Macro‐hybrid mixed variational two‐phase flow through fractured porous media

Macro‐hybrid mixed variational models of two‐phase flow, through fractured porous media, are analyzed at the mesoscopic and macroscopic levels. The mesoscopic models are treated in terms of nonoverlapping domain decompositions, in such a manner that the porous rock matrix system and the fracture network interact across rock–rock, rock–fracture, and fracture–fracture interfaces, with flux transmission conditions dualized. Alternatively, the models are scaled to a macroscopic level via an asymptotic process, where the width of the fractures tends to zero, and the fracture network turns out to be an interface system of one less spatial dimension, with variable high permeability. The two‐phase flow is characterized by a fractional flow dual mixed variational model. Augmented two‐field and three‐field variational reformulations are presented for regularization, internal approximations, and macro‐hybrid mixed finite element implementation. Also abstract proximal‐point penalty‐duality algorithms are derived and analyzed for parallel computing. Copyright © 2016 John Wiley & Sons, Ltd.     

On the Ramsey number of the triangle and the cube

The Ramsey number r(K ₃,Q _n ) is the smallest integer N such that every red-blue colouring of the edges of the complete graph K _N contains either a red n-dimensional hypercube, or a blue triangle. Almost thirty years ago, Burr and Erd?s conjectured that r(K ₃,Q _n )=2 ⁿ⁺¹?1 for every n∈?, but the first non-trivial upper bound was obtained only recently, by Conlon, Fox, Lee and Sudakov, who proved that r(K ₃,Q _n )?7000·2 ⁿ . Here we show that r(K ₃,Q _n )=(1+o(1))2 ⁿ⁺¹ as n→∞.     

Organocatalytic Enantioselective Synthesis of Pyrazoles Bearing a Quaternary Stereocenter

An efficient one‐pot asymmetric synthesis of pyrazoles bearing a chiral quaternary stereocenter has been developed. Quinine‐derived thiourea catalyzed the enantioselective addition of pyrazolones to isatin‐derived ketimines, providing the corresponding acetylated pyrazoles after in situ treatment with Ac₂O/Et₃N. The corresponding pyrazoles were afforded in high yields and excellent enantioselectivities.     

Inductive vs solvation effects in primary alkyl amines: determination of the standard potentials

The determination of the standard potential of alkyl primary amines is reported for the first time using the nanosecond equilibrium method. The versatility and accuracy of the method demonstrates that it is not only an alternative to the classical and modern electrochemical methods, but also a powerful tool for quantifying inductive and/or solvation effects in a related family of compounds. Two different trends were observed depending on alkyl chain length. For "short-chain" alkyl primary amines, where the solvation around the amino group is expected to be the same, the standard potential value appears to follow a linear relationship with the number of carbon atoms, which indicates that the methylene group (-CH2-) causes an inductive effect that is responsible for the stabilization of the amine cation radical. Meanwhile, the E(o) rises slightly to a constant potential value 1.500 V for "long-chain" unbranched alkyl primary amines. This interesting result can be explained by a steric inhibition of solvation around the amino group due to a fold of the long alkyl chain following a solvent exclusion mechanism.     

Role of the countercation in diastereoselective alkylations of pyramidalized bicyclic serine enolates. An easy approach to alpha-benzylserine

The use of a chiral serine equivalent as an excellent chiral building block has been demonstrated in the synthesis of alpha-benzylserine through a diastereoselective lithium enolate alkylation reaction and subsequent acid hydrolysis. The role of a coordinating countercation (lithium) in the alkylation reaction has been investigated. Theoretical studies have been performed in order to elucidate the stereochemical outcome of the alkylation process, which occurs with total retention of configuration.     

Observation of three behaviors in confined liquid water within a nanopool hosting proton-transfer reactions

In this contribution, we report on studies of rotational and diffusional dynamics of 7-hydroxyquinoline (7HQ) within a reverse micelle (RM) containing different amounts of water. Analyzed in terms of the wobbling-in-a-cone model, the data reveal structural and dynamical properties of the nanopool. We clearly observed three regions in the behavior of confined water molecules within the RM hosting a double proton-transfer reaction between the probe and water. This observation remarkably reproduces the change of calculated water density within this life-mimicking medium. The number of water molecules per AOT head in the transition regions changes from 2 to 5, the latter being very near to the full solvation number (6) of the RM heads. Moreover, the H-bonds breaking and making within the RM to give new structures of the probe strongly affect the environment fluidization in different extents, reflected in different relaxation times of these structures; however, they are of similar sizes. We discuss the role of RM confinement and the proton-transfer dynamics on the behavior of water and their relationships to the packing of water molecules in the studied range of concentrations.     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.     

Acylation,cyanoethylation and alkylation of methyl and phenyl indolylmagnesium salts: Influence of the substituents on the c- and N-reaction products

Analysis of the influence of the substitution on indolylmagnesium salts in the reaction with benzoyl chlo ride, acrylonitrile and methyl iodide, giving the C- and N-derivatives, have been carried out. The yield in the C- and N-product depends upon the electronic character and position of the substituent (methyl or phenyl) on the indole ring and of the ethereal solvent as well as the concentration and molar ratio of the reagents. The 2- or 3-phenyl substituted indolylmagnesium salts with acrylonitrile always gave the 1-(2-cyanoethyl)indole derivative.     

Fast imaging of the plume expansion produced by laser ablation of LiNbO3

Fast photography of the plume produced by laser ablation of LiNbO₃ in vacuum has been performed using an image intensified CCD (ICCD) camera in a time interval up to 2 7s after the laser pulse. Two differently oriented single crystalline LiNbO₃ targets were used. The results show that although the emission intensity of the laser-generated plume initially depends on the crystalline orientation of the target, it reaches a stationary state after several minutes which is the same for both targets orientations. Under these stationary conditions, the angular distribution of the Li atoms is found to be broader than that of Nb atoms. The observed less forward directed expansion of the Li species may explain the poor Li content normally observed in films grown by laser ablation of LiNbO₃ in vacuum.     

Critical parameters influencing the material distribution produced by pulsed laser deposition

The parameters that control the thickness distribution of thin films produced by pulsed laser deposition are investigated. It is found that highly asymmetric material distribution profiles can be obtained in vacuum when high energy densities are used and the target surface is positioned at the lens focus. The asymmetries are due to asymmetries in the spatial distribution of the beam. Under Ar gas pressure, the profile becomes symmetric and the distribution narrows as a consequence of collisions between the ejected species and the gas. In vacuum, decreasing the energy density, by decreasing the laser energy output or by moving the lens to defocus the beam, leads to symmetric distribution profiles. Nevertheless, in the first case a quite broad distribution and a low deposition rate are obtained, whereas in the second case the distribution is narrow and the deposition rate increases.