Mass conservative finite volume discretization of the continuity equations in multi-component mixtures

The Stefan–Maxwell equations for multi-component diffusion result in a system of coupled continuity equations for all species in the mixture. We use a generalization of the exponential scheme to discretize this system of continuity equations with the finite volume method. The system of continuity equations in this work is obtained from a non-singular formulation of the Stefan–Maxwell equations, where the mass constraint is not applied explicitly. Instead, all mass fractions are treated as independent unknowns and the constraint is a result of the continuity equations, the boundary conditions, the diffusion algorithm and the discretization scheme. We prove that with the generalized exponential scheme, the mass constraint can be satisfied exactly, although it is not explicitly applied. A test model from the literature is used to verify the correct behavior of the scheme.     

Analytical theory for permeation of condensable gases in a nanopore

The permeation of a condensable gas mixture in a pressure gradient is examined within a dynamic density functional theory (DDFT). The non-equilibrium density and flux profiles of gas molecules trapped within a nanopore are calculated for each species as a function of feed gas density. Because of important fluid–fluid interaction close to condensation the flux and density gradients are not related by constant transport diffusivities with the thermodynamic correction of uniform density. For long narrow pores the relation of the selectivity to the equilibrium adsorption isotherms is validated. Improved separation is achieved by combining preferential wall interaction and advantageous attraction between gas molecules of different species and examples are discussed. Results from experiments and simulations of permeation in binary mixtures near condensation are still rare and the theory provides a simple basis to study qualitative trends using known parameters.     

Selective self-organization of guest molecules in self-assembled molecular boxes

This article describes the synthesis and binding properties of highly selective noncovalent molecular receptors 1(3).(DEB)6 and 3(3).(DEB)6 for different hydroxyl functionalized anthraquinones 2. These receptors are formed by the self-assembly of three calix[4]arene dimelamine derivative molecules (1 or 3) and six diethylbarbiturate (DEB) molecules to give 1(3).(DEB)6 or 3(3).(DEB)6. Encapsulation of 2 occurs in a highly organized manner; that is, a noncovalent hydrogen-bonded trimer of 2 is formed within the hydrogen-bonded receptors 1(3).(DEB)6 and 3(3).(DEB)6. Both receptors 1(3).(DEB)6 and 3(3).(DEB)6 change conformation from staggered to eclipsed upon complexation to afford a better fit for the 2(3) trimer. The receptor selectivity toward different anthraquinone derivatives 2 has been studied using 1H NMR spectroscopy, X-ray crystallography, UV spectroscopy, and isothermal microcalorimetry (ITC). The pi-pi stacking between the electron-deficient center ring of the anthraquinone derivatives 2a-c and 2e-g and the relatively electron-poor melamine units of the receptor is the driving force for the encapsulation of the guest molecules. The selectivity of the hydrogen-bonded host for the anthraquinone derivatives is the result of steric interactions between the guest molecules and the calix[4]arene aromatic rings of the host.     

Synthesis of N-(Dimethylsulfamoyl)aldimines,a New Type of Aldimine Derivative

N-(Dimethylsulfamoyl)aldimines (3) a new type of shelf-stable aldimine derivatives, are readily prepared from aldehydes and N-(dimethylsulfamoyl)amide (2) in refluxing toluene.     

Solution- and solid-phase synthesis of 4-hydroxy-4,5-dihydroisoxazole derivatives from enantiomerically pure N-tosyl-2,3-aziridine alcohols

[reaction: see text] Enantiomerically pure N-tosyl-2,3-aziridine alcohols are directly converted into 4-hydroxy-4,5-dihydroisoxazole 2-oxides through oxidation to the corresponding aldehydes followed by in situ tandem nitroaldol-intramolecular cyclization. This study was concerned with (i) the selection of a suitable aziridine activation, (ii) the preparation of the target 4-hydroxy-4,5-dihydroisoxazole derivatives in solution, and (iii) the elaboration of a solid-phase process using hydroxy Merrifield-supported nitroacetic acid ester.     

Formation of a hydrogen-bonded receptor assembly in niosomal membranes

The formation of a hydrogen-bonded receptor in niosomal membranes is reported in this communication. The niosomes prepared from non-ionic surfactants C12EO3 and C14EO3 provide a stable system that allows the self-assembly of hydrogen-bonded receptors to occur in contact with aqueous environments. We demonstrate here by CD, TEM and Confocal Microscopy that the incorporation of the building blocks, calix[4]dimelamine 1 and PerBAR, within the niosomal membranes led to the formation of well-defined hydrogen-bonded assembly 13.(PerBAR)6 within these membranes.     

Ring-closing metathesis for the synthesis of side chain knotted pentapeptides inspired by vancomycin

A versatile method for the synthesis of bicyclic side chain knotted peptides inspired by vancomycin is described. The synthetic approach is based on the incorporation of a central amino acid derivative having two allylic groups-introduced by a Stille coupling-into pentapeptide 8 containing two allylated serine residues. Treatment of this bis-ring-closing metathesis precursor with 2nd generation Grubbs catalyst results in the formation of a bicyclic pentapeptide with the correct side chain to side chain connectivity pattern as observed in vancomycin: i- 2 --> i, i --> i + 2. Modelling studies using MacroModel hint at a cavity-like structure of the bicyclic pentapeptide which may bind suitable ligands.     

Vortical structures and turbulent bursts behind magnetic obstacles in transitional flow regimes

The present paper reports on numerical investigations of vortical structures in transient flow regimes generated by the local action of the Lorentz force on an electrically conductive fluid. The locally imposed non-uniform magnetic field generates similar effects as observed for flows over submerged solid obstacles. It is demonstrated that complex flow patterns can be generated by imposing magnetic fields of different strengths. The initial validation of the electromagnetically extended Navier-Stokes solver on unstructured numerical grids is performed in the low-Reynolds number range 100 ? Re ? 400 for different values of the magnetic interaction parameter. A generally good agreement is obtained in comparison with similar numerical studies of [Votyakov et al., 2007] and [Votyakov et al., 2008] for the low-Reynolds number cases. Then, a series of simulations are performed in transitional flow regimes (Re = 900) for different values of the interaction parameter (N = 3, … , 25). Simulations demonstrated the appearance of vortex-shedding phenomena similar to the flows behind solid obstacles. In contrast to the solid obstacles, the magnetic obstacles also generated the vortical flow patterns inside the magnetically affected regions. This feature can be used for the flow control of electrically conductive fluids, for efficient enhancements of the wall-heat transfer or for better mixing of passive scalars. Despite the laminar inflow conditions, turbulent bursts are observed in the magnetic wake region for the Re = 900 case. The velocity spectra and spatial distributions of the long-time averaged second-moments of the velocity field demonstrated that turbulence was locally sustained in the proximity of the magnetic wake edge.     

Generic and typical ranks of multi-way arrays

The concept of tensor rank was introduced in the 20s. In the 70s, when methods of Component Analysis on arrays with more than two indices became popular, tensor rank became a much studied topic. The generic rank may be seen as an upper bound to the number of factors that are needed to construct a random tensor. We explain in this paper how to obtain numerically in the complex field the generic rank of tensors of arbitrary dimensions, based on Terracini’s lemma, and compare it with the algebraic results already known in the real or complex fields. In particular, we examine the cases of symmetric tensors, tensors with symmetric matrix slices, complex tensors enjoying Hermitian symmetries, or merely tensors with free entries.