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.     

The existence of non-topological solitons in the self-dual Chern-Simons theory

In the recently discovered (2+1)-dimensional relativistic Chern-Simons model, self-duality can be achieved when the Higgs potential density assumes a special form for which both the asymmetric and symmetric vacua are ground state solutions. This important feature may imply the coexistence of static topological and non-topological vortex-like solutions inR ² but the latter have been rather elusive to a rigorous construction. Our main purpose in this paper is to prove the existence of non-topological radially symmetricN-vortex solutions in the self-dual Chern-Simons model. By a shooting method, we obtain a continuous family of gauge-distinctN-vortex solutions. Moreover, we are also able to classify all possible bare (or 0-vortex) solutions.     

The role of angular momentum in collision-induced vibration-rotation relaxation in polyatomics

Vibrational relaxation of the 6(1) level of S(1)((1)B(2u)) benzene is analyzed using the angular momentum model of inelastic processes. Momentum-(rotational) angular momentum diagrams illustrate energetic and angular momentum constraints on the disposal of released energy and the effect of collision partner on resultant benzene rotational excitation. A kinematic "equivalent rotor" model is introduced that allows quantitative prediction of rotational distributions from inelastic collisions in polyatomic molecules. The method was tested by predicting K-state distributions in glyoxal-Ne as well as J-state distributions in rotationally inelastic acetylene-He collisions before being used to predict J and K distributions from vibrational relaxation of 6(1) benzene by H(2), D(2), and CH(4). Diagrammatic methods and calculations illustrate changes resulting from simultaneous collision partner excitation, a particularly effective mechanism in p-H(2) where some 70% of the available 6(1)-->0(0) energy may be disposed into 0-->2 rotation. These results support the explanation for branching ratios in 6(1)-->0(0) relaxation given by Waclawik and Lawrance and the absence of this pathway for monatomic partners. Collision-induced vibrational relaxation in molecules represents competition between the magnitude of the energy gap of a potential transition and the ability of the colliding species to generate the angular momentum (rotational and orbital) needed for the transition to proceed. Transition probability falls rapidly as DeltaJ increases and for a given molecule-collision partner pair will provide a limit to the gap that may be bridged. Energy constraints increase as collision partner mass increases, an effect that is amplified when J(i)>0. Large energy gaps are most effectively bridged using light collision partners. For efficient vibrational relaxation in polyatomics an additional requirement is that the molecular motion of the mode must be capable of generating molecular rotation on contact with the collision partner in order to meet the angular momentum requirements. We postulate that this may account for some of the striking propensities that characterize polyatomic energy transfer.