The kinetics of oxiranes addition to bis/2-hydroxyalkyl/disulfides and bis/2-hydroxyalkyl/sulfides in the presence of N,N-dimethylcyclohexylamine

Rate constants for the reaction of oxiranes with bis/2-hydroxyalkyl/disulfides, bis/2-Hydroxyalkyl/sulfides, and 1,6-Hexanediol in the presence of N,N-dimethylcyclohexylamine were studied at the temperature range of 50–90°C. A mechanism of these reactions has been proposed and its kinetic equation has been presented.     

Numerical study of the flow in a three-dimensional thermally driven cavity

Solutions for the fully compressible Navier–Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied.     

Some fractal properties of the percolating backbone in two dimensions

A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that the fractal dimensionality of the backbone isd _f ^BB =1.61±0.01, the chemical dimensionality isd _t=1.40±0.01, and the fractal dimension of the minimum pathd _min=1.15 ± 0.02 for the two-dimensional triangular lattice.     

A tropical approach to secant dimensions

Tropical geometry yields good lower bounds, in terms of certain combinatorial-polyhedral optimisation problems, on the dimensions of secant varieties. The approach is especially successful for toric varieties such as Segre-Veronese embeddings. In particular, it gives an attractive pictorial proof of the theorem of Hirschowitz that all Veronese embeddings of the projective plane except for the quadratic one and the quartic one are non-defective; and indeed, no Segre-Veronese embeddings are known where the tropical lower bound does not give the correct dimension. Short self-contained introductions to secant varieties and the required tropical geometry are included.     

The discrete maximum principle for linear simplicial finite element approximations of a reaction-diffusion problem

This paper provides a sufficient condition for the discrete maximum principle for a fully discrete linear simplicial finite element discretization of a reaction-diffusion problem to hold. It explicitly bounds the dihedral angles and heights of simplices in the finite element partition in terms of the magnitude of the reaction coefficient and the spatial dimension. As a result, it can be computed how small the acute simplices should be for the discrete maximum principle to be valid. Numerical experiments suggest that the bound, which considerably improves a similar bound in [P.G. Ciarlet, P.-A. Raviart, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Eng. 2 (1973) 17-31.], is in fact sharp.     

ERROR ESTIMATES FOR THE TIME DISCRETIZATION FOR NONLINEAR MAXWELL＇S EQUATIONS

This paper is devoted to the study of a nonlinear evolution eddy current model of the type δtB（H） ＋ △↓× （ △↓ × H） =0 subject to homogeneous Dirichlet boundary conditions H × v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B（H）. We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B（H）.     

Self-consistent Monte Carlo simulations of the electron and ion distributions of inhomogeneous liquid alkali metals. II. Longitudinal and transverse density distributions in the liquid-vapor interface of binary metallic alloys

We present the results of Monte Carlo simulations of the liquid-vapor interface of sodium-cesium alloys. The longitudinal density profile of each alloy shows that the liquid-vapor interface consists of a well-defined monolayer of cesium sitting on top of a slab of the bulk alloy. Underneath the monolayer there is a slight excess of sodium. A comparison with a van der Waals analog of one of the alloys shows that the presence of the well-defined monolayer of cesium on the outside of the liquid-vapor interface is a feature peculiar to metallic mixtures. The transverse pair correlation functions of the cesium monolayer are insensitive to the composition of the bulk of the slab.     

1,5‐Dianilinopentane‐1,3,5‐trione: a crystal structure containing two polymorphic domains

Single crystals of the title compound, C₁₇H₁₆N₂O₃, were obtained by gas diffusion. The observed diffraction pattern is compatible with a superposition of reflections from two monoclinic unit cells with the space group C2/c. The two cells share the a and b axes but not the c axis. Both structures contain layers parallel to (001), with molecules connected by intermolecular N—H...O=C hydrogen bonds. The bonding between adjacent layers is weak. Layer displacements result in a crystal structure containing two closely related polymorphic domains. The structure of one polymorph can be derived from the structure of the other if subsequent layers are displaced by (a/4, b/4, 0) for odd‐numbered layers and by (a/4, −b/4, 0) for even‐numbered layers. Three different crystals were analysed and their observed diffraction patterns were similar, showing all three crystals to contain the polymorphic domain structure.