Synthesis and applications of chiral bis-THF in asymmetric synthesis

The synthesis of enantiopure bis-THF is described, starting from d-mannitol. Bis-THF is used as chiral ligand for organolithium reagents in four different reactions. The enantioselectivity provided by this ligand is moderate, and the asymmetric induction is in line with the expected model.     

An easy and fast way to determine the enantiomeric purity of substituted cyclanones

The determination of the enantiomeric purity of 2 or 3-substituted cyclanones, particularly cyclohexanones, is conveniently achieved by derivatisation into cyclic aminals with commercially available (R, R)-1,2-diphenylethylenediamine. The derivatisation procedure is directly done into the NMR tube, instantaneously, and ¹³C NMR allows an accurate measure of the ee.     

Patterns in parabolic problems with nonlinear boundary conditions

We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of eigenvalues and eigenfunctions of the Laplace operator in such domains. This information is used to show that the asymptotic dynamics of the heat equation in this domain is equivalent to the asymptotic dynamics of a system of two ordinary differential equations diffusively (weakly) coupled. The main tools employed are the invariant manifold theory and a uniform trace theorem.     

Equilibrium statistics of a vortex filament with applications

The thermodynamic functions and scaling exponents (including the Kolmogorov and Flory exponents) of a vortex filament in thermal equilibrium are calculated, giving a quantitative content to earlier qualitative analyses. The numerical results uncover a percolation property of vortex filaments near the maximum entropy state. The implications of the results for the onset of turbulence, for the structure of its inertial range, and for superfluid vortices are discussed. In particular, it is shown that vortex stretching pushes a vortex system to a polymeric state and a Kolmogorov spectrum.This work was supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contract DE-AC03-76SF-00098, and in part by the National Science Foundation under grant number DMS89-19074     

Modélisation du champ des vitesses de l'urine dans un bolus urétéralModelling of urine flow in an ureteral bolus

Urine transport is made from the kidney to the bladder through the ureter by isolated pockets called bolus. To determine the urine flow in a bolus, we use an adherence condition on the interface urine/wall. It gives us an infinite linear system verified by a set of parameters. An iterative and convergent algorithm allows us to solve this system and to determine analytically the components of the velocity vector in the bolus. To cite this article: A. Vogel et al., C. R. Mecanique 332 (2004).     

Constrained random walks and vortex filaments in turbulence theory

We consider a simplified model of vorticity configurations in the inertial range of turbulent flow, in which vortex filaments are viewed as random walks in thermal equilibrium subjected to the constraints of helicity and energy conservation. The model is simple enough so that its properties can be investigated by a relatively straightforward Monte-Carlo method: a pivot algorithm with Metropolis weighting. Reasonable values are obtained for the intermittency dimensionD, a Kolmogorov-like exponent , and higher moments of the velocity derivatives. Qualitative conclusions are drawn regarding the origin of non-gaussian velocity statistics and regarding analogies with polymers and with systems near a critical point.This work was supported in part by the Applied Mathematical Sciences Subprogram of the Office of Energy Research, US Department of Energy, under Contract Number DE-AC03-76SF000098     

Structure of 2-Amino-4-phenyl-9H-pyrimido[4,5-b]indole and Its Nitrate in Crystal and Solution

The crystal structures of 2-amino-4-phenyl-9H-pyrimido[4,5-b]indole and its nitrate were determined by XRD analysis. ¹³C NMR, XRD, and quantum-chemical data indicate that the acid proton is predominantly localized at the N(3) atom of the pyrimidine ring in both isolated nitrate molecules and in molecules in crystal and solution.     

Carbopalladation of nitriles: synthesis of 2,3-diarylindenones and polycyclic aromatic ketones by the Pd-catalyzed annulation of alkynes and bicyclic alkenes by 2-iodoarenenitriles

2-iodobenzonitrile, its derivatives, and various heterocyclic analogues undergo palladium(0)-catalyzed annulation onto diarylacetylenes or bicyclic alkenes to afford 2,3-diarylindenones and polycyclic aromatic ketones in very good to excellent yields. This reaction represents one of the first examples of the addition of an organopalladium moiety to the carbon-nitrogen triple bond of a nitrile. The reaction is compatible with a number of functional groups. A reaction mechanism, as well as a model accounting for the electronic effects of substituents on the aromatic ring of the nitrile, is proposed.