Riemann extensions and affine differential geometry

In order to define an affine immersion of manifolds in affine differential geometry, it is necessary to choose a set of normal planes to the immersed manifold. The theory is then developed after this choice has been made. However, it was shown by A.G.Walker [WA1] that a torsion-free affine connexion on a manifold determines canonically a pseudo-Riemannian metric on the cotangent bundle, called the Riemann-extension of the affine connexion. By making use of this pseudo-Riemannian metric it is possible to define an affine immersion without making a suitable choice of normal planes.     

Gas diffusion in glasses via a probabilistic molecular dynamics

A probabilistic protocol which makes possible the calculation of the diffusivity of light gases in amorphous materials from limited Monte Carlo and molecular dynamics data is presented. Diffusion coefficients are calculated for helium and methane in polystyrene, and for helium, neon, and methane in three pairs of polysulfone isomers. Results include diffusion coefficients as small as 10(-9) cm2/s and are in good agreement with results obtained from traditional molecular dynamics and with available experimental data.     

Molecular simulations of physical aging in polymer membrane materials

Poly(1-trimethylsilyl-1-propyne) (PTMSP), the most permeable polymer known, undergoes rapid physical aging. The permeability of PTMSP to gases and vapors decreases dramatically with physical aging. Cavity size (free volume) distributions were calculated in as-cast and aged PTMSP, using an energetic based cavity-sizing algorithm. The large cavities found in as-cast PTMSP disappear in aged PTMSP, which is consistent with the positron annihilation lifetime spectroscopy (PALS) measurements. We also characterized the connectivity of cavities in both as-cast and aged PTMSP membranes. Cavities are more connected in as-cast PTMSP than in aged PTMSP. The average cavity sizes calculated from computer simulation are in good agreement with PALS measurements. The transport and sorption properties of gases in as-cast and aged PTMSP are also measured by molecular simulation. Computer simulations showed the decrease of permeability and the increase of permeability selectivity in PTMSP membranes with physical aging, which agrees with experimental observations. The reduction in gas permeability with physical aging results mainly from the decrease of diffusion coefficients. Solubility coefficients show no significant changes with physical aging.