Static electric fields in an infinite plane condensor with one or three homogeneous layers

Various expressions are derived for the Green's functions for a point charge in an infinite plane condensor comprising one or three homogeneous isolating parallel dielectric layers. In view of numerical evaluations needed for calculating space charge effects in detectors (e.g. RPC's) the merits of these (series and integral) representations are discussed. It turns out that in most cases the integral representations are more favourable after their convergence has been improved. This is done by subtracting simple terms having the same asymptotic behaviour as certain too slowly converging terms and adding closed expressions resulting from the integration of the simple terms. The method is demonstrated in some detail. In addition analytic expressions for the weighting field of a strip electrode are derived which allow calculation of induced signals and crosstalk

Analytic expressions for static electric fields in an infinite plane condenser with one or three homogeneous layers

Expressions for the electrostatic field of a point charge in an infinite plane condenser comprising one or three homogeneous isolating parallel dielectric layers are presented. These solutions are essential for detector physics simulations of Parallel Plate Chambers (PPCs) and Resistive Plate Chambers (RPCs). In addition, expressions for the weighting field of a strip electrode are presented which allow calculation of induced signals and crosstalk in these detectors. A detailed discussion of the derivation of these solutions can be found in \cite{schnizer}

Mathematical optimization of a plate volume under a p-Laplace partial differential equation constraint by using standard software

A main aspect in the design of passenger cars with respect to pedestrian safety is the energy absorption capability of the engine hood. Besides that, the hood has to fulfill several other requirements. That makes it necessary to develop easy and fast to solve prediction models with little loss in accuracy for optimization purpose. Current simulation tools combined with standard optimization software are not well suited to deal with the above mentioned needs. The present paper shows the application of mathematical methods on a simplified self developed model to reduce the optimization effort. A linear and a nonlinear model are introduced and a way for solving both is pointed out. Finally it is shown, that it is possible to simplify models and get optimization results much faster by using mathematical theory. Such results can be used in support of the original problem or as an input to space mapping based optimization algorithms, such as surrogate optimization