Quasi-Herglotz functions and convex optimization.

We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modelling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.

Communication: Band bending at the interface in polyethylene-MgO nanocomposite dielectric.

Polymer nanocomposite dielectrics are promising materials for electrical insulation in high voltage applications. However, the physics behind their performance is not yet fully understood. We use density functional theory to investigate the electronic properties of the interfacial area in magnesium oxide-polyethylene nanocomposite. Our results demonstrate polyethylene conduction band matching with conduction bands of different surfaces of magnesium oxide. Such band bending results in long range potential wells of up to 2.6 eV deep. Furthermore, the fundamental influence of silicon treatment on magnesium oxide surface properties is assessed. We report a reduction of the surface-induced states at the silicon-treated interface. The simulations provide information used to propose a new model for charge trapping in nanocomposite dielectrics.