Harmonic functions of polynomial growth on certain complete manifolds

Given a complete manifold with a particular structure at infinity, we give the dimension of the space of harmonic functions with prescribed polynomial growth.     

On stability of rapid granular shear flows

We study stability properties of rapid granular flows that are described by the balance laws of mass, momentum and fluctuation energy with phenomenological relationships based upon dimensional arguments [12, 13]. Small disturbances propagating perpendicular to the shear plane are only studied. Calculations show that such flows are stable at small free path lengths of the granules but unstable if free path lengths are large. Received June 17, 1997     

External cavity quantum cascade laser for quartz tuning fork photoacoustic spectroscopy of broad absorption features

We demonstrate mid-infrared spectroscopy of large molecules with broad absorption features using a tunable external cavity quantum cascade laser. Absorption spectra for two different Freons are measured over the range 1130-1185 cm(-1) with 0.2 cm(-1) resolution via laser photoacoustic spectroscopy with quartz tuning forks as acoustic transducers. The measured spectra are in excellent agreement with published reference absorption spectra.     

On flows of granular materials

This article reviews the behavior of materials made up of a large assemblage of solid particles under rapid and quasi static deformations. The focus is on flows at relatively high concentrations and for conditions when the interstitial fluid plays an insignificant role. The momentum and energy exchange processes are then primarily governed by interparticle collisions and Coulomb-type frictional contact. We first discuss some physical behavior —dilatancy, internal friction, fluidization and particle segregation — that are typical to the understanding of granular flows. Bagnold's seminal Couette flow experiments and his simple stress analysis are then used to motivate the first constitutive theories that use a microstructural variable — the fluctuation energy or granular temperature — governing the subscale fluctuating motion. The kinetic theories formalize the derivation of the field equations of bulk mass, momentum and energy, and permit derivation of constitutive relations for stress, flux of fluctuation energy and its dissipation rate for simple particle assemblages and when frictional rubbing contact can be ignored. These statistical considerations also show that formulation of boundary conditions needs special attention. The frictional-collisional constitutive behavior in which both Coulomb-type rubbing contact and collisional encounters are significant are discussed. There is as yet no rigorous formulation. We finally present a phenomenological approach that describes rapid flows of granular materials under simultaneous transport of heat and close with a summary of stability analyses of the basic flow down an inclined plane.Dedicated to Professor Dr.-Ing. Franz Gustav Kollmann on the occasion of his sixtieth brithday     

Guest‐Induced Transformation of a Porphyrin‐Edged FeII4L6 Capsule into a CuIFeII2L4 Fullerene Receptor

The combination of a bent diamino(nickel(II) porphyrin) with 2‐formylpyridine and Fe^II yielded an Fe^II₄L₆ cage. Upon treatment with the fullerenes C₆₀ or C₇₀, this cage was found to transform into a new host–guest complex incorporating three Fe^II centers and four porphyrin ligands, in an arrangement that is hypothesized to maximize π interactions between the porphyrin units of the host and the fullerene guest bound within its central cavity. The new complex shows coordinative unsaturation at one of the Fe^II centers as the result of the incommensurate metal‐to‐ligand ratio, which enabled the preparation of a heterometallic cone‐shaped Cu^IFe^II₂L₄ adduct of C₆₀ or C₇₀.     

Carbon Dioxide Fixation and Sulfate Sequestration by a Supramolecular Trigonal Bipyramid

The subcomponent self‐assembly of a bent dialdehyde ligand and different cationic and anionic templates led to the formation of two new metallosupramolecular architectures: a Fe^II₄L₆ molecular rectangle was isolated following reaction of the ligand with iron(II) tetrafluoroborate, and a M₅L₆ trigonal bipyramidal structure was constructed from either zinc(II) tetrafluoroborate or cadmium(II) trifluoromethanesulfonate. The spatially constrained arrangement of the three equatorial metal ions in the M₅L₆ structures was found to induce small‐molecule transformations. Atmospheric carbon dioxide was fixed as carbonate and bound to the equatorial metal centers in both the Zn₅L₆ and Cd₅L₆ assemblies, and sulfur dioxide was hydrated and bound as the sulfite dianion in the Zn₅L₆ structure. Subsequent in situ oxidation of the sulfite dianion resulted in a sulfate dianion bound within the supramolecular pocket.     

Dividing a complex reaction involving a hypervalent iodine reagent into three limiting mechanisms by ab initio molecular dynamics

The electrophilic N‐trifluoromethylation of MeCN with a hypervalent iodine reagent to form a nitrilium ion, that is rapidly trapped by an azole nucleophile, is thought to occur via reductive elimination (RE). A recent study showed that, depending on the solvent representation, the S_N2 is favoured to a different extent over the RE. However, there is a discriminative solvent effect present, which calls for a statistical mechanics approach to fully account for the entropic contributions. In this study, we perform metadynamic simulations for two trifluoromethylation reactions (with N‐ and S‐nucleophiles), showing that the RE mechanism is always favoured in MeCN solution. These computations also indicate that a radical mechanism (single electron transfer) may play an important role. The computational protocol based on accelerated molecular dynamics for the exploration of the free energy surface is transferable and will be applied to similar reactions to investigate other electrophiles on the reagent. Based on the activation parameters determined, this approach also gives insight into the mechanistic details of the trifluoromethylation and shows that these commonly known mechanisms mark the limits within which the reaction proceeds. © 2015 Wiley Periodicals, Inc.