Singular nature of nonlinear macroscale effects in high-rate flow through porous mediaNature singulière des effets macroscopiques non linéaires dans un écoulement à hautes vitesses en milieux poreux

The quadratic law of laminar flow through porous media at high Reynolds numbers, which is well confirmed by the multiple experimental data, is shown to give rise to three fundamental paradoxes. All them can be resolved by assuming the singular structure of flow. The singularity is produced by the formation of jet brunches which invade the stagnant zones and sharply loss their kinetic energy. The numerical simulation confirms this effect. To cite this article: M. Panfilov et al., C. R. Mecanique 331 (2003).     

Global Conservative Solutions of the Camassa–Holm Equation

This paper develops a new approach in the analysis of the Camassa–Holm equation. By introducing a new set of independent and dependent variables, the equation is transformed into a semilinear system, whose solutions are obtained as fixed points of a contractive transformation. These new variables resolve all singularities due to possible wave breaking. Returning to the original variables, we obtain a semigroup of global solutions, depending continuously on the initial data. Our solutions are conservative, in the sense that the total energy equals a constant, for almost every time.     

Anisotropy resolved multidimensional emission spectroscopy (ARMES): A new tool for protein analysis

Structural analysis of proteins using the emission of intrinsic fluorophores is complicated by spectral overlap. Anisotropy resolved multidimensional emission spectroscopy (ARMES) overcame the overlap problem by the use of anisotropy, with chemometric analysis, to better resolve emission from different fluorophores. Total synchronous fluorescence scan (TSFS) provided information about all the fluorophores that contributed to emission while anisotropy provided information about the environment of each fluorophore. Here the utility of ARMES was demonstrated via study of the chemical and thermal denaturation of human serum albumin (HSA).     

Aromatic Interactions in Organocatalyst Design: Augmenting Selectivity Reversal in Iminium Ion Activation

Substituting N‐methylpyrrole for N‐methyindole in secondary‐amine‐catalysed Friedel–Crafts reactions leads to a curious erosion of enantioselectivity. In extreme cases, this substrate dependence can lead to an inversion in the sense of enantioinduction. Indeed, these closely similar transformations require two structurally distinct catalysts to obtain comparable selectivities. Herein a focussed molecular editing study is disclosed to illuminate the structural features responsible for this disparity, and thus identify lead catalyst structures to further exploit this selectivity reversal. Key to effective catalyst re‐engineering was delineating the non‐covalent interactions that manifest themselves in conformation. Herein we disclose preliminary validation that intermolecular aromatic (CH–π and cation–π) interactions between the incipient iminium cation and the indole ring system is key to rationalising selectivity reversal. This is absent in the N‐methylpyrrole alkylation, thus forming the basis of two competing enantio‐induction pathways. A simple L ‐valine catalyst has been developed that significantly augments this interaction.     

Functionalization of Intramolecular Frustrated Lewis Pairs by 1,1‐Carboboration with Conjugated Enynes

The vicinal P/B frustrated Lewis pair (FLP) Mes₂PCH₂CH₂B(C₆F₅)₂ undergoes 1,1‐carboboration reactions with the Me₃Si‐substituted enynes to give ring‐enlarged functionalized C₃‐bridged P/B FLPs. These serve as active FLPs in the activation of dihydrogen to give the respective zwitterionic [P]H⁺/[B]H^? products. One such product shows activity as a metal‐free catalyst for the hydrogenation of enamines or a bulky imine. The ring‐enlarged FLPs contain dienylborane functionalities that undergo “bora‐Nazarov”‐type ring‐closing rearrangements upon photolysis. A DFT study had shown that the dienylborane cyclization of such systems itself is endothermic, but a subsequent C₆F₅ migration is very favorable. Furthermore, substituted 2,5‐dihydroborole products are derived from cyclization and C₆F₅ migration from the photolysis reaction. In the case of the six‐membered annulation product, a subsequent stereoisomerization reaction takes place and the resultant compound undergoes a P/B FLP 1,2‐addition reaction with a terminal alkyne with rearrangement.     

An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

Let \(\mathcal {U}=\{U(t,s)\}_{t\ge s\ge 0}\) be a strongly continuous and exponentially bounded evolution family acting on a complex Banach space X and let \(\mathcal {X}\) be a certain Banach function space of X-valued functions. We prove that the growth bound of the family \(\mathcal {U}\) is less than or equal to \(-\frac{1}{c(\mathcal {U}, \mathcal {X})}\) provided that the convolution operator \(f\mapsto \mathcal {U}*f\) acts on \(\mathcal {X}.\) It is well known that under the latter assumption, the convolution operator is bounded and then \(c(\mathcal {U}, \mathcal {X})\) denotes (ad-hoc) its norm in \(\mathcal {L}(\mathcal {X}).\) As a consequence, we prove that if \(\sup \nolimits _{s\ge 0}\int \nolimits _{s}^\infty \Vert U(t,s)\Vert dt=u_1(\mathcal {U})<\infty ,\) then \(\omega _0(\mathcal {U})u_1(\mathcal {U})\le -1.\) Finally, we give an example showing that the accuracy of the estimates may be quite accurate.     

Dispersion de Taylor généralisée à un fluide à propriétés physiques variablesGeneralized Taylor dispersion for heterogeneous fluid

The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. To cite this article: C. Felder et al., C. R. Mecanique 332 (2004).