Numerical analysis of conservative unstructured discretisations for low Mach flows

Unstructured meshes allow easily representing complex geometries and to refine in regions of interest without adding control volumes in unnecessary regions. However, numerical schemes used on unstructured grids have to be properly defined in order to minimise numerical errors. An assessment of a low Mach algorithm for laminar and turbulent flows on unstructured meshes using collocated and staggered formulations is presented. For staggered formulations using cell‐centred velocity reconstructions, the standard first‐order method is shown to be inaccurate in low Mach flows on unstructured grids. A recently proposed least squares procedure for incompressible flows is extended to the low Mach regime and shown to significantly improve the behaviour of the algorithm. Regarding collocated discretisations, the odd–even pressure decoupling is handled through a kinetic energy conserving flux interpolation scheme. This approach is shown to efficiently handle variable‐density flows. Besides, different face interpolations schemes for unstructured meshes are analysed. A kinetic energy‐preserving scheme is applied to the momentum equations, namely, the symmetry‐preserving scheme. Furthermore, a new approach to define the far‐neighbouring nodes of the quadratic upstream interpolation for convective kinematics scheme is presented and analysed. The method is suitable for both structured and unstructured grids, either uniform or not. The proposed algorithm and the spatial schemes are assessed against a function reconstruction, a differentially heated cavity and a turbulent self‐igniting diffusion flame. It is shown that the proposed algorithm accurately represents unsteady variable‐density flows. Furthermore, the quadratic upstream interpolation for convective kinematics scheme shows close to second‐order behaviour on unstructured meshes, and the symmetry‐preserving is reliably used in all computations. Copyright © 2016 John Wiley & Sons, Ltd.     

Reaction of 2-Phenyl-3-Hydroxy-4-Thioxo-3,4-Dihydroquinazoline Sodium Salt With Imidoyl Chlorides: Synthesis of Heteroaryl Sulfenamides

A number of heteroaryl sulfenamides have been prepared through [3,3]-sigmatropic rearrangement in the reaction of 2-phenyl-3-hydroxy-4-thioxo-3,4-dihydroquinazoline sodium salt with diaryl imidoyl chlorides under mild and neutral conditions.     

Interaction of two spin subsystems with different wavevectors

The possibility of the transition of a spin system from an incommensurable to a commensurable phase via a phase with different wavevectors of individual subsystems is shown in the mean-field approximation.     

Vinyl C-F cleavage by Os(H)3Cl(P(i)Pr3)2

Os(H)(3)ClL(2) (L = P(i)Pr(3)) reacts at 20 degrees C with vinyl fluoride in the time of mixing to produce OsHFCl([triple bond]CCH(3))L(2) and H(2). In a competitive reaction, the liberated H(2) converts vinyl fluoride to C(2)H(4) and HF in a reaction catalyzed by Os(H)(3)ClL(2). A variable-temperature NMR study reveals these reactions proceed through the common intermediate OsHCl(H(2))(H(2)C=CHF)L(2), via OsClF(=CHMe)L(2) and OsHCl(H(2))(C(2)H(4))L(2), all of which are detected. DFT(B3PW91) calculations of the potential energy and free energy at 298 K of possible intermediates show the importance of entropy to account for their thermodynamic accessibility. Calculations of unimolecular C-F cleavage of coordinated C(2)H(3)F confirms the high activation energy of this process. Catalysis by HF is thus suggested to account for the fast observed reactions, and scavenging of HF with NEt(3) changes the product to exclusively Os(H)(2)Cl(CCH(3))L(2). The analogous reaction of Os(H)(3)ClL(2) with H(2)C=CF(2) produces exclusively OsHFCl(=CCH(3))L(2) and HF, and the latter is again suggested to catalyze C-F scission via the observed intermediates Os(H)(2)Cl(CF(2)CH(3))L(2) and OsHCl(=CFMe)L(2).     

Quantum chaos and 1/f noise

It is shown that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum behavior of such a signal for different systems suggests the following conjecture: The energy spectra of chaotic quantum systems are characterized by 1/f noise.     

Raman spectroscopic determination of inosine nucleoside in nucleotides

Raman spectroscopy has been applied to the analytical determination of inosine nucleoside in nucleotides. Spectral characteristics of aqueous solutions of lithium, potassium and magnesium salts of inosine 5'-monophosphoric acid are described. Two characteristic bands located at 1553 and 1593 cm(-1) whose frequencies are not sensitive either to the nucleotide concentration or to alkaline cations present in the medium, have been used for this purpose. The concentration ranges over which the method was applicable were 2.5-80 and 11.5-80 mg ml(-1) of inosine using the 1553 and 1593 cm(-1) bands, respectively, with relative standard deviations of 2.5 and 4.0% and detection limits of 0.25 and 1.16% (w/w). As the above bands are not generated by the standard nucleobases, this method can be applied to the quantitative determination of inosine in transfer ribonucleic acids.