A finite element-spherical harmonics model for radiative transfer in inhomogeneous clouds. Part II. some applications

EVENT has been used to examine the effects of 3D cloud structure, distribution, and inhomogeneity on the scattering of visible solar radiation and the resulting 3D radiation field. Large eddy simulation and aircraft measurements are used to create realistic cloud fields which are continuous or broken with smooth or uneven tops. The values, patterns and variance in the resulting downwelling and upwelling radiation from incident visible solar radiation at different angles are then examined and compared to measurements. The results from EVENT confirm that 3D cloud structure is important in determining the visible radiation field, and that these results are strongly influenced by the solar zenith angle. The results match those from other models using visible solar radiation, and are supported by aircraft measurements of visible radiation, providing confidence in the new model.

Wave functions for the methane molecule

If the potential field due to the nuclei in the methane molecule is expanded in terms of a set of spherical harmonics about the carbon nucleus, only the terms involving s, f, and higher harmonic functions differ from zero in the equilibrium configuration. Wave functions have been calculated for the equilibrium configuration, first including only the spherically symmetric s term in the potential, and secondly including both the s and the f terms. In the first calculation the complete Hartree-Fock S.C.F. wave functions were determined; in the second calculation a variation method was used to determine the best form of the wave function involving f harmonics. The resulting wave functions and electron density functions are presented and discussed

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.

The determination of molecular orientation in uniaxially compressed PMMA by X-ray scattering

A procedure is presented for obtaining full molecular orientation information from wide angle X-ray scattering patterns of deformed non-crystalline polymers. The method is based on the analysis of experimental and calculated scattering patterns into their spherical harmonics. The results obtained for PMMA are compared with values predicted by the pseudo affine and affine deformation schemes.

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.

Vibrational intensities in methane

The absorption intensities of the two infra-red active vibrations in methane have been obtained from a perturbation calculation on the equilibrium wave functions derived in the preceding paper. The perturbation field is the change in the potential field due to the nuclei which results from moving the nuclei in the vibrational coordinate concerned, and a simplified form of second order perturbation theory, developed by Pople and Schofield, is used for the calculation. The main approximation involved is the neglect of f and higher harmonics in the spherical harmonic expansion of the nuclear field. The resulting dipole moment derivatives are approximately three times larger than the experimental values, but they show qualitative features and sign relationships which are significant.

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](+).