Extension of spherical nonparametric estimators to nonisotropic kernels: An oceanographic application

In a recently published paper. spherical nonparametric estimators were applied to feature-track ensembles to determine a range of statistics for the atmospheric features considered. This approach obviates the types of bias normally introduced with traditional estimators. New spherical isotropic kernels with local support were introduced. Ln this paper the extension to spherical nonisotropic kernels with local support is introduced, together with a means of obtaining the shape and smoothing parameters in an objective way. The usefulness of spherical nonparametric estimators based on nonisotropic kernels is demonstrated with an application to an oceanographic feature-track ensemble.

Spherical nonparametric estimators applied to the UGAMP model integration for AMIP

The aim of this paper is essentially twofold: first, to describe the use of spherical nonparametric estimators for determining statistical diagnostic fields from ensembles of feature tracks on a global domain, and second, to report the application of these techniques to data derived from a modern general circulation model. New spherical kernel functions are introduced that are more efficiently computed than the traditional exponential kernels. The data-driven techniques of cross-validation to determine the amount elf smoothing objectively, and adaptive smoothing to vary the smoothing locally, are also considered. Also introduced are techniques for combining seasonal statistical distributions to produce longer-term statistical distributions. Although all calculations are performed globally, only the results for the Northern Hemisphere winter (December, January, February) and Southern Hemisphere winter (June, July, August) cyclonic activity are presented, discussed, and compared with previous studies. Overall, results for the two hemispheric winters are in good agreement with previous studies, both for model-based studies and observational studies.

Ruthenium complexes of C,C '-bis(ethynyl)carboranes: an investigation of electronic interactions mediated by spherical pseudo-aromatic spacers

The complexes [Ru(1-C=C-1,10-C2B8H9)(dppe)Cp*] (3a), [Ru(1-C C-1,12-C2B10H11)(dppe)-Cp*] (3b), [{Ru(dppe)Cp*}(2){mu-1,10-(C C)(2)-1,10-C2B8H8}] (4a) and [{Ru(dppe)Cp*}(2){mu-1,12-(C C)2- 1,12-C2B10-H-10}] (4b), which form a representative series of mono- and bimetallic acetylide complexes featuring 10- and 12-vertex carboranes embedded within the dethynyl bridging ligand, have been prepared and structurally characterized. In addition, these compounds have been examined spectroscopically (UV-is-NIR, IR) in all accessible redox states. The significant separation of the two, one-electron anodic waves observed in the cyclic voltammograms of the bimetallic complexes 4a and 4b is largely independent of the nature of the electrolyte and is attributed to stabilization of the intermediate redox products [4a](+) and [4b](+) through interactions between the metal centers across a distance of ca. 12.5 angstrom. The mono-oxidized bimetallic complexes (4a](+) and [4b](+) exhibit spectroscopic properties consistent with a description of these species in terms of valence-localized (class II) mixed-valence compounds, including a unique low-energy electronic absorption band, attributed to an, IVCT-type transition that tails into the IR region. DFT calculations with model systems [4a-H](+) and [4b-H](+) featuring simplified ligand sets reproduce the observed spectroscopic data and localized electronic structures for the mixed-valence cations [4a](+) and [4b](+).

Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow

A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number (Re-U), axial flow Reynolds number (Re-W), cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers. (c) 2006 Elsevier Ltd. All rights reserved.

pH-mediated interactions between poly(acrylic acid) and methylcellulose in the formation of ultrathin multilayered hydrogels and spherical nanoparticles

Poly(acrylic acid) forms insoluble hydrogen-bonded interpolymer complexes with methylcellulose in aqueous solutions under acidic conditions. In this work the reaction heats and binding constants were determined for the complexation between poly(acrylic acid) and methylcellulose by isothermal titration calorimetry at different pH and findings are correlated with the aggregation processes occurring in this system. The principal contribution to the complexation heat results from primary polycomplex particle aggregation. Transmission electron microscopy of nanoparticles produced at pH 1.4 and 2.4 demonstrated that they are spherical and dense structures. The nanoparticles ranged from 80 to 200 nm, whereas particles formed at pH 3.2 were 20-30 nm and were stabilized against aggregation by a network of uncomplexed macromolecules. For the first time, multilayered materials were developed on the basis of hydrogen-bonded complexes of poly(acrylic acid) and methylcellulose using layer-by-layer deposition on a glass surface. The thickness of these films was a linear function of the number of deposition cycles. The materials were subsequently cross-linked by thermal treatment, resulting in ultrathin hydrogels which detached from the glass substrate upon swelling. The swelling capacity of ultrathin hydrogels differed from the swelling of the thicker films of a similar chemical composition.

Oriented vehicles travelling in spherical space

This paper tackles the path planning problem for oriented vehicles travelling in the non-Euclidean 3-Dimensional space; spherical space S3. For such problem, the orientation of the vehicle is naturally represented by orthonormal frame bundle; the rotation group SO(4). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to control systems defined on Lie groups. The oriented vehicles, in this case, are constrained to travel at constant speed in a forward direction and their angular velocities directly controlled. In this paper we identify controls that induce steady motions of these oriented vehicles and yield closed form parametric expressions for these motions. The paths these vehicles trace are defined explicitly in terms of the controls and therefore invariant with respect to the coordinate system used to describe the motion.

Unit-cell approximation for diblock−copolymer brushes grafted to spherical particles

This paper examines the equilibrium phase behavior of thin diblock-copolymer films tethered to a spherical core, using numerical self-consistent field theory (SCFT). The computational cost of the calculation is greatly reduced by implementing the unit-cell approximation (UCA) routinely used in the study of bulk systems. This provides a tremendous reduction in computational time, permitting us to map out the phase behavior more extensively and allowing us to consider far larger particles. The main consequence of the UCA is that it omits packing frustration, but evidently the effect is minor for large particles. On the other hand, when the particles are small, the UCA calculation can be readily followed up with the full SCFT, the comparison to which conveniently allows one to quantitatively assess the effect of packing frustration.

Calculating the tetrahedral bond angle using spherical polars and the dot product

A proof using the methane tetrahedroid bond angle can be obtained by using spherical polar coordinates to calculate the Cartesian coordinates of the hydrogen atoms, then using the dot product of vectors.

Computational modes and grid imprinting on five quasi-uniform spherical C-grids

Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations. We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid, despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity.