The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

Feature tracking on the unit-sphere

Techniques used in a previous study of the objective identification and tracking of meteorological features in model data are extended to the unit sphere. An alternative feature detection scheme is described based on cubic interpolation for the sphere and local maximization. The extension of the tracking technique, used in the previous study, to the unit sphere is described. An example of the application of these techniques to a global relative vorticity field from a model integration are presented and discussed.

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.

A life less ordinary: The ritualization of the domestic sphere in later prehistoric Europe

This article, which is based on the fourteenth McDonald Lecture, considers two tensions in contemporary archaeology. one is between interpretations of specific structures, monuments and deposits as the result of either 'ritual' 'practical' activities in the past, and the other is between an archaeology that focuses on subsistence and adaptation and one that emphasizes cognition, meaning, and agency. It suggests that these tensions arise from an inadequate conception of ritual itself. Drawing on recent studies of ritualization, it suggests that it might be more helpful to consider how aspects of domestic life took on special qualities in later prehistoric Europe. The discussion is based mainly on Neolithic enclosures and other monuments, Bronze Age and Iron Age settlement sites and the Viereckschanzen of central Europe. it may have implications for field archaeology as well as social archaeology, and also for those who study the formation of the archaeological record.

Influence of aluminum hydroxide on potassium release from two Colombian soils

The effect of sesquioxides on the mechanisms of chemical reactions that govern the transformation between exchangeable potassium (Kex) and non-exchangeable K (Knex) was studied on acid tropical soils from Colombia: Caribia with predominantly 2 : 1 clay minerals and High Terrace with predominantly 1 : 1 clay minerals and sesquioxides. Illite and vermiculite are the main clay minerals in Caribia followed by kaolinite, gibbsite, and plagioclase, and kaolinite is the major clay mineral in High Terrace followed by hydroxyl-Al interlayered vermiculite, quartz, and pyrophyllite. The soils have 1.8 and 0.5% of K2O, respectively. They were used either untreated or prepared by adding AlCl3 and NaOH, which produced aluminum hydroxide. The soils were percolated continuously with 10mM NH4OAc at pH 7.0 and 10 mM CaCl2 at pH 5.8 for 120 h at 6 mL h(-1) to examine the release of Kex and Knex. In the untreated soils, NH4+ and Ca-2(+) released the same amounts of Kex from Caribia, whereas NH4+ released about twice as much Kex as Ca2+ from High Terrace. This study proposes that the small ionic size of NH4+ (0.54nm) enables it to enter more easily into the K sites at the broken edges of the kaolinite where Ca2+ (0.96 nm) cannot have access. As expected for a soil dominated by 2 : 1 clay minerals, Ca2+ caused Knex to be released from Caribia with no release by NH4+. No Knex was released by either ion from High Terrace. After treatment with aluminum hydroxide, K release from the exchangeable fraction was reduced in Caribia due to the blocking of the exchange sites but release of Knex was not affected. The treatment increased the amount of Kex released from the High Terrace soil and the release of Knex remained negligible although with Ca2+ the distinction between Kex and Knex was unclear. The increase in Kex was attributed to the initially acidic conditions produced by adding AlCl3 which may have dissolved interlayered aluminum hydroxide from the vermiculite present, thus exposing trapped K as exchangeable K. The subsequent precipitation of aluminum hydroxide when NaOH was added did not interfere with the release of this K, and so was probably formed mostly on the surface of the dominant kaolinite. Measurement of availability of K by standard methods using NH4 salts could result in overestimates in High Terrace and this may be a more general shortcoming of the methods in kaolinitic soils.

Molecular aluminum hydrides identified by inelastic neutron scattering during H-2 regeneration of catalyst-doped NaAlH4

Catalyst-doped sodium aluminum hydrides have been intensively studied as solid hydrogen carriers for onboard proton-exchange membrane (PEM) fuel cells. Although the importance of catalyst choice in enhancing kinetics for both hydrogen uptake and release of this hydride material has long been recognized, the nature of the active species and the mechanism of catalytic action are unclear. We have shown by inelastic neutron scattering (INS) spectroscopy that a volatile molecular aluminum hydride is formed during the early stage of H-2 re-eneration of a depleted, catalyst-doped sodium aluminum hydride. Computational modeling of the INS spectra suggested the formation of AlH3 and oligomers (AlH3)(n) (Al2H6, Al3H9, and Al4H12 clusters), which are pertinent to the mechanism of hydrogen storage. This paper demonstrates, for the first time, the existence of these volatile species.

Effect of Stretching on the Structure of Cylinder- and Sphere-Forming Styrene-Isoprene-Styrene Block Copolymers

Two styrene-isoprene-styrene block copolymers Vector 4111 and 4113, exhibiting cylindrical (18 wt % PS) and spherical (16 wt % PS) morphology, respectively, have been examined under uniaxial elongation up to 200% strain. On the basis of stress-strain data, mechanical properties are compared for isotropic and oriented polystyrene domains. The structure at various stages of deformation has been determined from SAXS patterns in three planes and two principal deformation directions with respect to orientation. Samples showed a very high degree of hexagonal packing, resulting in an X-ray pattern taken parallel to the cylinder alignment approaching single crystal ordering. Cylinders were aligned with the closest packed planes parallel to film surface. Particular attention has been paid to a lattice deformation process occurring during the first stretching and relaxation cycle. For a copolymer with oriented cylindrical morphology the deformation was affine up to 120% strain. The microdomain spacing was calculated parallel and perpendicular to the stretching direction. The cylindrical microstructure orientation, quantified by Hermans' orientation factor reduced during elongation of oriented polymer, while the elongation of isotropic sample caused an increase of orientation. Deformation of all studied morphologies was reversible.

Parallel Monte Carlo sampling scheme for sphere and hemisphere

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. Monte Carlo methods for solving the rendering equation use sampling of the solid angle subtended by unit hemisphere or unit sphere in order to perform the numerical integration of the rendering equation. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Our aim is to construct and study the parallel sampling scheme for hemisphere and sphere. First we apply the symmetry property for partitioning of hemisphere and sphere. The domain of solid angle subtended by a hemisphere is divided into a number of equal sub-domains. Each sub-domain represents solid angle subtended by orthogonal spherical triangle with fixed vertices and computable parameters. Then we introduce two new algorithms for sampling of orthogonal spherical triangles. Both algorithms are based on a transformation of the unit square. Similarly to the Arvo's algorithm for sampling of arbitrary spherical triangle the suggested algorithms accommodate the stratified sampling. We derive the necessary transformations for the algorithms. The first sampling algorithm generates a sample by mapping of the unit square onto orthogonal spherical triangle. The second algorithm directly compute the unit radius vector of a sampling point inside to the orthogonal spherical triangle. The sampling of total hemisphere and sphere is performed in parallel for all sub-domains simultaneously by using the symmetry property of partitioning. The applicability of the corresponding parallel sampling scheme for Monte Carlo and Quasi-D/lonte Carlo solving of rendering equation is discussed.

Efficiency and purity control in the preparation of pure and/or aluminum-doped barium ferrites by hydrothermal methods using ferrous ions as reactants

The synthesis of hexagonal barium ferrite (BaFe12O19) was studied under hydrothermal conditions by a method in which a significant amount of ferrous chloride was introduced along side ferric chloride among the starting materials. Though all of the Fe2+ ions in the starting material were converted to Fe3+ ions in the final product, Fe2+ was confirmed to participate differently from the Fe3+ used in the conventional method in the mechanism of forming barium ferrite. Indeed the efficiency of the synthesis and the quality of the product and the lack of impurities such as Fe2O3 and BaFe2O4 were improved when Fe2+ was included. However, the amount of ferrous ions that could be included to obtain the desired product was limited with an optimum ratio of 2:8 for FeCl2/FeCl3 when only 2h of reaction time were needed. It was also found that the role of trivalent Fe3+ could be successfully replaced by Al3+. Up to 50% of their on could be replaced by Al3+ in the reactants to produce Al- doped products. It was also found that the ratio of Fe2+/M3+ could be increased in the presence of Al3+ to produce high quality barium ferrite.

Reversible sphere-to-lamellar wetting transition at the interface of a diblock copolymer system

We use ellipsometry to investigate a transition in the morphology of a sphere-forming diblock copolymer thin-film system. At an interface the diblock morphology may differ from the bulk when the interfacial tension favours wetting of the minority domain, thereby inducing a sphere-to-lamella transition. In a small, favourable window in energetics, one may observe this transition simply by adjusting the temperature. Ellipsometry is ideally suited to the study of the transition because the additional interface created by the wetting layer affects the polarisation of light reflected from the sample. Here we study thin films of poly(butadiene-ethylene oxide) (PB-PEO), which order to form PEO minority spheres in a PB matrix. As temperature is varied, the reversible transition from a partially wetting layer of PEO spheres to a full wetting layer at the substrate is investigated.

Self-consistent field theory for diblock copolymers grafted to a sphere

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.