Combined compact difference method for solving the incompressible Navier–Stokes equations

This paper presents a numerical method for solving the two‐dimensional unsteady incompressible Navier–Stokes equations in a vorticity–velocity formulation. The method is applicable for simulating the nonlinear wave interaction in a two‐dimensional boundary layer flow. It is based on combined compact difference schemes of up to 12th order for discretization of the spatial derivatives on equidistant grids and a fourth‐order five‐ to six‐alternating‐stage Runge–Kutta method for temporal integration. The spatial and temporal schemes are optimized together for the first derivative in a downstream direction to achieve a better spectral resolution. In this method, the dispersion and dissipation errors have been minimized to simulate physical waves accurately. At the same time, the schemes can efficiently suppress numerical grid‐mesh oscillations. The results of test calculations on coarse grids are in good agreement with the linear stability theory and comparable with other works. The accuracy and the efficiency of the current code indicate its potential to be extended to three‐dimensional cases in which full boundary layer transition happens. Copyright © 2011 John Wiley & Sons, Ltd.     

2‐(6‐Bromo­pyridin‐2‐yl)‐6‐methyl‐[1,3,6,2]­diox­aza­borocane,a new stable (pyridin‐2‐yl)­boronic acid derivative

The crystal structure of the first reported non‐substituted N‐methyl­diox­aza­borocane confirms that the presence of a methyl group attached to the N atom introduces an NB bond length that is longer than that in a simple diox­aza­borocane ring. The presence of more N atoms in the vicinity of the B atom in the title compound [systematic name: 6a‐(6‐bromo­pyridin‐2‐yl)‐3a‐methyl‐2,3,4,5‐tetra­hydro‐1,6‐dioxa‐3a‐aza‐6a‐borapentalene], C₁₀H₁₄BBrN₂O₂, does not modify significantly any structural parameter in the diox­aza­borocane ring. On the other hand, a small asymmetry appears in the bond angles of the pyridine C atom next to the B atom.     

Ètude des reactions de nitration de l'acetamido-3 ethyl-9 carbazole

The nitration of 3-acetamido-, 3-formamido- and 3-carbethoxyamino-9-ethylcarbazoles has been studied. Nitration of 3-acetamido-9-ethylcarbazole substituted the 6 position while 3-formamido- and 3-carbethoxyamino-9-ethylcarbazoles gave 4-nitro derivatives. The nitration of three compounds in the 4- and 6-positions was accomplished. Further substitution of 3-acetamido- and 3-carbethoxyamino- derivatives yielded the 4,6,8-trinitro compounds. Assignment of the structures was based on nmr spectral studies and on unequivocal syntheses.     

Triazino-1,2,4-[4,5-a] indoles. V. Etude du dioxo-1,4 tetrahydro-1,2,3,4 triazino-1,2,4-[4,5-a] indole

1,4-Dioxo - 1,2,3,4- tetrahydro- 1,2,4- triazino[4,5-a] indole (1) was synthesized either by cyclising the N-carbethoxyhydraxizide of indole-2 carboxylic acid (4) or by alkaline rearrangement of 2-(2-indolyl)-5-oxadiazolone (6). The methylation reactions of the dilactam 1 were achieved with dimethyl sulfate or diazo-methane and afforded mixtures of O-methylated and N-methylated derivatives which were isolated and the structure of which were asigned. The tautomerism of dilactam 1 was studied using O-and N-methylated derivatives. The lactim-lactam structure 1a pre-ponderated in solution.     

Trimetallic NiMoW/Al<Subscript>2</Subscript>O<Subscript>3</Subscript> hydrotreating catalyst based on H<Subscript>4</Subscript>SiMo<Subscript>3</Subscript>W<Subscript>9</Subscript>O<Subscript>40</Subscript> mixed heteropoly acid

Trimetallic NiMoW/Al₂O₃ catalyst was prepared using mixed H₄SiMo₃W₉O₄₀ heteropoly acid of Keggin structure and nickel citrate. Bimetallic NiMo/Al₂O₃ and NiW/Al₂O₃ catalysts based on H₄SiMo₁₂O₄₀ and H₄SiW₁₂O₄₀, respectively, were synthesized as reference samples. The use of mixed H₄SiMo₃W₉O₄₀ heteropoly acid as an oxide precursor allows the tungsten sulfidation degree and the degree of promotion of active phase particles to be increased. The hydrodesulfurization activity is enhanced as compared to NiW/Al₂O₃ catalyst. The synergistic enhancement of the activity of the NiMo₃W₉/Al₂O₃ catalyst relative to the bimetallic analogs is probably caused by formation of new mixed promoted active sites for direct desulfurization.     

Comparison of the interaction of dihydrocholesterol and cholesterol with sphingolipid or phospholipid Langmuir monolayers

We report here a study of the interaction of dihydrocholesterol (DChol) with palmitoyl-oleoyl-phosphatidylcholine (POPC) or sphingomyelin (SM) in Langmuir monolayers. DChol and cholesterol (Chol) have very close chemical structures, and DChol is often used in place of Chol because of its better stability. Surface pressure measurements and experiments of desorption induced by beta-cyclodextrin show that POPC-DChol monolayers behave similarly to POPC-Chol ones: condensing effects of DChol and Chol on POPC and desorption percentages are in the same range. Moreover Brewster angle microscopy (BAM) experiments performed on these monolayers show that on the whole they are both homogenous. The analysis of mean molecular areas versus DChol percentage shows that this sterol is also able to induce SM condensation at low surface pressure. The condensation of SM molecules is particularly strong at 30 mol% of DChol. At higher surface pressure, the condensation efficiency of DChol decreases and monolayers behave more ideally, even if an inflection point is always observed at 30 mol% of DChol. However, desorption percentages, clearly lower than those obtained with POPC-DChol monolayers, show that DChol is kept at the interface. At last BAM images show also differences in the behaviour of SM-DChol and SM-Chol monolayers. These differences could be due to the different compressibility and conformation of the A/B rings in the two sterols and the rigidity of the sphingosine chain. They suggest that the use of DChol in place of Chol has to be done carefully in the presence of SM.     

Stochastic Chaos and Markov Blankets

In this treatment of random dynamical systems, we consider the existence—and identification—of conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions has interesting implications for the information geometry of internal states. In brief, this geometry can be read as a physics of sentience, where internal states look as if they are inferring external states. However, the existence of such partitions—and the functional form of the underlying densities—have yet to be established. Here, using the Lorenz system as the basis of stochastic chaos, we leverage the Helmholtz decomposition—and polynomial expansions—to parameterise the steady-state density in terms of surprisal or self-information. We then show how Markov blankets can be identified—using the accompanying Hessian—to characterise the coupling between internal and external states in terms of a generalised synchrony or synchronisation of chaos. We conclude by suggesting that this kind of synchronisation may provide a mathematical basis for an elemental form of (autonomous or active) sentience in biology.     

2‐Bromo‐6‐(4,4,5,5‐tetramethyl‐1,3,2‐dioxaborolan‐2‐yl)pyridine,a new unexpected bifunctional building block for combinatorial chemistry

The first reported structure of a pyridin‐2‐ylboron derivative, viz. the title compound, C₁₁H₁₅BBrNO₂, (I), is compared with its regioisomer 2‐bromo‐5‐(4,4,5,5‐tetra­methyl‐1,3,2‐dioxa­borolan‐2‐yl)­pyridine, (II) [Sopková‐de Oliveira Santos, Lancelot, Bouillon & Rault (2003). Acta Cryst. C59, o111o113 ]. Structural differences are observed, firstly in the orientation of the dioxaborolane ring with respect to the pyridine ring and secondly in the bond angles of the BO₂ group. These differences do not explain the experimentally observed differences in chemical reactivity between (I) and (II) but do confirm the relatively lower stability of (I). However, ab initio calculations of the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital), based on the known crystal structures of the two compounds, show different distributions, which correspond to the differences observed during chemical reactions.     

Investigating the role of c-Jun N-terminal kinases in the proliferation of Werner syndrome fibroblasts using diaminopyridine inhibitors

To develop more potent small molecules with enhanced free radical scavenger properties, a series of N-substituted isatin derivatives was synthesized, and the cytoprotective effect on the apoptosis of PC12 cells induced by H₂O₂ was screened. All these compounds were found to be active, and N-ethyl isatin was found with the most potent activity of 69.7% protective effect on PC12 cells. Structure-activity relationship analyses showed the bioactivity of N-alkyl isatins decline as the increasing of the chain of the alkyl group, furthermore odd-even effect was found in the activity, which is interesting for further investigation.