Modified Eulerian–Lagrangian formulation for hydrodynamic modeling

We present the modified Eulerian–Lagrangian (MEL) formulation, based on non-divergent forms of partial differential balance equations, for simulating transport of extensive quantities in a porous medium. Hydrodynamic derivatives are written in terms of modified velocities for particles propagating phase and component quantities along their respective paths. The particles physically interpreted velocities also address the heterogeneity of the matrix and fluid properties. The MEL formulation is also implemented to parabolic Partial Differential Equations (PDE’s) as these are shown to be interchangeable with equivalent PDE’s having hyperbolic – parabolic characteristics, without violating the same physical concepts. We prove that the MEL schemes provide a convergent and monotone approximation also to PDE’s with discontinuous coefficients. An extension to the Peclet number is presented that also accounts for advective dominant PDE’s with no reference to the fluid velocity or even when this velocity is not introduced.In Sorek et al. [27], a mathematical analysis for a linear system of coupled PDE’s and an example of nonlinear PDE’s, proved that the finite difference MEL, unlike an Eulerian scheme, guaranties the absence of spurious oscillations. Currently, we present notions of monotone interpolation associated with the MEL particle tracking procedure and prove the convergence of the MEL schemes to the original balance equation also for discontinuous coefficients on the basis of difference schemes approximating PDE’s. We provide numerical examples, also with highly random fields of permeabilities and/or dispersivities, suggesting that the MEL scheme produces resolutions that are more consistent with the physical phenomenon in comparison to the Eulerian and the Eulerian–Lagrangian (EL) schemes.     

A Novel and Simple Synthesis of 2-(Trifluoromethyl)-4H-thiochromen-4-ones

Abstract

Alkyl 2-mercaptophenyl ketones react with trifluoroacetic anhydride in the presence of triethylamine to give 2-(trifluoromethyl)-4H-thiochromen-4-ones, which are transformed into the corresponding pyrazoles by treatment with hydrazine hydrate and into 1,1-dioxides by oxidation with H₂O₂ in AcOH.     

Synthesis of 6-aryl- and 5-aroylcomanic acids from 5-aroyl-2-carbethoxy-4-pyrones via a deformylative rearrangement and ring-opening/ring-closure sequence

The reaction of 1-aryl-2-(dimethylaminomethylene)butane-1,3-diones with diethyl oxalate in the presence of sodium hydride in THF gave ethyl 5-aroyl-4-oxo-4H-pyran-2-carboxylates, from which 4-oxo-6-aryl-4H-pyran-2-carboxylic acids (6-arylcomanic acids) were obtained in high yields via acid-catalyzed deformylative rearrangement. 5-Aroyl-4-oxo-4H-pyran-2-carboxylic acids (5-aroylcomanic acids) were prepared via а ring-opening/ring-closure sequence by the reaction of 5-aroyl-2-carbethoxy-4-pyrones with piperidine and subsequent basic hydrolysis and acidification.     

Unexpected cleavage of the Cpy–Cpy bond in the reaction of 2,2′-bipyridine N,N′-diimines with acetylenes

An unusual cleavage of the C_py–C_py bond in the reaction of 2,2′-bipyridine N,N′-diimine and its C-methyl substituted derivatives with acetylenes is described. The effect of the solvent on the yield of 7,7′-bipyrazolo[1,5-a]pyridine-2,2′,3,3′-tetracarboxylates and the products of cleavage of the C_py–C_py bond has been studied. The mechanism of the cleavage reaction is discussed on the basis of DFT calculations.     

Substituted chromones in [3+2] cycloadditions with nonstabilized azomethine ylides: synthesis of 1-benzopyrano[2,3-c]pyrrolidines and 1-benzopyrano[2,3-c:3,4-c′]dipyrrolidines

Chromones bearing electron-withdrawing substituents at the 2- or 3-position react with nonstabilized azomethine ylides to produce 1-benzopyrano[2,3-c]pyrrolidines in good yields. Reactions of 3-cyanochromones proceed diastereoselectively to give 1-benzopyrano[2,3-c]pyrrolidines and tetrahydro-1H-spiro[chromeno[2,3-c]pyrrol-9,5′-oxazolidine]-9a-carbonitriles, depending on the reactant ratio, as a result of a 1,3-dipolar cycloaddition of the azomethine ylide at the double bond and carbonyl group of the chromone system. The latter undergoes demethylenation and recyclization into a novel hexahydrochromeno[2,3-c:3,4-c′]dipyrrole tetracyclic system on heating with hydrochloric acid.     

Large‐acceptance diamond planar refractive lenses manufactured by laser cutting

For the first time, single‐crystal diamond planar refractive lenses have been fabricated by laser micromachining in 300 µm‐thick diamond plates which were grown by chemical vapour deposition. Linear lenses with apertures up to 1 mm and parabola apex radii up to 500 µm were manufactured and tested at the ESRF ID06 beamline. The large acceptance of these lenses allows them to be used as beam‐conditioning elements. Owing to the unsurpassed thermal properties of single‐crystal diamond, these lenses should be suitable to withstand the extreme flux densities expected at the planned fourth‐generation X‐ray sources.     

Interaction in the molten system Rb2O‐P2O5‐TiO2‐NiO. Crystal structure of the langbeinite‐related Rb2Ni0.5Ti1.5(PO4)3

The interaction in the molten system Rb₂O‐P₂O₅‐TiO₂‐NiO was investigated at different molar ratios Rb/P = 0.5‐1.3, fixed Ti/P = 0.15, Ti/Ni = 1.0 at temperature range 1073–953 K. The conditions of formation of complex phosphates RbTi₂(PO₄)₃, Rb₂Ni_0.5Ti_1.5(PO₄)₃ and RbNiPO₄ have been determined. The new phosphate Rb₂Ni_0.5Ti_1.5(PO₄)₃ (space group P2₁3, a = 9.9386(2) Å) has been obtained and investigated by the single crystal X‐ray diffraction and FTIR‐spectroscopy. It has langbeinite‐like structure, that is built up from mixed (Ni/Ti)O₆‐octahedra and РО₄‐tetrahedra. Rubidium atoms are located in closed cavities of 3D‐framework.     

Photolysis of 3-(1-acyl-5-aryl-3-pyrazolinyl)coumarins—Effective Fluorescence Decay

Photophysical characteristics of new 3-(1-acyl-5-aryl-3-pyrazolinyl)coumarins have been measured. These coumarin derivatives are found to be effective fluorophores and show high values of quantum yields of fluorescence both in nonpolar and in polar solvents. The 3-(1-acyl-5-aryl-3-pyrazolinyl)coumarins turned to be photosensitive compounds and undergo photolysis under irradiation in the range of 310–465 nm. Photolysis is suggested to include retro-cyclization and retro-condensation steps. The process is accompanied by a sharp drop of fluorescence that can be of interest for the creation of new media in optical recording of information.     

Photochromic Free MOF‐Based Near‐Infrared Optical Switch

We demonstrate herein an all‐optical switch based on stimuli‐responsive and photochromic‐free metal–organic framework (HKUST‐1). Ultrafast near‐infrared laser pulses stimulate a reversible 0.4 eV blue shift of the absorption band with up to 200 s^?1 rate due to dehydration and concomitant shrinking of the structure‐forming [Cu₂C₄O₈] cages of HKUST‐1. Such light‐induced switching enables the remote modulation of intensities of photoluminescence of single crystals of HKUST‐1 as well visible radiation passing through the crystal by 2 order of magnitude. This opens up the possibility of utilyzing stimuli‐responsive MOFs for all‐optical data processing devices.