Grain size analyses in tin-lead glazes based on 2d-sections

A problem in the archaeometric classification of Catalan Renaissance pottery is the fact, that the clay supply of the pottery workshops was centrally organized by guilds, and therefore usually all potters of a single production centre produced chemically similar ceramics. However, analysing the glazes of the ware usually a large number of inclusions in the glaze is found, which reveal technological differences between single workshops. These inclusions have been used by the potters in order to opacify the transparent glaze and to achieve a white background for further decoration. In order to distinguish different technological preparation procedures of the single workshops, at a Scanning Electron Microscope the chemical composition of those inclusions as well as their size in the two-dimensional cut is recorded. Based on the latter, a frequency distribution of the apparent diameters is estimated for each sample and type of inclusion. Following an approach by S.D. Wicksell (1925), it is principally possible to transform the distributions of the apparent 2D-diameters back to those of the true three-dimensional bodies. The applicability of this approach and its practical problems are examined using different ways of kernel density estimation and Monte-Carlo tests of the methodology. Finally, it is tested in how far the obtained frequency distributions can be used to classify the pottery

Refinement criteria for global illumination using convex funcions

In several computer graphics areas, a refinement criterion is often needed to decide whether to go on or to stop sampling a signal. When the sampled values are homogeneous enough, we assume that they represent the signal fairly well and we do not need further refinement, otherwise more samples are required, possibly with adaptive subdivision of the domain. For this purpose, a criterion which is very sensitive to variability is necessary. In this paper, we present a family of discrimination measures, the f-divergences, meeting this requirement. These convex functions have been well studied and successfully applied to image processing and several areas of engineering. Two applications to global illumination are shown: oracles for hierarchical radiosity and criteria for adaptive refinement in ray-tracing. We obtain significantly better results than with classic criteria, showing that f-divergences are worth further investigation in computer graphics. Also a discrimination measure based on entropy of the samples for refinement in ray-tracing is introduced. The recursive decomposition of entropy provides us with a natural method to deal with the adaptive subdivision of the sampling region

Interactions between grain size and composition of sediments: two examples

Two contrasting case studies of sediment and detrital mineral composition are investigated in order to outline interactions between chemical composition and grain size. Modern glacial sediments exhibit a strong dependence of the two parameters due to the preferential enrichment of mafic minerals, especially biotite, in the fine-grained fractions. On the other hand, the composition of detrital heavy minerals (here: rutile) appears to be not systematically related to grain-size, but is strongly controlled by location, i.e. the petrology of the source rocks of detrital grains. This supports the use of rutile as a well-suited tracer mineral for provenance studies. The results further suggest that (i) interpretations derived from whole-rock sediment geochemistry should be flanked by grain-size observations, and (ii) a more sound statistical evaluation of these interactions require the development of new tailor-made statistical tools to deal with such so-called two-way compositions

A Log-linear model of grain size influence on the geochemistry of sediments

Sediment composition is mainly controlled by the nature of the source rock(s), and chemical (weathering) and physical processes (mechanical crushing, abrasion, hydrodynamic sorting) during alteration and transport. Although the factors controlling these processes are conceptually well understood, detailed quantification of compositional changes induced by a single process are rare, as are examples where the effects of several processes can be distinguished. The present study was designed to characterize the role of mechanical crushing and sorting in the absence of chemical weathering. Twenty sediment samples were taken from Alpine glaciers that erode almost pure granitoid lithologies. For each sample, 11 grain-size fractions from granules to clay (ø grades <-1 to >9) were separated, and each fraction was analysed for its chemical composition. The presence of clear steps in the box-plots of all parts (in adequate ilr and clr scales) against ø is assumed to be explained by typical crystal size ranges for the relevant mineral phases. These scatter plots and the biplot suggest a splitting of the full grain size range into three groups: coarser than ø=4 (comparatively rich in SiO2, Na2O, K2O, Al2O3, and dominated by “felsic” minerals like quartz and feldspar), finer than ø=8 (comparatively rich in TiO2, MnO, MgO, Fe2O3, mostly related to “mafic” sheet silicates like biotite and chlorite), and intermediate grains sizes (4≤ø <8; comparatively rich in P2O5 and CaO, related to apatite, some feldspar). To further test the absence of chemical weathering, the observed compositions were regressed against three explanatory variables: a trend on grain size in ø scale, a step function for ø≥4, and another for ø≥8. The original hypothesis was that the trend could be identified with weathering effects, whereas each step function would highlight those minerals with biggest characteristic size at its lower end. Results suggest that this assumption is reasonable for the step function, but that besides weathering some other factors (different mechanical behavior of minerals) have also an important contribution to the trend. Key words: sediment, geochemistry, grain size, regression, step function

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

Pose Refinement of Active Models using Forces in 3D

A new algorithm is described for refining the pose of a model of a rigid object, to conform more accurately to the image structure. Elemental 3D forces are considered to act on the model. These are derived from directional derivatives of the image local to the projected model features. The convergence properties of the algorithm is investigated and compared to a previous technique. Its use in a video sequence of a cluttered outdoor traffic scene is also illustrated and assessed.

A Newton method for pose refinement of 3D models

Different optimization methods can be employed to optimize a numerical estimate for the match between an instantiated object model and an image. In order to take advantage of gradient-based optimization methods, perspective inversion must be used in this context. We show that convergence can be very fast by extrapolating to maximum goodness-of-fit with Newton's method. This approach is related to methods which either maximize a similar goodness-of-fit measure without use of gradient information, or else minimize distances between projected model lines and image features. Newton's method combines the accuracy of the former approach with the speed of convergence of the latter.

Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

Does reactive surface area depend on grain size? Results from pH 3, 25 circle C far-from-equilibrium flow-through dissolution experiments on anorthite and biotite

Laboratory determined mineral weathering rates need to be normalised to allow their extrapolation to natural systems. The principle normalisation terms used in the literature are mass, and geometric- and BET specific surface area (SSA). The purpose of this study was to determine how dissolution rates normalised to these terms vary with grain size. Different size fractions of anorthite and biotite ranging from 180-150 to 20-10 mu m were dissolved in pH 3, HCl at 25 degrees C in flow through reactors under far from equilibrium conditions. Steady state dissolution rates after 5376 h (anorthite) and 4992 h (biotite) were calculated from Si concentrations and were normalised to initial- and final- mass and geometric-, geometric edge- (biotite), and BET SSA. For anorthite, rates normalised to initial- and final-BET SSA ranged from 0.33 to 2.77 X 10(-10) mol(feldspar) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 5.74 to 8.88 X 10(-10) mol(feldspar) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.11 to 1.65 mol(feldspar) g(-1) s(-1). For biotite, rates normalised to initial- and final-BET SSA ranged from 1.02 to 2.03 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 3.26 to 16.21 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric edge SSA ranged from 59.46 to 111.32 x 10(-12) mol(biotite) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.81 to 6.93 X 10(-12) mol(biotite) g(-1) s(-1). For all normalising terms rates varied significantly (p <= 0.05) with grain size. The normalising terms which gave least variation in dissolution rate between grain sizes for anorthite were initial BET SSA and initial- and final-geometric SSA. This is consistent with: (1) dissolution being dominated by the slower dissolving but area dominant non-etched surfaces of the grains and, (2) the walls of etch pits and other dissolution features being relatively unreactive. These steady state normalised dissolution rates are likely to be constant with time. Normalisation to final BET SSA did not give constant ratios across grain size due to a non-uniform distribution of dissolution features. After dissolution coarser grains had a greater density of dissolution features with BET-measurable but unreactive wall surface area than the finer grains. The normalising term which gave the least variation in dissolution rates between grain sizes for biotite was initial BET SSA. Initial- and final-geometric edge SSA and final BET SSA gave the next least varied rates. The basal surfaces dissolved sufficiently rapidly to influence bulk dissolution rate and prevent geometric edge SSA normalised dissolution rates showing the least variation. Simple modelling indicated that biotite grain edges dissolved 71-132 times faster than basal surfaces. In this experiment, initial BET SSA best integrated the different areas and reactivities of the edge and basal surfaces of biotite. Steady state dissolution rates are likely to vary with time as dissolution alters the ratio of edge to basal surface area. Therefore they would be more properly termed pseudo-steady state rates, only appearing constant because the time period over which they were measured (1512 h) was less than the time period over wich they would change significantly. (c) 2006 Elsevier Inc. All rights reserved.

Effects of manure and fertilizer on grain yield, soil carbon and phosphorus in a 13-year field trial in semi-arid Kenya

Long-term indicators of soil fertility were assessed by measuring grain yield, soil organic carbon (SOC) and soil Olsen phosphorous for a P-deficient soil. In one set of treatments, goat manure was applied annually for 13 years at 0, 5 and 10 t ha(-1), and intercrops of sorghum/cowpea, millet/green gram and maize/pigeonpea were grown. Yield depended on rainfall and trends with time were not identifiable. Manure caused an upward trend in SOC, but 10 t ha(-1) manure did not give significantly more SOC than 5 t ha(-1). Only 10 t ha(-1) manure increased Olsen P. Measurements of both SOC and Olsen P are recommended. In another set of treatments, manure was applied for four years; the residual effect lasted another seven to eight years when assessed by yield, SOC and Olsen P Treatment with mineral fertilizers provided the same rates of N and P as 5 t hat manure and yields from manure and fertilizer were similar. Fertilizer increased Olsen P but not SOC. Management systems with occasional manure application and intermediate fertilizer applications should be assessed. Inputs and offtakes of C, N and P were measured for three years. Approximately 16, 25 and 11% of C, N and P respectively were stabilized into soil organic matter from 5 t ha(-1) a(-1) manure. The majority of organic P was fixed as soil inorganic P.