On the Generalization of the Hébraud–Lequeux Model to Multidimensional Flows

In this article we build a model for multidimensional flows in soft glassy materials. The construction of the model is based on the ideas of Hébraud and Lequeux, but care is taken to build a frame-indifferent multidimensional model. The main goal of this article is to prove that the methodology we have developed to study the well-posedness and the glass transition for the original Hébraud–Lequeux model can be successfully generalized. Thus, this work may be used as a starting point for more sophisticated studies in the modeling of general flows of glassy materials.     

Straightforward access to enantioenriched pyrazyl alcohols using chiral organomagnesiates

The clean iodine-metal exchange of iodopyrazine and subsequent enantioselective addition of the intermediate pyrazyl magnesiate to aldehydes using ((R,R)-TADDOLate)Bu₂MgLi₂ is reported. New chiral pyrazylalcohols were obtained in enantiomeric excesses of up to 90%.     

Copper catalyzed tandem conjugated borylation–aldol reaction

We investigated the tandem conjugated borylation–aldol reaction catalyzed by copper complexes. After identification and optimisation of the catalytic system, the scope of the reaction was evaluated and the diastereoselectivity was studied on both linear and cyclic activated alkenes. Finally, the use of some selected borylated aldol adducts in two classical transformations was investigated.     

An upper bound for validity limits of asymptotic analytical approaches based on normal form theory

Perturbation methods are routinely used in all fields of applied mathematics where analytical solutions for nonlinear dynamical systems are searched. Among them, normal form theory provides a reliable method for systematically simplifying dynamical systems via nonlinear change of coordinates, and is also used in a mechanical context to define Nonlinear Normal Modes (NNMs). The main recognized drawback of perturbation methods is the absence of a criterion establishing their range of validity in terms of amplitude. In this paper, we propose a method to obtain upper bounds for amplitudes of changes of variables in normal form transformations. The criterion is tested on simple mechanical systems with one and two degrees-of-freedom, and for complex as well as real normal form. Its behavior with increasing order in the normal transform is established, and comparisons are drawn between exact solutions and normal form computations for increasing levels of amplitudes. The results clearly establish that the criterion gives an upper bound for validity limit of normal transforms.     

[1,3]Oxazolo[3,2-b][1,2,4]triazoles: a versatile synthesis of a novel heterocycle

An efficient one-pot microwave approach for the synthesis of novel [1,3]oxazolo[3,2-b][1,2,4]triazoles is described.