Solubility of Solid 2-Methyl-1,3-butadiene (Isoprene) in Liquid Argon and Nitrogen at the Standard Boiling Points of the Solvents

The solubility of solid 2-methyl-1,3-butadiene (isoprene) in liquid argon at a temperature of 87.3 K and in liquid nitrogen at 77.4 K has been measured by the filtration method. The hydrocarbon contents in solutions were determined using gas chromatography. GC–MS was used to identify impurities in the solute. The experimental value of the mole fraction solubility of solid isoprene in liquid argon at 87.3 K is (1.41 ± 0.27) × 10^–6 and (1.56 ± 0.36) × 10^–7 in liquid nitrogen at 77.4 K. The Preston–Prausnitz method was used for calculation of the solubilities of solid hydrocarbon in liquid argon in the temperature range 84.0–110.0 K and in liquid nitrogen from 64.0 to 90.0 K. The solvent–solute interaction parameters l ₁₂ were also calculated. At 90.0 K liquid argon is a better solvent for isoprene than is liquid nitrogen. The experimental values of the solubilities of isoprene in liquid argon and nitrogen were compared with results obtained for selected unsaturated and aromatic hydrocarbons.     

Solubility of Solid 2,3-Dimethylbutane and Cyclopentane in Liquid Argon and Nitrogen at the Standard Boiling Points of the Solvents

The solubilities of solid 2,3-dimethylbutane and cyclopentene in liquid argon at a temperature of 87.3 K and in liquid nitrogen at 77.4 K have been measured by the filtration method. The hydrocarbon contents in solutions were determined using gas chromatography. GC–MS was used to identify impurities in solutes. The experimental value of the mole fraction solubility of solid 2,3-dimethyl-butane in liquid argon at 87.3 K is (8.26 ± 1.60) × 10^–6 and (2.77 ± 0.94) × 10^–8 in liquid nitrogen at 77.4 K. The experimental value of the mole fraction solubility of solid cyclopentene in liquid argon at 87.3 K is (5.11 ± 0.44) × 10^–6 and (4.60 ± 0.76) × 10^–8 in liquid nitrogen at 77.4 K. The Preston–Prausnitz method was used for calculation of the solubilities of solid hydrocarbons in liquid argon in the temperature range 84.0–110.0 K and in liquid nitrogen from 64.0 to 90.0 K. The solvent–solute interaction parameters l ₁₂ were also calculated. At 90.0 K liquid argon is a better solvent for investigated solid hydrocarbons than is liquid nitrogen.     

Analysis of the anisotropy of group velocity error due to spatial finite difference schemes from the solution of the 2D linear Euler equations

Numerical differencing schemes are subject to dispersive and dissipative errors, which in one dimension, are functions of a wavenumber. When these schemes are applied in two or three dimensions, the errors become functions of both wavenumber and the direction of the wave. For the Euler equations, the direction of flow and flow velocity are also important. Spectral analysis was used to predict the error in magnitude and direction of the group velocity of vorticity–entropy and acoustic waves in the solution of the linearised Euler equations in a two‐dimensional Cartesian space. The anisotropy in these errors, for three schemes, were studied as a function of the wavenumber, wave direction, mean flow direction and mean flow Mach number. Numerical experiments were run to provide confirmation of the developed theory. Copyright © 2012 John Wiley & Sons, Ltd.     

Some Aspects of Magnetic Filtration Theory for Removal of Fine Particles from Aqueous Suspensions

The magnetic filtration theory was evaluated to intensify the filtration of industrial fluids by magnetic filters. Effects of filtration velocity and external magnetic field intensity on filter performance were investigated and the dependence of the logarithmic efficiency coefficient on filtration velocity was questioned. It was concluded that change in the magnetic susceptibility of the dispersion particles, caused by external magnetic field, and change in the flow rate properties of the liquid alongside the filter pores are the most essential factors to be considered in the design, development, and modeling of magnetic filtration systems in various industrial areas.     

TMTSF2X Salts. Preparation,Structure and Effect of the Anions

The preparation of the TMTSF molecule and some of its properties are reviewed. The preparation of metallic and superconducting TMTSF X salts is described and some structural aspects are discussed, with emphasis of possible order-disorder transitions when X is a non-centrosymmetric anion. Preliminary results for TMTSF₂ TeF₅ which remain conducting to at least 5 K are presented.     

A Brylinski filtration for affine Kac–Moody algebras

Braverman and Finkelberg have recently proposed a conjectural analogue of the geometric Satake isomorphism for untwisted affine Kac–Moody groups. As part of their model, they conjecture that (at dominant weights) Lusztig's q-analog of weight multiplicity is equal to the Poincare series of the principal nilpotent filtration of the weight space, as occurs in the finite-dimensional case. We show that the conjectured equality holds for all affine Kac–Moody algebras if the principal nilpotent filtration is replaced by the principal Heisenberg filtration. The main body of the proof is a Lie algebra cohomology vanishing result. We also give an example to show that the Poincare series of the principal nilpotent filtration is not always equal to the q-analog of weight multiplicity. Finally, we give some partial results for indefinite Kac–Moody algebras.     

Shear modulus determination in model hydrogels by means of elongated magnetic nanoprobes

The mechanical characterization of complex soft matter by quasi-static magnetometry using nanoscopic magnetic probes is demonstrated for model hydrogels doped with two types of elongated magnetic nanoparticles. Chemically crosslinked poly(acrylamide) (PAAm) hydrogels serve as the matrix in which nickel nanorods or weakly magnetized hematite (α-Fe₂O₃) ellipsoids are embedded as local probes. We investigated the swelling behavior of the ferrogels in order to verify that their equilibrium swelling degree in water is not influenced by the probes, shows a good correlation with the Frenkel–Flory–Rehner model. The proposed magnetomechanical method relies on a correlation between the shear modulus of the PAAm hydrogel matrix and the coercive fields of the corresponding isotropic ferrogels. By extending the Stoner–Wohlfarth model for single-domain blocked magnetic particles by a term for particle rotation in an elastic matrix, information on the shear modulus of the matrix can be obtained. Comparison of the results with the expected relation from rubber elasticity theory illustrates both the general potential as well as the limits of the approach. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Robust multilevel methods for quadratic finite element anisotropic elliptic problems

This paper discusses a class of multilevel preconditioners based on approximate block factorization for conforming finite element methods employing quadratic trial and test functions. The main focus is on diffusion problems governed by a scalar elliptic partial differential equation with a strongly anisotropic coefficient tensor. The proposed method provides a high robustness with respect to non‐grid‐aligned anisotropy, which is achieved by the interaction of the following components: (i) an additive Schur complement approximation to construct the coarse‐grid operator; (ii) a global block (Jacobi or Gauss–Seidel) smoother complementing the coarse‐grid correction based on (i); and (iii) utilization of an augmented coarse grid, which enhances the efficiency of the interplay between (i) and (ii). The performed analysis indicates the high robustness of the resulting two‐level method. Moreover, numerical tests with a nonlinear algebraic multilevel iteration method demonstrate that the presented two‐level method can be applied successfully in the recursive construction of uniform multilevel preconditioners of optimal or nearly optimal order of computational complexity. Copyright © 2013 John Wiley & Sons, Ltd.