New approach to the Lax‐Wendroff modified differential equation for linear and nonlinear advection

The paper presents an enhanced analysis of the Lax‐Wendroff difference scheme—up to the eighth‐order with respect to time and space derivatives—of the modified‐partial differential equation (MDE) of the constant‐wind‐speed advection equation. The modified equation has been so far derived mainly as a fourth‐order equation. The Π ‐form of the first differential approximation (differential approximation or equivalent equation) derived by expressing the time derivatives in terms of the space derivatives is used for presenting the MDE. The obtained coefficients at higher order derivatives are analyzed for indications of the character of the dissipative and dispersive errors. The authors included a part of the stencil applied for determining the modified differential equation up to the eighth‐order of the analyzed modified differential equation for the second‐order Lax‐Wendroff scheme. Neither the derived coefficients at the space derivatives of order p ∈ (7 – 8) in the modified differential equation for the Lax‐Wendroff difference scheme nor the results of analyses on the basis of these coefficients of the group velocity, phase shift errors, or dispersive and dissipative features of the scheme have been published. The MDEs for 2 two‐step variants of the Lax‐Wendroff type difference schemes and the MacCormack predictor–corrector scheme (see MacCormack's study) constructed for the scalar hyperbolic conservation laws are also presented in this paper. The analysis of the inviscid Burgers equation solution with the initial condition in a form of a shock wave has been discussed on their basis. The inviscid Burgers equation with the source is also presented. The theory of MDE started to develop after the paper of C. W. Hirt was published in 1968.     

Synthesis of 4‐Substituted Piperidines via a Mild and Scalable Two‐Step Cu2O‐Mediated Decarboxylation of Cyanoesters

A four‐step, high‐yielding, kilogram‐scale protocol to prepare aldehyde 5 is reported. The key reaction is a mild, two‐step Cu₂O‐mediated decarboxylation of cyanoester 3 that proceeds in excellent yield. The general applicability of this methodology has also been explored.     

New insight into the electronic structure of iron(IV)‐oxo porphyrin compound I. A quantum chemical topological analysis

The electronic structure of iron‐oxo porphyrin π‐cation radical complex Por^·+Fe^IV?O (S? H) has been studied for doublet and quartet electronic states by means of two methods of the quantum chemical topology analysis: electron localization function (ELF) η(r) and electron density ρ(r). The formation of this complex leads to essential perturbation of the topological structure of the carbon–carbon bonds in porphyrin moiety. The double C?C bonds in the pyrrole anion subunits, represented by pair of bonding disynaptic basins V_i=1,2(C,C) in isolated porphyrin, are replaced by single attractor V(C,C)_i=1–20 after complexation with the Fe cation. The iron–nitrogen bonds are covalent dative bonds, N→Fe, described by the disynaptic bonding basins V(Fe,N)_i=1–4, where electron density is almost formed by the lone pairs of the N atoms. The nature of the iron–oxygen bond predicted by the ELF topological analysis, shows a main contribution of the electrostatic interaction, Fe^δ+···O^δ?, as long as no attractors between the C(Fe) and C(O) core basins were found, although there are common surfaces between the iron and oxygen basines and coupling between iron and oxygen lone pairs, that could be interpreted as a charge‐shift bond. The Fe? S bond, characterized by the disynaptic bonding basin V(Fe,S), is partially a dative bond with the lone pair donated from sulfur atom. The change of electronic state from the doublet (M = 2) to quartet (M = 4) leads to reorganization of spin polarization, which is observed only for the porphyrin skeleton (?0.43e to 0.50e) and S? H bond (?0.55e to 0.52e). © 2012 Wiley Periodicals, Inc.     

Polythiol binding to biologically relevant metal ions

The coordination properties of three peptides with CXXC motif: Ac-GCASCDNCRACKK-NH(2), Ac-GCASCDNCRAAKK-NH(2) and Ac-GCASCDNARAAKK-NH(2) as donors of four, three and two thiol ligands for Ni(2+),Cd(2+), Zn(2+) and Bi(3+) were studied by potentiometric titrations, UV-Vis and CD spectra measurements. Since the stability of the complexes is closely connected with the amount of the metal-bound cysteine sulfurs, competition plots of the complexes of peptides with 2, 3 and 4 cysteines further prove the involvement of all thiols in the metal ion binding. Furthermore, the sulfur-bound zinc complexes appear to be much more stable than the sulfur-bound nickel ones. The stabilities of the studied complexes decreases in the series Bi(3+) ? Cd(2+) > Zn(2+) > Ni(2+).     

Anodic oxidation of oxidized forms of coenzymes Q(10) and Q(0) on carbon electrodes in acetic acid solutions

The anodic oxidation of oxidized forms of coenzyme Q₁₀ (ubiquinone, CoQ₁₀) and Q₀ (CoQ₀) on a glassy carbon macroelectrode (GC) and on a carbon fiber microelectrode (CF) was investigated in acetic acid using voltammetric techniques. Voltammograms recorded on these electrodes show well-defined peaks or waves in the potential range of above 1.5 V (vs. Ag/AgCl). The existence of these signals cannot be connected with the well-known redox couple CoQ/CoQH₂ but may be attributed to the irreversible and diffusion-controlled two-electron oxidation of methoxy groups in molecules of coenzymes. The overall number of electrons involved in the anodic oxidation of CoQ₁₀ is higher than for CoQ₀. This indicates that oxidation also proceeds in an unsaturated isoprene side chain. Smaller oxidation potentials for CoQ₁₀ in comparison to such unsaturated fatty acids as oleic, linoleic and linolenic ones indicate that this compound can show direct antioxidative properties. The antioxidative power of CoQ₁₀ is much smaller than that of reduced CoQ₁₀ (ubiquinol) and α-tocopherol. The results presented can be useful in the determination of this compound in real samples and in the assessment of biochemical properties of CoQ₁₀ in living cells.     

Hybrid RANS/LES of flow and heat transfer in round impinging jets

Fluid flow and convective heat transfer predictions are presented of round impinging jets for several combinations of nozzle-plate distances H/D = 2, 6 and 13.5 (where D is the nozzle diameter) and Reynolds numbers Re = 5000, 23,000 and 70,000 with the newest version of the k-ω model of Wilcox (2008) and three hybrid RANS/LES models. In the RANS mode of the hybrid RANS/LES models, the k-ω model is recovered. Three formulations are considered to activate the LES mode. The first model is similar to the hybrid models of Davidson and Peng (2003) and Kok et al. (2004). The turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the definition of the RANS eddy viscosity. As grid size, a maximum measure of the hexahedral grid cell is used. The second model has the same k-equation, but the eddy viscosity is the minimum of the k-ω eddy viscosity and the Smagorinsky eddy viscosity, following a proposal by Batten et al. (2004). The Smagorinsky eddy viscosity is formed with the cube root of the cell volume. The third model has, again, the same k-equation, but has an eddy viscosity which is an intermediate between the eddy viscosities of the first and second models. This is reached by using the cube root of the cell volume in the eddy viscosity formula of the first model.The simulation results are compared with experimental data for the high Reynolds number cases Re = 23,000 and Re = 70,000 and LES data for the low-Reynolds number case Re = 5000. The Reynolds numbers are defined with the nozzle diameter and the bulk velocity at nozzle outlet. At low nozzle-plate distance (the impingement plate is in the core of the jet), turbulent kinetic energy is overpredicted by RANS in the stagnation flow region. This leads to overprediction of the heat transfer rate along the impingement plate in the impact zone. At high nozzle-plate distance (the impingement plate is in the mixed-out region of the jet), the turbulence mixing is underpredicted by RANS in the shear layer of the jet which gives a too high length of the jet core. This also results in overprediction of the heat transfer rate in the impingement zone caused by too big temperature gradients at impingement.All hybrid RANS/LES models are able to correct the heat transfer overprediction of the RANS model. For good predictions at low nozzle-plate distance, it is necessary to sufficiently resolve the formation and development of the near-wall vortices in the jet impingement region. At high nozzle-plate distance, the essence is to capture the evolution and breakup of the flow unsteadiness in the shear layer of the jet, so that accurate mean and fluctuating velocity profiles are obtained in the impingement region. Although the models have a quite different theoretical justification and generate a quite different eddy viscosity in some flow regions, their overall results are very comparable. The reason is that in zones that are crucial for the results, the models behave similarly.     

Comparative density functional theory and post-Hartree-Fock (CCSD, CASSCF) studies on the electronic structure of halogen nitrites ClONO and BrONO using quantum chemical topology

In this paper, the electronic structures of cis- and trans-ClONO and BrONO are studied at the CCSD∕aug-cc-pVTZ, CASSCF(14,12)/aug-cc-pVTZ, and B3LYP/aug-cc-pVTZ computational levels. For the Cl-O bond, topological analysis of the electron density field, ρ(r), shows the prevalence of the shared-electron type bond (?(2)ρ((3,-1)) < 0). The Br-O bond, however, represents the closed-shell interaction (?(2)ρ((3,-1)) > 0). Topological analysis of the electron localization function, η(r), and electron localizability indicator (ELI-D), (D) (σ)(r), shows that the electronic structure of the central N-O bond is very sensitive to both electron correlation improvements (coupled-cluster single double (CCSD), CASSCF, density functional theory (DFT)) and bond length alteration. Depending on the method used, the N-O bond can be characterized as a "normal" N-O bond with a disynaptic V(N,O) basin (DFT); a protocovalent N-O bond with two monosynaptic, V(N) and V(O), basins (CCSD, CASSCF); or a new type, first discovered for FONO, characterized by a single monosynaptic, V(N) basin (CCSD, DFT). The total basin population oscillates between 0.46-0.96 e (CCSD) and 0.86-1.02 e (CASSCF). The X-O bond is described by the single disynaptic basin, V(X,O), with a basin population between 0.76 and 0.81 e (CCSD) or 0.77 and 0.85 e (CASSCF). Analysis of the localized electron detector distribution for the cis-Cl-O1-N=O2 shows a manifold in the Cl···O2 region, associated with decreased electron density.     

Electrochemical and STM studies of 1-thio-β-D-glucose self-assembled on a Au(111) electrode surface

In this study, a Au(111) electrode is functionalized with a monolayer of 1-thio-β-D-glucose (β-Tg), producing a hydrophilic surface. A monolayer of β-Tg was formed on a Au(111) surface by either (1) potential-assisted deposition with the thiol in a supporting electrolyte or (2) passive incubation of a gold substrate in a thiol-containing solution. For each method, the properties of the β-Tg monolayer were investigated using cyclic voltammetry (CV), differential capacitance (DC), and chronocoulometry. In addition, electrochemical scanning tunneling microscopy (EC-STM) was used to obtain images of the self-assembled monolayer with molecular resolution. Potential-assisted assembly of β-Tg onto a Au(111) electrode surface was found to be complicated by oxidation of β-Tg molecules. The EC-STM images revealed formation of a passive layer containing honeycomb-like domains characteristic of a formation of S(8) rings, indicating the S-C bond may have been cleaved. In contrast, passive self-assembly of thioglucose from a methanol solution was found to produce a stable, disordered monolayer of β-Tg. Since the passive assembly method was not complicated by the presence of a faradaic process, it is the method of choice for modifying the gold surface with a hydrophilic monolayer.     

Numerical investigation of mid-infrared emission from Pr^{3+} doped GeAsGaSe fibre

The experimentally obtained luminescence characteristics of a praseodymium (Pr $^{3+})$ doped chalcogenide glass fiber are studied numerically using a rate equation approach. The numerical model includes both the radiative and non-radiative transition paths whilst it neglects the up-conversion processes. Photoluminescence spectra at mid-infrared wavelengths ranging from 3.5 to 6   ${\upmu }$ m were obtained by using two pump wavelengths: 1.55 and 1.94   ${\upmu }$ m. A good agreement between the experiment and theory is obtained for the photoluminescence decay profiles.