Uncertainty quantification in a chemical system using error estimate-based mesh adaption

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.     

Alkoxyallene‐ynes: Selective Preparation of Bicyclo[5.3.0] Ring Systems Including a δ‐Alkoxy Cyclopentadienone

The development of an intramolecular rhodium(I)‐catalyzed Pauson–Khand reaction of alkoxyallene‐ynes with a proximal alkoxy group is reported. This reaction, in the presence of a [Rh(cycloocta‐1,5‐diene)Cl]₂/propane‐1,3‐diylbis(diphenylphosphane) system under a CO atmosphere, constitutes a powerful tool for selectively accessing carbo‐ and heterobicyclo[5.3.0] frameworks featuring an enol ether moiety. Through this procedure, a straightforward access to guaiane skeletons with a tertiary hydroxy group at the C10 position was achieved.     

Application of Tsunoda reagent to the convenient synthesis of drug-like pyrazoles

The versatility of the under-utilised (cyanomethylene)tributylphosphorane (CMBP, Tsunoda reagent) was demonstrated on two occasions in a drug discovery context. Firstly, the high reactivity of the phosphorane allowed the alkylation of a weakly acidic pyrazole when standard Mitsunobu conditions were unsuccessful. Secondly, the clean reaction profile generally obtained using CMBP allowed the direct use of the crude mixture in a subsequent Suzuki cross coupling. This reagent has utility when isolation of the Mitsunobu reaction product (e.g. containing a boronate) is not desirable.     

Excited Brownian motions as limits of excited random walks

We obtain the convergence in law of a sequence of excited (also called cookies) random walks toward an excited Brownian motion. This last process is a continuous semi-martingale whose drift is a function, say ??, of its local time. It was introduced by Norris, Rogers and Williams as a simplified version of Brownian polymers, and then recently further studied by the authors. To get our results we need to renormalize together the sequence of cookies, the time and the space in a convenient way. The proof follows a general approach already taken by Tóth and his coauthors in multiple occasions, which goes through Ray-Knight type results. Namely we first prove, when ?? is bounded and Lipschitz, that the convergence holds at the level of the local time processes. This is done via a careful study of the transition kernel of an auxiliary Markov chain which describes the local time at a given level. Then we prove a tightness result and deduce the convergence at the level of the full processes.     

Influence of the Metal Ion on the Two‐Photon Absorption Properties of Lanthanide Complexes Including Near‐IR Emitters

The synthesis of tris(2‐thenoyltrifluoroacetonate)lanthanide(III) complexes featuring a diethylaminostyryl‐2,2′‐bipyridine coligand was achieved for lanthanum; the near‐infrared (NIR) emitters neodymium, erbium, and ytterbium; and the transition‐metal yttrium. The photophysical properties were thoroughly studied, and it was demonstrated that the conjugated bipyridine ligand acts as a good antenna for the sensitization of the NIR emitters. The two‐photon absorption (TPA) properties of all five complexes were investigated by using both two‐photon excited fluorescence and the Z‐scan method. We demonstrate that the nature of the rare earth ion has almost no influence on the TPA properties centered on the conjugated bipyridyl ligand. Finally, we show that Yb^III is sensitized by a two‐photon antenna effect, and that Nd^III is mostly sensitized by a one‐photon process involving direct excitation of forbidden f–f transitions.