Hypersurfaces in hyperbolic space with support function

Based on [19], we develop a global correspondence between immersed hypersurfaces ?:Mⁿ→Hⁿ⁺¹$?:{\mathrm{M}}^n\to {\mathbb{H}}^{n+1}$ satisfying an exterior horosphere condition, also called here horospherically concave hypersurfaces, and complete conformal metrics e^2ρ_gSn$e^{2\rho }{g}_{{\mathbb{S}}^n}$ on domains Ω in the boundary Sⁿ${\mathbb{S}}^n$ at infinity of Hⁿ⁺¹${\mathbb{H}}^{n+1}$, where ρ   is the horospherical support function, _∂∞?(Mⁿ)=∂Ω${\partial }_{\infty }?({\mathrm{M}}^n)=\partial \mathrm{\Omega }$, and Ω is the image of the Gauss map G:Mⁿ→Sⁿ$G:{\mathrm{M}}^n\to {\mathbb{S}}^n$. To do so we first establish results on when the Gauss map G:Mⁿ→Sⁿ$G:{\mathrm{M}}^n\to {\mathbb{S}}^n$ is injective. We also discuss when an immersed horospherically concave hypersurface can be unfolded along the normal flow into an embedded one. These results allow us to establish general Alexandrov reflection principles for elliptic problems of both immersed hypersurfaces in Hⁿ⁺¹${\mathbb{H}}^{n+1}$ and conformal metrics on domains in Sⁿ${\mathbb{S}}^n$. Consequently, we are able to obtain, for instance, a strong Bernstein theorem for a complete, immersed, horospherically concave hypersurface in Hⁿ⁺¹${\mathbb{H}}^{n+1}$ of constant mean curvature.     

Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests

This article reports on the potential of application of LES in the calculation of turbulent two-phase flows, in the case where each phase is resolved and interfaces remain much larger than the mesh size. In comparison with single-phase flow, successful application of LES to resolve two-phase flow problems should account for the complex interaction between turbulence and interfaces. Non-linear transfers of turbulent energy across the interface have to be accurately modeled. The derivation of the complete filtered two-phase flow governing equations has been formulated to deal with turbulence at the interface in a comprehensive and practical way. Explicit filtering of 2D direct numerical simulations has been employed to evaluate the order of magnitude of the new subgrid contributions. A parametric study on the academic test case of two counter-rotative vortices and a more complex test case of phase inversion in a closed box have been utilized to perform an order of magnitude analysis of different transport mechanisms. Important features of turbulent energy transfer across the interface have been discussed. Analyses of the numerical results have been conducted to derive conclusions on the relative importance of the different subgrid scale contributions, and modeling issues and solutions are provided.     

H2 evolution and molecular electrocatalysts: determination of overpotentials and effect of homoconjugation

In an effort to standardize the determination of overpotential values for H(2)-evolving catalysts in non-aqueous solvents and allow a reliable comparison of catalysts prepared and assayed by different groups, we propose to adopt the half-wave potential as reference potential. We provide a simple method for measuring it from usual stationary cyclic voltammograms, and we derive the formulas to which the measured potential should be compared, taking into account the effect of homoconjugation. We also revisit tabulated values of the standard reduction potential of protons in nonaqueous solvents, E(H+/H(2))°.     

Effects of surface properties of different substrates on fine structure of plasma-polymerized SiOCH films prepared from hexamethyldisiloxane (HMDSO)

In this study, Doppler broadening energy spectroscopy (DBES) combined with slow positron beam was used to discuss the effect of substrate types on the fine structure of a plasma-polymerized SiOCH layer as a function of depth. From the SEM pictures, the SiOCH films formed on different substrates showed hemispherical macrostructures, and the deposition rate was dependent on the mean pore size. It appears that the morphology of the plasma-polymerized SiOCH films was associated with the porosity-related characteristics of the substrate such as the size/shape of pores. As deposited on the MCE-022 substrate (mixed cellulose esters membrane with a mean pore size of 0.22 μm) with a nodular structure, the SiOCH films had pillar-like structures and high gas permeabilities. DBES results showed that the SiOCH films deposited on different substrates were composed of three layers: the SiOCH bulk layer, the transition layer, and the substrate. It was observed that the microstructure of the SiOCH films was affected layer by layer; a higher surface pore size in the substrates induced thicker transition layers with higher microporosities and led to thinner bulk layers having higher S parameter values during the plasma polymerization. It was also observed that the change in O(2)/N(2) selectivity was consistent with the DBES analysis results. The gas separation performance and DBES analysis results agreed with each other.     

Selenium‐ and Tellurium‐Containing Multifunctional Redox Agents as Biochemical Redox Modulators with Selective Cytotoxicity

Various human diseases, including different types of cancer, are associated with a disturbed intracellular redox balance and oxidative stress (OS). The past decade has witnessed the emergence of redox‐modulating compounds able to utilize such pre‐existing disturbances in the redox state of sick cells for therapeutic advantage. Selenium‐ and tellurium‐based agents turn the oxidizing redox environment present in certain cancer cells into a lethal cocktail of reactive species that push these cells over a critical redox threshold and ultimately kill them through apoptosis. This kind of toxicity is highly selective: normal, healthy cells remain largely unaffected, since changes to their naturally low levels of oxidizing species produce little effect. To further improve selectivity, multifunctional sensor/effector agents are now required that recognize the biochemical signature of OS in target cells. The synthesis of such compounds provides interesting challenges for chemistry in the future.     

Quinobis(imidazolylidene): Synthesis and Study of an Electron‐Configurable Bis(N‐Heterocyclic Carbene) and Its Bimetallic Complexes

Reaction of bromanil with N,N′‐dimesitylformamidine followed by deprotonation with NaN(SiMe₃)₂ afforded 1,1′,3,3′‐tetramesitylquinobis(imidazolylidene) ( 1 ), a bis(N‐heterocyclic carbene) (NHC) with two NHC moieties connected by a redox active p‐quinone residue, in 72 % yield of isolated compound. Bimetallic complexes of 1 were prepared by coupling to FcN₃ ( 2 ) or FcNCS ( 3 ; Fc=ferrocenyl) or coordination to [M(cod)Cl] ( 4 a or 4 b , where M=Rh or Ir, respectively; cod=1,5‐cyclooctadiene). Treatment of 4 a and 4 b with excess CO(g) afforded the corresponding [M(CO)₂Cl] complexes 5 a and 5 b , respectively. Analysis of 2 – 5 by NMR spectroscopy and X‐ray diffraction indicated that the electron‐deficient quinone did not significantly affect the inherent spectral properties or coordination chemistry of the flanking imidazolylidene units, as compared to analogous NHCs. Infrared spectroscopy and cyclic voltammetry revealed that decreasing the electron density at ML_n afforded an increase in the stretching energy and a decrease in the reduction potential of the quinone, indicative of metal–quinone electronic interaction. Differential pulse voltammetry and chronoamperometry of the metal‐centered oxidations in 2 – 4 revealed two single, one‐electron peaks. Thus, the metal atoms bound to 1 are oxidized at indistinguishable potentials and do not appear electronically coupled. However, the metal–quinone interaction was used to increase the electron density at coordinated metal atoms. Infrared spectroelectrochemistry revealed that the average ν_CO values for 5 a and 5 b decreased by 14 and 15 cm^?1, respectively, upon reduction of the quinone embedded within 1 . These shifts correspond to 10 and 12 cm^?1 decreases in the Tolman electronic parameter of this ditopic ligand.