A flux-form version of the conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed sphere grid

A conservative semi-Lagrangian cell-integrated transport scheme (CSLAM) was recently introduced, which ensures global mass conservation and allows long timesteps, multi-tracer efficiency, and shape preservation through the use of reconstruction filtering. This method is fully two-dimensional so that it may be easily implemented on non-cartesian grids such as the cubed-sphere grid. We present a flux-form implementation, FF-CSLAM, which retains the advantages of CSLAM while also allowing the use of flux-limited monotonicity and positivity preservation and efficient tracer sub-cycling. The methods are equivalent in the absence of flux limiting or reconstruction filtering.FF-CSLAM was found to be third-order accurate when an appropriately smooth initial mass distribution and flow field (with at least a continuous second derivative) was used. This was true even when using highly deformational flows and when the distribution is advected over the singularities in the cubed sphere, the latter a consequence of the full two-dimensionality of the method. Flux-limited monotonicity preservation, which is only available in a flux-form method, was found to be both less diffusive and more efficient than the monotone reconstruction filtering available to CSLAM. Despite the additional overhead of computing fluxes compared to CSLAM’s cell integrations, the non-monotone FF-CSLAM was found to be at most only 40% slower than CSLAM for Courant numbers less than one, with greater overhead for successively larger Courant numbers.     

Investigation of the radical copolymerization and terpolymerization of maleic anhydride and norbornenes by an in situ 1H NMR analysis of kinetics and by the mercury method: Evidence for the lack of charge‐transfer‐complex propagation

The radical copolymerization of electron‐deficient maleic anhydride (MA) and electron‐rich norbornene (NB) derivatives with 2,2′‐azobis(isobutyronitrile) (AIBN) in dioxane‐d₈ has been monitored in situ by ¹H NMR spectroscopy with free induction decays recorded every 30 min at 60, 70, or 84 °C. The ratios of the monomer pairs were varied in some cases. The NB derivatives employed in this study included bicyclo[2.2.1]hept‐2‐ene (NB), t‐butyl 5‐norbornene‐2‐carboxylate, methyl 5‐norbornene‐2‐methyl‐2‐carboxylate, and ethyl tetracyclo[4.4.0.1^2,5.1^7,10]dodec‐3‐ene‐8‐carboxylate. Decomposition of AIBN, consumption of the monomers, feed ratios, endo/exo ratios, copolymer compositions, and copolymer yields were studied as a function of polymerization time. Furthermore, a homopolymerizable third monomer (t‐butyl methacrylate, methacrylic acid, t‐butyl acrylate, or acrylic acid) was added to the NB/MA 1/1 system, revealing that the methacrylic monomer polymerizes rapidly in the early stage and that the ratio of MA to NB in the terpolymer strongly deviates from 1/1. In contrast, however, the acrylic monomers are more uniformly incorporated into the polymer. Nevertheless, these studies indicate that MA and NB do not always behave as a pair in radical polymerization and disproves the commonly believed charge‐transfer mechanism. Electron‐deficient fumaronitrile was also included in the kinetics study. To further understand the copolymerization mechanism, MA and NB were competitively reacted with a cyclohexyl radical generated by the treatment of cyclohexylmercuric chloride with sodium borohydride (mercury method). A gas chromatographic analysis of the reaction mixtures has revealed that a cyclohexyl radical reacts with MA almost exclusively in competition and that the cyclohexyl adduct of MA essentially accounts for all the products in a mass balance experiment, eliminating a possibility of the formation of an adduct involving the MA–NB charge‐transfer complex. Thus, the participation of a charge‐transfer complex in the copolymerization of MA and NB cannot be important. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3521–3542, 2000     

Influence of the substituent on azobenzene side-chain polyester optical storage materials

A number of poly(1,3-propylenetetradecanedioates) or poly(1,3-propyleneadipates) with pendant p-substitued azobenzenes linked through a hexylene spacer in the 2-position are prepared. The substituents comprise: cyano, nitro, methoxy, hydrogen, methyl, n-butyl, phenyl, fluoro, trifluoromethyl, chloro, and bromo. ¹³C NMR spectroscopic and molecular mass investigations substantiate good film forming characteristics. The optical storage performance of thin polyester films are investigated through polarization holography. The resulting diffraction efficiency is mapped and discussed as a function of irradiation power and exposure time. Polytetradecanedioates with cyano-, nitro-, methyl-, fluoro-, or trifluoro-methyl-azobenzene reach more than 50% diffraction efficiency. Investigations of anisotropy induced at different temperatures reveal that the polyesters are only photosensitive in a narrow temperature range around T_g.     

Multivariate Dispersion Models

We introduce a class of multivariate dispersion models suitable as error distributions for generalized linear models with multivariate non-normal responses. The models preserve some of the main properties of the multivariate normal distribution, and include the elliptically contoured distributions and certain other known distributions as special cases. We give explicit methods for constructing multivariate proper dispersion models. This is exemplified by constructing multivariate gamma, Laplace, hyperbola, and von Mises distributions.     

Differential operators and the Frobenius pull back of the tangent bundle on G/P

In this paper we study the sheaf of differential operators on a flag manifold X in characteristic p>0. We generalize the non-vanishing theorem of Haastert on the associated filtration of . We make use of the lifting of X to characteristic zero and the complex geometry of X. Received: 27 March 1998     

Asymptotics of High Order Noise Corrections

We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.