Minimal orbits of isotropy actions for the classical root systems with simply-laced Dynkin diagrams

Wir betrachten die Lage der eindeutigen minimalen Hauptbahn einer Isotropiewirkung eines einfach zusammenhängenden symmetrischen Raumes kompakten Typs mit Wurzelsystem A_n bzw. D_n. Nach einer Identifizierung des Bahnenraumes mit einer verallgemeinerten Weyl-Kammer, geben wir für A_n die Lage der minimalen Hauptbahn in der dominanten verallgemeinerten Weyl-Kammer explizit an. Für D_n geben wir ein Ergebnis an, welches es uns erlaubt die Lage der minimalen Hauptbahn in der dominanten verallgemeinerten Weyl-Kammer aus den Nullstellen eines Polynoms zu bestimmen, dessen Form wir explizit angeben

A Generic Parametric Modeling Engine Targeted Towards Multidisciplinary Design: Goals and Concepts

This paper presents the design concept of a generic parametric modeling engine that is completely decoupled from geometry generation. Driven by requirements extracted from preliminary multidisciplinary airplane design, the presented software architecture provides a platform that enables an interplay of different modeling and simulation tools on the one hand, and their efficient execution in a parametric tree on the other hand. An integrated plugin system allows users to define custom plugins exposing arbitrary types and functions. All geometric functionality is provided via plugins, decoupling it entirely from the parametric engine. First, we specify the goals that the software framework needs to fulfill, elaborating on the requirements encountered in early aircraft design. Then, we describe the software architecture and its modules, realized as a C++ library. As such, the software is a back-end that can be used by third party developers to create user-friendly and interoperable tools. The core of the framework is a parametric engine called grunk with its integrated plugin system and serialization functionality. The key feature of grunk is the possibility for users to define custom types in plugins and their use in the parametric tree. Geometric modeling functionalities are provided through the plugins grocc and geo: the first integrating OpenCascade Technology's functionalities and the latter extending it. A major feature on the geometry side is the provision of derivatives through algorithmic differentiation, making the framework particularly suitable for gradient-based optimization applications. Finally, we demonstrate the use of the software via examples and show the results