Polynomial identities,indices, and duality for theN=1 superconformal modelSM(2, 4v)

We prove polynomial identities for theN=1 superconformal modelSM(2, 4v) which generalize and extend the known Fermi/Bose character identities. Our proof uses theq-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations forq-series on the fermionic side. We use these polynomials to demonstrate a dual relation underqq ^–1 betweenSM(2, 4v) andM(2v–1, 4v). We also introduce a genralization of the Witten index which is expressible in terms of the Rogers false theta functions.Dedicated to the memory of Claude Itzykson.     

Kinetics of nonisothermal polymer crystallization

We adopt a cluster size distribution model to investigate the kinetics of nonisothermal polymer crystallization. The time dependencies of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots) are presented for different cooling rates. The incubation period is also investigated at different cooling rates and initial temperatures. The relationship between cooling rates and incubation time is presented graphically and compared with experimental measurements. The initial temperature (relative to melting point) has a significant effect on nonisothermal crystallization. A comparison of moment and numerical solutions of the population balance equations shows the influence of Ostwald ripening. Agreement between modeling results and experimental measurements at different cooling rates supports the application of the distribution kinetics model for nonisothermal crystallization.     

Spatial localization of ligand binding sites from electron current density surfaces calculated from NMR chemical shift perturbations

Rapid, accurate structure determination of protein-ligand complexes is an essential component in structure-based drug design. We have developed a method that uses NMR protein chemical shift perturbations to spatially localize a ligand when it is complexed with a protein. Chemical shift perturbations on the protein arise primarily from the close proximity of electron current density from the ligand. In our approach the location of the center of the electron current density for a ligand aromatic ring was approximated by a point-dipole, and dot densities were used to represent ligand positions that are allowed by the experimental data. The dot density is increased in the region of space that is consistent for the most data. A surface can be formed in regions of the highest dot density that correlates to the center of the ligand aromatic ring. These surfaces allow for the rapid evaluation of ligand binding, which is demonstrated on a model system and on real data from HCV NS3 protease and HCV NS3 helicase, where the location of ligand binding can be compared to that obtained from difference electron density from X-ray crystallography.     

Distribution kinetics of polymer crystallization and the Avrami equation

Cluster distribution kinetics is adopted to explore the kinetics of polymer crystallization. Population balance equations based on crystal size distribution and concentration of amorphous polymer segments are solved numerically and the related dynamic moment equations are also solved. The model accounts for heterogeneous or homogeneous nucleation and crystal growth. Homogeneous nucleation rates follow the classical surface-energy nucleation theory. Different mass dependences of growth and dissociation rate coefficients are proposed to investigate the fundamental features of nucleation and crystal growth. A comparison of moment solutions with numerical solutions examines the validity of the model. The proposed distribution kinetics model provides a different interpretation of the familiar Avrami equation.     

The vibrational predissociation spectra of the H5O2 +RGn(RG = Ar,Ne) clusters: correlation of the solvent perturbations in the free OH and shared proton transitions of the Zundel ion

Predissociation spectra of the H(5)O(2) (+)RG(n)(RG = Ar,Ne) cluster ions are reported in energy regions corresponding to both the OH stretching (3350-3850 cm(-1)) and shared proton (850-1950 cm(-1)) vibrations. The two free OH stretching bands displayed by the Ne complex are quite close to the band origins identified earlier in bare H(5)O(2) (+) [L. I. Yeh, M. Okumura, J. D. Myers, J. M. Price, and Y. T. Lee, J. Chem. Phys. 91, 7319 (1989)], indicating that the symmetrical H(5)O(2) (+) "Zundel" ion remains largely intact in H(5)O(2) (+)Ne. The low-energy spectrum of the Ne complex is simpler than that observed previously for H(5)O(2) (+)Ar, and is dominated by two sharp transitions at 928 and 1047 cm(-1), with a weaker feature at 1763 cm(-1). The H(5)O(2) (+)Ar(n),n = 1-5 spectra generally exhibit complex band structures reflecting solvent-induced symmetry breaking of the Zundel core ion. The extent of solvent perturbation is evaluated with electronic structure calculations, which predict that the rare gas atoms should attach to the spectator OH groups of H(5)O(2) (+) rather than to the shared proton. In the asymmetric complexes, the shared proton resides closer to the more heavily solvated water molecule, leading to redshifts in the rare gas atom-solvated OH stretches and to blueshifts in the shared proton vibrations. The experimental spectra are compared with recent full-dimensional vibrational calculations (diffusion Monte Carlo and multimode/vibrational configuration interaction) on H(5)O(2) (+). These results are consistent with assignment of the strong low-energy bands in the H(5)O(2) (+)Ne spectrum to the vibration of the shared proton mostly along the O-O axis, with the 1763 cm(-1) band traced primarily to the out-of-phase, intramolecular bending vibrations of the two water molecules.     

Lattice-Boltzmann simulation of coalescence-driven island coarsening

A two-dimensional lattice-Boltzmann model (LBM) with fluid-fluid interactions was used to simulate first-order phase separation in a thin fluid film. The intermediate asymptotic time dependence of the mean island size, island number concentration, and polydispersity were determined and compared with the predictions of the distribution-kinetics model. The comparison revealed that the combined effects of growth, coalescence, and Ostwald ripening control the phase transition process in the LBM simulations. However, the overall process is dominated by coalescence, which is independent of island mass. As the phase transition advances, the mean island size increases, the number of islands decrease, and the polydispersity approaches unity, which conforms to the predictions of the distribution-kinetics model. The effects of the domain size on the intermediate asymptotic island size distribution, scaling form of the island size distribution, and the crossover to the long-term asymptotic behavior were elucidated.     

Stabilization and rovibronic spectra of the T-shaped and linear ground-state conformers of a weakly bound rare-gas-homonuclear dihalogen complex: He...Br2

Laser-induced fluorescence spectra of Br(2) entrained in a He supersonic expansion have been recorded in the Br(2) B-X, 8-0, 12-0, and 21-0 spectral regions at varying downstream distances, and thus different temperature regimes. Features associated with transitions of the T-shaped and linear He...Br(2)(X,nu(") = 0) complexes are identified. The changes in the relative intensities of the T-shaped and linear features with cooling in the expansion indicate that the linear conformer is energetically more stable than the T-shaped conformer. A He + Br(2)(X,nu(") = 0) ab initio potential-energy surface, computed at the coupled cluster level of theory with a large, flexible basis set, is used to calculate the binding energies of the two conformers, 15.8 and 16.5 cm(-1) for the T-shaped and linear complexes, respectively. This potential and an excited-state potential [M. P. de Lara-Castells, A. A. Buchachenko, G. Delgado-Barrio, and P. Villareal, J. Chem. Phys. 120, 2182 (2004)] are used to calculate the excitation spectra of He...(79)Br(2)(X,nu(") = 0) in the Br(2) B-X, 12-0 region. The calculated spectra are used to make spectral assignments and to determine the energies of the excited-state intermolecular vibrational levels accessed in the observed transitions. Temperature-dependent laser-induced fluorescence spectra and a simple thermodynamic model [D. S. Boucher, J. P. Darr, M. D. Bradke, R. A. Loomis, and A. B. McCoy, Phys. Chem. Chem. Phys. 6, 5275 (2004)] are used to estimate that the linear conformer is 0.4(2) cm(-1) more strongly bound than the T-shaped conformer. Two-laser action spectroscopy experiments reveal that the binding energy of the linear He...(79)Br(2)(X,nu(") = 0) conformer is 17.0(8) cm(-1), and that of the T-shaped He...(79)Br(2)(X,nu(") = 0) conformer is then 16.6(8) cm(-1), in good agreement with the calculated values.     

Partitioning and adsorption in gas-liquid-solid chromatography: Models of temporal moments for retention and variance

Summary The resolution of gaseous chemical species in gasliquid-solid chromatography is influenced by absorption (partitioning) in the liquid and adsorption at the liquid-solid interface. We consider fundamental mass transfer models with adsorption and partitioning effects for solid chromatographic supports covered with thin films of stationary liquid. The dynamic models, based on mass-balance partial-differential equations, include the significant phenomena: convection, axial dispersion, gas-liquid mass transfer, intraparticle diffusion, and liquid-solid adsorption. Expressions for retention time and band variance (first and second temporal moments) are presented and evaluated for four distinct models: (1) capillary tube with inner surface covered with a uniform-thickness liquid film, (2) column of nonporous spheres covered with a uniform-thickness liquid film, (3) porous spherical particles with intraparticle pores covered with a uniform-thickness liquid film, (4) porous spherical particles with intraparticle pores completely filled with liquid.     

Probing the dependence of long-range, four-atom interactions on intermolecular orientation: 2. Molecular deuterium and iodine monochloride

Laser-induced fluorescence and action spectroscopy experiments have identified multiple conformers of the D2...ICl van der Waals complex for both ortho-D2 (o-D2) and para-D2 (p-D2). As with the analogous H2...ICl van der Waals complexes [Darr, J. P.; Crowther, A. C.; Loomis, R. A.; Ray, S. E.; McCoy, A. B. J. Phys. Chem. A 2007, 111, 13387], the C2v conformer with the deuterium molecule localized at the iodine atom end of the dihalogen is significantly more stable than the asymmetric conformer that has the deuterium positioned orthogonally to the ICl bond axis, D0' = 223.9(2.4) versus 97.3(8)-103.9(3) cm(-1) for p-D2...I(35)Cl(X, v'=0). For both conformers, complexes containing p-D2 are found to be more strongly bound than those with o-D2. The electronically excited D2...ICl(A, v') and D2...ICl(B, v') complexes are found to have equilibrium geometries that are nearly the same as those of the ground-state asymmetric structures. Calculated D2...ICl(B, v'=3) energies and probability amplitudes obtained using a simple scaled He + ICl(B, v'=3) potential provide clues to the nature of the different excited-state levels accessed.