated errors in the presence of incomplete sky coverage; non-homogeneous, correlated instrumental noise; and foreground emission is a problem of central importance for the extraction of cosmological information from the cosmic microwave background. We develop a Monte Carlo approach for the maximum likelihood estimation of the power spectrum. The method is based on an identity for the Bayesian posterior as a marginalization over unknowns. Maximization of the posterior involves the computation of expectation values as a sample average from maps of the cosmic microwave background and foregrounds given some current estimate of the power spectrum or cosmological model, and some assumed statistical characterization of the foregrounds. Maps of the CMB are sampled by a linear transform of a Gaussian white noise process, implemented numerically with conjugate gradient descent. For time series data with N_{t} samples, and N pixels on the sphere, the method has a computational expense $KO[N^{2} +- N_{t} +AFw-log N_{t}], where K is a prefactor determined by the convergence rate of conjugate gradient descent. Preconditioners for conjugate gradient descent are given for scans close to great circle paths, and the method allows partial sky coverage for these cases by numerically marginalizing over the unobserved, or removed, region.Comment: submitted to Ap

Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting

In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing: given a matrix $X$ formed as the sum of an unknown diagonal matrix and an unknown low rank positive semidefinite matrix, decompose $X$ into these constituents. The second problem we consider is to determine the facial structure of the set of correlation matrices, a convex set also known as the elliptope. This convex body, and particularly its facial structure, plays a role in applications from combinatorial optimization to mathematical finance. The third problem is a basic geometric question: given points $v_1,v_2,...,v_n\in \R^k$ (where $n > k$) determine whether there is a centered ellipsoid passing \emph{exactly} through all of the points. We show that in a precise sense these three problems are equivalent. Furthermore we establish a simple sufficient condition on a subspace $U$ that ensures any positive semidefinite matrix $L$ with column space $U$ can be recovered from $D+L$ for any diagonal matrix $D$ using a convex optimization-based heuristic known as minimum trace factor analysis. This result leads to a new understanding of the structure of rank-deficient correlation matrices and a simple condition on a set of points that ensures there is a centered ellipsoid passing through them.Comment: 20 page

Student teachers’ understanding and acceptance of evolution and the nature of science

The focus of this study was student teachers at a South African university enrolled in a Bachelor of Education (B.Ed.) programme and a Postgraduate Certificate in Education (PGCE), respectively. The purpose of this study was to explore students’ understanding and acceptance of evolution and beliefs about the nature of science (NOS), and to discover if these understandings and acceptances changed with the level of their studies. In so doing, we wished to determine if there is a relationship between their understanding of evolution and the NOS, and their level of acceptance of evolution. The study is located within a quantitative framework. Questionnaires were administered to pre-service teachers, who were enrolled in the School of Education. All participants had chosen Biology as their teaching specialisation. Three instruments were included in the questionnaires. The findings revealed that students in the B.Ed. programme have a poorer understanding of evolution and NOS than the graduate group (PGCE), and that there is no significant difference in understanding between different levels within the B.Ed. group. A further significant finding was that acceptance of evolution is independent of changes in conceptual understanding of evolution and independent of changes in beliefs about the NOS.Keywords: acceptance; beliefs; evolution; nature of science; understandin