Turbulent Energy Scale-Budget Equations for nearly Homogeneous Sheared Turbulence

For moderate Reynolds numbers, the isotropic relation between second-order and third-order moments for velocity increments (Kolmogorov's equation) is not respected, reflecting a non-negligible correlation between the scales responsible for the injection, transfer and dissipation of the turbulent energy. For (shearless) grid turbulence, there is only one dominant large-scale phenomenon, which is the non-stationarity of statistical moments resulting from the decay of energy downstream of the grid. In this case, the extension of Kolmogorov's analysis, as carried out by Danaila, Anselmet, Zhou and Antonia, J. Fluid Mech. 391, 1999 359-369) is quite straightforward. For shear flows, several large-scale phenomena generally coexist with similar amplitudes. This is particularly the case for wall-bounded flows, where turbulent diffusion and shear effects can present comparable amplitudes. The objective of this work is to quantify, in a fully developed turbulent channel flow and far from the wall, the influence of these two effects on the scale-by-scale energy budget equation. A generalized Kolmogorov equation is derived. Relatively good agreement between the new equation and hot-wire measurements is obtained in the outer region (40 < x ⁺ ₃ < 150) of the channel flow, for which the turbulent Reynolds number is R _λ≈ 36.     

The magic effect of endocyclic but non-sterically hindering biisoquinoline chelates: From fast-moving molecular shuttles to [3]rotaxanes

The use of 8,8′-diaryl-substituted 3,3′-biisoquinolines allows the construction of new multi-component assemblies that are inaccessible with the 2,9-diaryl-substituted 1,10-phenanthroline ligands previously developed by the Sauvage group. This is due to the sterically non-hindering nature of the new chelates, which makes three-component entanglements around octahedral metal centres such as iron(II), cobalt(II) and ruthenium(II) readily possible. Among the newly synthesized molecular assemblies are [3]rotaxanes and [3]pseudorotaxanes in which two molecular strings pass through a single macrocycle, as well as molecular shuttles that exhibit greatly improved shuttling kinetics when compared to previously investigated molecular machines that are based on copper(I)/copper(II) redox chemistry.     

Synthesis and characterization of high surface area TiO2/SiO2 mesostructured nanocomposite

Recently titania synthesis was reported using various structuration procedures, leading to the production of solid presenting high surface area but exhibiting moderate thermal stability. The study presents the synthesis of TiO₂/SiO₂ nanocomposites, a solid that can advantageously replace bulk titania samples as catalyst support. The silica host support used for the synthesis of the nanocomposite is a SBA-15 type silica, having a well-defined 2D hexagonal pore structure and a large pore size. The control of the impregnation media is important to obtain dispersed titania crystals into the porosity, the best results have been obtained using an impregnation in an excess of solvent. After calcination at low temperature (400 °C), nanocomposites having titania nanodomains (～2–3 nm) located inside the pores and no external aggregates visible are obtained. This nanocomposite exhibits high specific surface area (close to that of the silica host support, even with a titania loading of 55 wt.%) and a narrow pore size distribution. Surprisingly, the increase in calcination temperature up to 800 °C does not allow to detect the anatase to rutile transition. Even at 800 °C, the hexagonal mesoporous structure of the silica support is maintained, and the anatase crystal domain size is evaluated at ～10 nm, a size close to that of the silica host support porosity (8.4 nm). Comparison of their physical properties with the results presented in literature for bulk samples evidenced that these TiO₂/SiO₂ solids are promising in term of thermal stability.     

Expanded Pyridiniums: Bis‐cyclization of Branched Pyridiniums into Their Fused Polycyclic and Positively Charged Derivatives—Assessing the Impact of Pericondensation on Structural,Electrochemical, Electronic,and Photophysical Features

This study evaluates the impact of the extension of the π‐conjugated system of pyridiniums on their various properties. The molecular scaffold of aryl‐substituted expanded pyridiniums (referred to as branched species) can be photochemically bis‐cyclized into the corresponding fused polycyclic derivatives (referred to as pericondensed species). The representative 1,2,4,6‐tetraphenylpyridinium ( 1^H ) and 1,2,3,5,6‐pentaphenyl‐4‐(p‐tolyl)pyridinium ( 2^Me ) tetra‐ and hexa‐branched pyridiniums are herein compared with their corresponding pericondensed derivatives, the fully fused 9‐phenylbenzo[1,2]quinolizino[3,4,5,6‐def]phenanthridinium ( 1^H f ) and the hitherto unknown hemifused 9‐methyl‐1,2,3‐triphenylbenzo[h]phenanthro[9,10,1‐def]isoquinolinium ( 2^Me f ). Combined solid‐state X‐ray crystallography and solution NMR experiments showed that stacking interactions are barely efficient when the pericondensed pyridiniums are not appropriately substituted. The electrochemical study revealed that the first reduction process of all the expanded pyridiniums occurs at around ?1 V vs. SCE, which indicates that the lowest unoccupied molecular orbital (LUMO) remains essentially localized on the pyridinium core regardless of pericondensation. In contrast, the electronic and photophysical properties are significantly affected on going from branched to pericondensed pyridiniums. Typically, the number of absorption bands increases with extended activity towards the visible region (down to ca. 450 nm in MeCN), whereas emission quantum yields are increased by three orders of magnitude (at ca. 0.25 on average). A relationship is established between the observed differential impact of the pericondensation and the importance of the localized LUMO on the properties considered: predominant for the first reduction process compared with secondary for the optical and photophysical properties.     

Vladimir Sergeevich Anashin

On the occasion of the 60th birthday of Professor Vladimir Sergeevich Anashin, we present a review of his significant scientific research and related activities.     

Topological Graph Polynomial and Quantum Field Theory Part II: Mehler Kernel Theories

We define a new topological polynomial extending the Bollobás–Riordan one, which obeys a four-term reduction relation of the deletion/contraction type and has a natural behaviour under partial duality. This allows to write down a completely explicit combinatorial evaluation of the polynomials, occurring in the parametric representation of the non-commutative Grosse–Wulkenhaar quantum field theory. An explicit solution of the parametric representation for commutative field theories based on the Mehler kernel is also provided.     

Accurate a posteriori error evaluation in the reduced basis method

In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this Note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and illustrated on a simple example.     

Multidimensional extension of the Morse–Hedlund theorem

A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence x$x$ over a finite alphabet is ultimately periodic if and only if, for some n$n$, the number of different factors of length n$n$ appearing in x$x$ is less than n+1$n+1$. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let d≥2$d\ge 2$. A legitimate extension to a multidimensional setting of the notion of periodicity is to consider sets of Z^d${\mathbb{Z}}^d$ definable by a first order formula in the Presburger arithmetic 〈Z;<,+〉$〈\mathbb{Z};<,+〉$. With this latter notion and using a powerful criterion due to Muchnik, we exhibit a complete extension of the Morse–Hedlund theorem to an arbitrary dimension d$d$ and characterize sets of Z^d${\mathbb{Z}}^d$ definable in 〈Z;<,+〉$〈\mathbb{Z};<,+〉$ in terms of some functions counting recurrent blocks, that is, blocks occurring infinitely often.     

Superacid-Mediated Late-Stage Aromatic Polydeuteration of Pharmaceuticals

The field of medicinal chemistry is currently witnessing a deuterium rush owing to the remarkable properties of this element as bioisoster of hydrogen atom. Aromatic hydrogen isotope exchange (HIE) is one of the most studied strategies nowadays as it promises to access deuterium-modified drugs directly from their non-labeled parents. While most of the recent studies focus on metal-catalyzed C−H activation strategy, the use of superacidic conditions has been largely overlooked. This study shows that the use of TfOD as reaction medium allows the late-stage polydeuteration of a broad library of pharmaceuticals bearing a wide array of functional groups, complementing existing procedures.     

Enantioselective Approach for Expanding the Three-Dimensional Space of Tetrahydroquinoline to Develop BET Bromodomain Inhibitors**

The pharmaceutical industry has a pervasive need for chiral specific molecules with optimal affinity for their biological targets. However, the mass production of such compounds is currently limited by conventional chemical routes, that are costly and have an environmental impact. Here, we propose an easy access to obtain new tetrahydroquinolines, a motif found in many bioactive compounds, that is rapid and cost effective. Starting from simple raw materials, the procedure uses a proline-catalyzed Mannich reaction followed by the addition of BF₃ ⋅ OEt₂, which generates a highly electrophilic aza-ortho-quinone methide intermediate capable of reacting with different nucleophiles to form the diversely functionalized tetrahydroquinoline. Moreover, this enantioselective one-pot process provides access for the first time to tetrahydroquinolines with a cis-2,3 and trans-3,4 configuration. As proof of concept, we demonstrate that a three-step reaction sequence, from simple and inexpensive starting compounds and catalysts, can generate a BD2-selective BET bromodomain inhibitor with anti-inflammatory effect.