Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation

We employ a piecewise-constant, discontinuous Galerkin method for the time discretization of a sub-diffusion equation. Denoting the maximum time step by k, we prove an a priori error bound of order k under realistic assumptions on the regularity of the solution. We also show that a spatial discretization using continuous, piecewise-linear finite elements leads to an additional error term of order h ² max (1,logk ^− 1). Some simple numerical examples illustrate this convergence behaviour in practice. We thank the University of New South Wales for financial support provided by a Faculty Research Grant.     

Theoretical determination of the favorable mechanism of the reaction between AlX and HX (X = Br, Cl, and F)

The reaction mechanism between AlX and HX (X = Br, Cl, and F) have been characterized in detail using DFT as well as the ab initio method. The reaction yielding AlX₃ and molecular hydrogen was calculated to be highly exothermic. The present calculations also show that the possible routes to the trihalides species start more favorable with the primary insertion product AlX₂H than with the biadduct AlX(HX)₂ one.      

Electro‐Optical Properties of Polymer‐Dispersed Liquid Crystals

This paper deals with the electro‐optic (EO) properties of polymer‐dispersed liquid crystals (PDLCs). Several systems are considered to analyze the effects of preparation conditions and film characteristics on the EO response functions. Particular emphasis is put on systems based on mixtures of the commercial compound ASX‐95, the difunctional acrylate tripropylene diacrylate and the eutectic mixture of low‐molecular‐weight liquid crystals E7. Other systems are considered to assess the influence of monomer functionality on EO properties using for example the trifunctional glycerylpropoxytriacrylate. Various modes of preparing PDLCs are considered based on the mechanism of polymerization‐induced phase separation using either electron‐beam (EB) or UV radiation curing processes. The dose is changed in both techniques to improve film strength and determine which method leads to the best samples in terms of EO response functions. Other important parameters, such as film thickness, composition and applied voltage, are also considered to evaluate the impact on these functions. The article focuses on a comparison of EO performances of films elaborated by exposure to EB and UV radiations. Under similar conditions, one definitively finds a net superiority of the former technique. In addition this technique does not require any photoinitiator and leads to a higher conversion of the monomeric compounds, i.e. higher mechanical strength and less severe aging conditions.