Low-volume-fraction limit for polymer fluids

We study a stationary, purely viscous polymer flow through a porous medium modelled as a periodic array of cells consisted of a fluid part and a solid one. Solid parts of the domain present impermeable obstacles, whose impact on fluid flow may be seen as a slowing factor through averaged quantities such as the permeability function, obtained by the homogenization process. In that way, the influence of the microstructure is implemented in the homogenized equations through a kind of nonlinear Darcy's law. Our goal is to find more explicitly the dependence of the permeability function on the size η of the obstacle in the unit cell and the so-called low-volume-fraction limit. Main difficulties arise from the nonlinear character of the power-law viscosity and the apparent weak convergence of the solutions involved.     

Computing the bipartite edge frustration of fullerene graphs

Bipartite edge frustration of a graph is defined as the smallest number of edges that have to be deleted from the graph to obtain a bipartite spanning subgraph. We show that for fullerene graphs this quantity can be computed in polynomial time and obtain explicit formulas for the icosahedral fullerenes. We also report some computational results and discuss a potential application of this invariant in the context of fullerene stability.     

Transport equations for chiral fermions to order ? and electroweak baryogenesis: Part II

This is the second in a series of two papers. While in Paper I [Ann. Phys. 314 (2004) 208] we derive semiclassical Boltzmann transport equations and study their flow terms, here we make use of the results from that paper and address the collision terms. We use a model Lagrangean, in which fermions couple to scalars through Yukawa interactions and approximate the self-energies by the one-loop expressions. This approximation already contains important aspects of thermalization and scatterings required for quantitative studies of transport in plasmas. We compute the CP-violating contributions to both the scalar and the fermionic collision term. CP-violating sources appear at order ? in gradient and in a weak coupling expansion, as a consequence of a CP-violating split in the fermionic dispersion relation. This represents the first controlled calculation of CP-violating collisional sources, thus establishing the existence of `spontaneous' baryogenesis sources in the collision term. The calculation is performed by the use of the spin quasiparticle states established in Paper I. Next, we present the relevant leading order calculation of the relaxation rates for the spin states and relate them to the more standard relaxation rates for the helicity states. We also analyze the associated fluid equations, make a comparison between the source arising from the semiclassical force in the flow term and the collisional source, and observe that the semiclassical source tends to be more important in the limit of inefficient diffusion/transport.     

Ligand differentiated complementary Rh-catalyst systems for the enantioselective desymmetrization of meso-cyclic anhydrides

Two distinct systems for the rhodium-catalyzed enantioselective desymmetrization of meso-cyclic anhydrides have been developed. Each system has been optimized and are compatible with the use of in situ prepared organozinc reagents. Rhodium/PHOX species efficiently catalyze the addition of alkyl nucleophiles to glutaric anhydrides, while a rhodium/phosphoramidite system is effective in the enantioselective arylation of succinic and glutaric anhydrides.     

Conversion of alpha-haloaldehydes into acylating agents by an internal redox reaction catalyzed by nucleophilic carbenes

Reactivity umpolung allows us to consider nontraditional bond disconnections. We report herein that treatment of an alpha-haloaldehyde with a nucleophile in the presence of catalytic amounts of nucleophilic carbenes results in an internal redox reaction giving rise to a dehalogenated acylating agent as an intermediate by a new reaction manifold. A brief illustration of the scope of this reaction is presented along with evidence supporting the direct intervention of the carbene in the acylation step.     

A highly enantioselective catalytic intramolecular Stetter reaction

A family of chiral triazolium salts has been developed for inducing the asymmetric intramolecular Stetter reaction. The use of an aminoindanol-derived catalyst affords optimal results, with the product keto esters formed in 82-97% ee and very good chemical yield. Aromatic and aliphatic aldehydes are equally competent substrates for this reaction. The reaction conditions are reasonably mild and allow the isolation of the newly formed stereocenter without epimerization, although the presumed carbenic intermediates are strong bases.