Virtual element methods for parabolic problems on polygonal meshes

The virtual element method (VEM) is a recent technology that can make use of very general polygonal/polyhedral meshes without the need to integrate complex nonpolynomial functions on the elements and preserving an optimal order of convergence. In this article, we develop for the first time, the VEM for parabolic problems on polygonal meshes, considering time‐dependent diffusion as our model problem. After presenting the scheme, we develop a theoretical analysis and show the practical behavior of the proposed method through a large array of numerical tests. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2110–2134, 2015     

Effect of temperature on the physical properties of two ionic liquids

Density, speed of sound, refractive index, and dynamic viscosity of the ionic liquids (ILs) 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide, BMpyr NTf₂, and trihexyl(tetradecyl) phosphonium dicyanamide, P₆₆₆₁₄ dca, were studied as a function of temperature at atmospheric pressure. Thermal expansion coefficient, α_p, molecular volumes, and standard entropies of these ILs were calculated from the experimental density values. The solubility of three aromatic components (benzene, toluene, and ethylbenzene) in the selected ILs was carried out at T = 298.15 K and atmospheric pressure and compared with literature values for sulfolane.     

On non-Newtonian p-fluids. The pseudo-plastic case

In the following we study a class of stationary Navier-Stokes equations with shear dependent viscosity, under the non-slip (Dirichlet) boundary condition. We consider pseudo-plastic fluids. A fluid is said pseudo-plastic, or shear thinning, if in Eq. (1.1) below one has p<2. We are interested in global (i.e., up to the boundary) regularity results, in dimension n=3, for the second order derivatives of the velocity and the first order derivatives of the pressure. We consider a cubic domain Ω and impose the non-slip boundary condition only on two opposite faces. On the other faces we assume periodicity, as a device to avoid effective boundary conditions. This choice is made so that we work in a bounded domain Ω and simultaneously with a flat boundary.     

Test of bell’s inequality using the one-atom micromaser

We examine a local realist bound in the case of a one-atom micromaser. It is shown that such a bound is violated using a simplified treatment of the micromaser. We consider the effect of dissipation in a proposed experiment with the real micromaser. It is seen that the magnitude of violation of a Bell-type inequality depends significantly on the cavity parameters.     

Very short F—H⋯F hydrogen bond in l‐argininium fluoride hydrogen fluoride

There are two symmetry‐independent formula units of the title compound, C₆H₁₅N₄O₂⁺·F^?·HF, per cell. Both cations have a zwitterionic form, protonated at both the guanidyl and amino groups. The two symmetry‐independent cations differ in their conformation. In one of them the C_γ atom is in a gauche position to both the amino and carboxyl groups, while in the other this atom is trans to the amino group. The two anions have very similar geometry. The F^? ions are strongly hydrogen bonded to an HF molecule [F—H?F 2.233 (2) and 2.248 (3) Å], thereby forming an asymmetric non‐linear bifluoride anion. These F?F distances are the shortest reported for an asymmetric HF₂^? anion.     

Benzyl 5‐carboxy‐4‐ethyl‐3‐methyl­pyrrole‐2‐carboxyl­ate

In the title compound, C₁₆H₁₇NO₄, the benzyl­oxy­carbonyl group is anti to the pyrrolic N atom. The mol­ecules are joined into head‐to‐head dimers by hydrogen bonds involving the carboxyl­ic acid groups. There is orientational disorder of these groups over two positions with approximately equal occupancy. A weaker hydrogen bond between the pyrrolic N atom and the carbonyl O atom of the benzyl­oxy­carbonyl group joins the dimers into chains running parallel to the [110] direction.