Anomalous kinetics in diffusion limited reactions linked to non-Gaussian concentration probability distribution function

We investigate anomalous reaction kinetics related to segregation in the one-dimensional reaction-diffusion system A + B → C. It is well known that spatial fluctuations in the species concentrations cause a breakdown of the mean-field behavior at low concentration values. The scaling of the average concentration with time changes from the mean-field t(-1) to the anomalous t(-1/4) behavior. Using a stochastic modeling approach, the reaction-diffusion system can be fully characterized by the multi-point probability distribution function (PDF) of the species concentrations. Its evolution is governed by a Fokker-Planck equation with moving boundaries, which are determined by the positivity of the species concentrations. The concentration PDF is in general non-Gaussian. As long as the concentration fluctuations are small compared to the mean, the PDF can be approximated by a Gaussian distribution. This behavior breaks down in the fluctuation dominated regime, for which anomalous reaction kinetics are observed. We show that the transition from mean field to anomalous reaction kinetics is intimately linked to the evolution of the concentration PDF from a Gaussian to non-Gaussian shape. This establishes a direct relationship between anomalous reaction kinetics, incomplete mixing and the non-Gaussian nature of the concentration PDF.     

Formal homo-Nazarov and other cyclization reactions of activated cyclopropanes

The Nazarov cyclization of divinyl ketones gives access to cyclopentenones. Replacing one of the vinyl groups by a cyclopropane leads to a formal homo‐Nazarov process for the synthesis of cyclohexenones. In contrast to the Nazarov reaction, the cyclization of vinyl‐cyclopropyl ketones is a stepwise process, often requiring harsh conditions. Herein, we describe two different approaches for further polarization of the three‐membered ring of vinyl‐cyclopropyl ketones to allow the formal homo‐Nazarov reaction under mild catalytic conditions. In the first approach, the introduction of an ester group α to the carbonyl on the cyclopropane gave a more than tenfold increase in reaction rate, allowing us to extend the scope of the reaction to non‐electron‐rich aryl donor substituents in the β position to the carbonyl on the cyclopropane. In this case, a proof of principle for asymmetric induction could be achieved using chiral Lewis acid catalysts. In the second approach, heteroatoms, especially nitrogen, were introduced β to the carbonyl on the cyclopropane. In this case, the reaction was especially successful when the vinyl group was replaced by an indole heterocycle. With a free indole, the formal homo‐Nazarov cyclization on the C3 position of indole was observed using a copper catalyst. In contrast, a new cyclization reaction on the N1 position was observed with Brønsted acid catalysts. Both reactions were applied to the synthesis of natural alkaloids. Preliminary investigations on the rationalization of the observed regioselectivity are also reported.     

Photocatalytic Synthesis of Polycyclic Indolones

In this work, a photocatalytic strategy for a rapid and modular access to polycyclic indolones starting from readily available indoles is reported. This strategy relies on the use of redox-active esters in combination with an iridium-based photocatalyst under visible-light irradiation. The generation of alkyl radicals through decarboxylative single electron reductions enables intramolecular homolytic aromatic substitutions with a pending indole moiety to afford pyrrolo- and pyridoindolone derivatives under mild conditions. Furthermore, it was demonstrated that these radicals could also be engaged into cascades consisting of an intermolecular Giese-type addition followed by an intramolecular homolytic aromatic substitution to rapidly assemble valuable azepinoindolones.     

GaInAs/AlInAs superlattice oscillators for optical to mm-wave conversion

A simple optical to mm-wave conversion device is reported. It is based upon a GaInAs/AlInAs superlattice designed to produce mm-wave generation through the miniband negative conductance. It is driven by a light signal modulated near the oscillator fundamental frequency in order to obtain optical injection locking. The present paper stresses different material and non-linear transport properties necessary to optimise such devices at optical communications wavelengths.     

Remainder Pade Approximants for the Exponential Function

Following our earlier research, we propose a new method for obtaining the complete Pade table of the exponential function. It is based on an explicit construction of certain Pade approximants, not for the usual power series for exp at 0 but for a formal power series related in a simple way to the remainder term of the power series for exp. This surprising and nontrivial coincidence is proved more generally for type II simultaneous Pade approximants for a family with distinct complex a's and we recover Hermite's classical formulas. The proof uses certain discrete multiple orthogonal polynomials recently introduced by Arvesu, Coussement, and van Assche, which generalize the classical Charlier orthogonal polynomials.     

Access to β‐Lactams by Enantioselective Palladium(0)‐Catalyzed C(sp3)?H Alkylation

β‐Lactams are very important structural motifs because of their broad biological activities as well as their propensity to engage in ring‐opening reactions. Transition‐metal‐catalyzed C H functionalizations have emerged as strategy enabling yet uncommon highly efficient disconnections. In contrast to the significant progress of Pd⁰‐catalyzed C H functionalization for aryl–aryl couplings, related reactions involving the formation of saturated C(sp³) C(sp³) bonds are elusive. Reported here is an asymmetric C H functionalization approach to β‐lactams using readily accessible chloroacetamide substrates. Important aspects of this transformation are challenging C(sp³) C(sp³) and strain‐building reductive eliminations to for the four‐membered ring. In general, the β‐lactams are formed in excellent yields and enantioselectivities using a bulky taddol phosphoramidite ligand in combination with adamantyl carboxylic acid as cocatalyst.     

Nombres D’Euler, approximants de Padé et constante de Catalan

Résumé Au moyen d’une méthode d’approximation de Padé introduite par Prévost dans [13], nous construisons des familles d’approximations rationnelles rapidement convergentes vers la constante de Catalan G. Bien que cela ne suffise pas à prouver l’irrationalité de G, nous montrons le lien inattendu avec la méthode hypergéométrique récemment mise en avant dans l’étude diophantienne des fonction ζ de Riemann et β de Dirichlet, ce qui nous permet de prouver la ≪ conjecture des dénominateurs ≫ de [17].

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Mathematics Subject Classification Primary—11J99, 41A21, 05A40     

A fast and robust fictitious domain method for modelling viscous flows in complex mixers: The example of propellant make‐down

This work deals with the development of a fast three‐dimensional numerical strategy for the simulation of viscous fluid flow in complex mixing systems. The proposed method is based on a distributed Lagrange multiplier fictitious domain method and the use of the low‐cost MINI finite element. Contrary to the previous fictitious domain method developed by our group a few years ago, the underlying partial differential equations are solved here in a coupled manner using a consistent penalty technique. The method is discussed in detail and its precision is assessed by means of experimental data in the case of an agitated vessel. A comparison made with our existing fictitious domain method and its decoupled Uzawa‐based solver clearly shows the advantages of resorting to the MINI finite element and fully coupled solution strategy. The new technique is then applied to the simulation of the flow of a Newtonian viscous fluid in a three‐blade planetary mixer in the context of the production of solid propellants. Copyright © 2008 John Wiley & Sons, Ltd.     

Operando discrimination of fast and slow active grains within a cycling electrode for lithium battery

The impact of the formation of an electrolyte based decomposition layer on the distribution of the active grain kinetics has been investigated operando within a cycling electrode for lithium battery. It is demonstrated, from fitting procedure of the electrochemical responses and from operando XRD experiments, that as the passive film forms, slow reacting grains appear within the working electrode and operate simultaneously with faster grains. Slow grains are macroscopically distributed, presumably at the electrolyte side of the electrode. Discrimination of the electrochemical response pertaining to each type of grains allows rationalizing their contribution to the capacity fading dynamics.     

Three-dimensional adaptive finite element computations and applications to non-Newtonian fluids

An adaptive strategy for the finite element solution of three-dimensional viscous flow problems is defined and implemented. The solution strategy is based on an advancing front mesh generator making use of binary data structures for fast geometrical data handling. The error is estimated a posteriori with a residual-type bound. The error estimate is shown to exhibit proper convergence for tetrahedral elements. Its combination with the mesh generator and an interpolation scheme for unstructured meshes is shown to generate adaptive meshes and to reduce the solution cost for a given error level, as illustrated by the isothermal flow of a shear-thinning fluid.