Experimental determination and prediction of (solid + liquid) phase equilibria for binary mixtures of heavy alkanes and fatty acids methyl esters

Solid–liquid equilibria for three binary mixtures of {n-eicosane (1) + methyl palmitate (2)}, {n-tetracosane (1) + methyl stearate (2)} and {n-octacosane (1) + methyl stearate (2)} were measured using differential scanning calorimeter. Simple eutectic behaviours for these systems were observed. The experimental results were correlated by means of the modified UNIFAC (Larsen and Gmehling versions), UNIQUAC and ideal models. The root-mean-square deviations of the solubility temperatures for all measured data vary from 0.21 K (for UNIQUAC model) to 1.07 K (for Ideal model) and depend on the particular model used. The best solubility correlation was obtained with UNIQUAC model.     

A practical implementation of high‐order RKDG models for the 1D open‐channel flow equations

This paper comprises an implementation of a fourth‐order Runge–Kutta discontinuous Galerkin (RKDG4) scheme for computing the open‐channel flow equations. The main features of the proposed methodology are simplicity and easiness in the implementation, which may be of possible interest to water resources numerical modellers. A version of the RKDG4 is blended with the Roe Riemann solver, an adaptive high‐order slope limiting procedure, and high‐order source terms approximations. A comparison of the performance of the proposed method with lower‐order RKDG models is performed showing a benefit of considering the RKDG4 model. The scheme is applied to computerize the Saint Venant system by considering benchmark tests that have exact solutions. Finally, numerical results are illustrated discussing the performance of the proposed high‐order model. Copyright © 2008 John Wiley & Sons, Ltd.     

Classification of torsion-free genus zero congruence groups

We study and classify all torsion-free genus zero congruence subgroups of the modular group.

     

A ruthenium(II) complex with p‐cymene and (S)‐2‐(anilinomethyl)pyrrolidine

The title compound, [(S)‐2‐(anilino­methyl)­pyrrolidine‐N,N′]‐chloro(η⁶‐para‐cymene)­ruthenium(II) chloride, [RuCl‐(C₁₀H₁₄)(C₁₁H₁₆N₂)]Cl, has been synthesized by the reaction of [RuCl₂(p‐cymene)]₂ (p‐cymene is para‐iso­propyl­toluene) with (S)‐2‐(anilinomethyl)­pyrrolidine in triethyl­amine/2‐propanol. The Ru atom is in a pseudo‐tetrahedral environment coordinated by a chloride ligand, the aromatic hydro­carbon is linked in a η⁶ manner and the amine is linked via its two N atoms. The chloride anion is involved in hydrogen bonding with the di­amine moieties through N—H?Cl interactions, with N?Cl distances of 3.273 (4) and 3.352 (4) Å.     

High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs

We consider the problem of Lagrange polynomial interpolation in high or countably infinite dimension, motivated by the fast computation of solutions to partial differential equations (PDEs) depending on a possibly large number of parameters which result from the application of generalised polynomial chaos discretisations to random and stochastic PDEs. In such applications there is a substantial advantage in considering polynomial spaces that are sparse and anisotropic with respect to the different parametric variables. In an adaptive context, the polynomial space is enriched at different stages of the computation. In this paper, we study an interpolation technique in which the sample set is incremented as the polynomial dimension increases, leading therefore to a minimal amount of PDE solving. This construction is based on the standard principle of tensorisation of a one-dimensional interpolation scheme and sparsification. We derive bounds on the Lebesgue constants for this interpolation process in terms of their univariate counterpart. For a class of model elliptic parametric PDE’s, we have shown in Chkifa et al. (Modél. Math. Anal. Numér. 47(1):253–280, 2013) that certain polynomial approximations based on Taylor expansions converge in terms of the polynomial dimension with an algebraic rate that is robust with respect to the parametric dimension. We show that this rate is preserved when using our interpolation algorithm. We also propose a greedy algorithm for the adaptive selection of the polynomial spaces based on our interpolation scheme, and illustrate its performance both on scalar valued functions and on parametric elliptic PDE’s.     

Inexact proximal point method for general variational inequalities

In this paper, we suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor-corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.     

On‐line Determination of Particle Size Distributions in Flowing Dispersions

Emulsions are of great importance to industry. They are involved in many engineering operations, including chemical reactions, extraction, emulsification and suspension polymerization, etc. However, an important problem for these processes is how to control the size distribution of the dispersed phase. Indeed, off‐line analysis of the emulsion may generate uncertainties due to sampling and dilution of the product, which are likely to change the dispersion state and physico‐chemical properties. In this work, an on‐line optical method is proposed to characterize dispersed media in real flowing conditions. This method is based on the time‐analysis of back‐scattered light fluctuations. The present paper deals with the development of this method and its application to dispersions of alumina in water. The results obtained with the on‐line optical method are compared with those acquired by classical laser light scattering and microscopy.     

Structure determination of Na3DySi6O15 and crystal chemistry of zektzerite related compounds

The crystal structure of Na₃DySi₆O₁₅ has been solved and refined to an R₁=2.97% (wR₂=8.25%) for 1311 independent reflections. The compound was found to crystallize within the orthorhombic system with the space group Cmca (Z=8) and the lattice parameters: a=14.590(7) Å, b=17.813(4) Å, c=10.519(2) Å, V=2734.0 Å³, D_cal=3.11 g/cm³. The structure of Na₃DySi₆O₁₅ is a filled variant of the zektzerite with S like corrugated double chains of [SiO₄] tetrahedral, connected via Na⁺ and Dy³⁺ cations and running parallel to c-axis. The three-dimensional network results from the packing of these chains along [100] by skewering them in rods represented by the tunnels delimited by the S shape of the silicate chains. One of the main peculiar features of the Na₃DySi₆O₁₅ structure is the location of Na⁺ in tetrahedral sites with rather short Na-O bond lengths (2×2.243 and 2×2.262 Å).     

Enzymatic detoxification of jojoba meal and effect of the resulting meal on food intake in rats

When defatted jojoba meal is used as animal food, it causes food-intake reduction and growth retardation. Detoxification procedures by chemical, microbiological, and solvent extraction methods are reported by several authors. Here we report a successful detoxification of jojoba meal using enzymes. We establish reaction conditions that yield new meal which has the same nutritional qualities in proteins as the original meal. The enzymatic reaction gives rise to one major compound to which the structure of an amide is assigned on the basis of IR, 1H and 13C NMR spectra. The effect of the resulting jojoba meal on the food intake in rats is checked. In contrast, the detoxified meal containing the amide derivatives shows no toxicological activity since rats receiving oral administration of the obtained meal show normal growth. Thus, it is expected that this meal could be used as an animal feed ingredient.