Preface

Journal of Statistical Physics -     

A co‐ordinate system independent streamwise upwind method for fluid flow computation

A new co‐ordinate invariant streamwise upwind formulation for convection dominated flows is developed. The eddy diffusivity/viscosity is added directly to the equations in order to remove the oscillations in the solution. The equations then can be solved by any high‐order scheme and the solution retains the accuracy of the high‐order scheme. The accuracy and reduced lateral thickness growth rate are demonstrated with several numerical examples, including pure convective flows and lid‐driven cavity flow. The lateral spreading due to the numerical diffusion is controlled by the anisotropic tensor. Copyright © 2004 John Wiley & Sons, Ltd.     

Every group has a terminating transfinite automorphism tower

Iteratively taking the automorphism group of any group leads, transfinitely, to a fixed point.

     

Direct measurement of the radiative lifetime of the A2Σ+(υ′ = 0, K′ = 1, J′ = 32) state of OH and OD

The radiative lifetime of the A²Σ⁺(υ′ = 0, K′ = 1, J′ = 3/2) state of OH and OD has been directly measured by following the decay of fluorescence excited by light from a frequency doubled dye laser. Stern-Volmer extrapolation of the results to zero pressure gave τ(OH) = 788 ± 13 ns and τ(OD) = 754 ± 12 ns.     

A simple sum rule for total radiative decay rates in diatomics

The quantity (ν³μ_e²), which occurs in expressions for the total radiative decay rate for an excited vibronic state of a diatomic, is evaluated as a simple expectation value for the initial state. In test calculations this expectation value agrees with the exact sum over states within ≈0.2%.     

An alternative multipolar expansion for intermolecular potential functions

We have derived a new multipolar expansion for intermolecular potential-energy functions with applications in molecular physics, theoretical chemistry, and mathematical physics. The new formulation employs a separation of radial and angular terms with a simple index structure that leads to computational efficiency and ease of physical interpretation. For the case of the Coulomb interaction, we compare the present formulation with two conventional multipole expansions: the Cartesian tensor and the irreducible spherical tensor expansions. The new formalism leads to efficient numerical algorithms that are useful for general applications beyond intermolecular potentials. In addition to the electrostatic Coulomb interaction, we illustrate the formalism with applications to special function theory and a bipolar expansion involved in potential theory.     

Electrophilic lactonization as a tool in acyclic stereocontrol. Synthesis of serricornin

Several electrophilic lactonization procedures have been explored as a means of functionalizing olefinic carboxylic acids with relative asymmetric induction, Iodolactonization of δ,? -unsaturated acids under conditions of thermodynamic control exhibits good 1,2- and 1,3-, but not 1,4-induction in the formation of δ-lactones. Mercurilactonization proceeds with good stereocontrol in the formation of both γ- and δ-lactones (1,2-induction), but suffers from the difficulty of elimination during reductive demercuration; phenylselenolactonization with N-(phenylseleno)phthalimide is apparently kinetically controlled, affording high induction with 10, a strongly sterically biased substrate leading to a δ-lactone, but not with 16, which leads to a γ-lactone. In contrast, hydroxymethyllactonization proceeds with good stereocontrol in the case of 26, the ester of 10, but not with the analogous ester of 16. The lactones resulting from cyclization of 10 and 13 were converted in stereospecific fashion into each of the stereoisomers of(±)-serricornin.     

Syntheses of reactive fluorescent stains derived from 5(2)-aryl-2(5)-(4-pyridyl)oxazoles and bifunctionally reactive linkers

Several bifunctionally reactive linkers containing halide or sulfonate ester groups were prepared. The linkers were used to quaternize 5-(4-methoxyphenyl)-2-(4-pyridyl)oxazole and 2-(6-chromanyl)-5-(4-pyridyl)oxazole to produce fluorescent stains that contained a reactive group such as an isothiocyanate, an N-hydroxysuccinimidyl ester, a maleimide, or an oxirane. The stains were derivatized with either 1-propylamine, 1-propanethiol, or piperidine, as appropriate, to help in characterization. The stains may serve as more photostable alternatives to fluoresceins or coumarins.