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Stabilität und Dynamik der Verfassungsprinzipien des Grundgesetzes der Bundesrepublik Deutschland
(2014)
Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. Consequently, stabilization techniques have been proposed A popular stabilization method is Baumgarte's technique, but the choice of parameters to make it robust has been unclear in practice. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.
Many methods have been proposed for the stabilization of higher index differential-algebraic equations (DAEs). Such methods often involve constraint differentiation and problem stabilization, thus obtaining a stabilized index reduction. A popular method is Baumgarte stabilization, but the choice of parameters to make it robust is unclear in practice. Here we explain why the Baumgarte method may run into trouble. We then show how to improve it. We further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature. Our approach is to (i) consider stabilization of ODEs with invariants, (ii) discretize the stabilizing term in a simple way, generally different from the ODE discretization, and (iii) use orthogonal projections whenever possible. The best methods thus obtained are related to methods of coordinate projection. We discuss them and make concrete algorithmic suggestions.
The interest in extensions of the logic programming paradigm beyond the class of normal logic programs is motivated by the need of an adequate representation and processing of knowledge. One of the most difficult problems in this area is to find an adequate declarative semantics for logic programs. In the present paper a general preference criterion is proposed that selects the ‘intended’ partial models of generalized logic programs which is a conservative extension of the stationary semantics for normal logic programs of [Prz91]. The presented preference criterion defines a partial model of a generalized logic program as intended if it is generated by a stationary chain. It turns out that the stationary generated models coincide with the stationary models on the class of normal logic programs. The general wellfounded semantics of such a program is defined as the set-theoretical intersection of its stationary generated models. For normal logic programs the general wellfounded semantics equals the wellfounded semantics.
I perform and analyse the first ever calculations of rotating stellar iron core collapse in {3+1} general relativity that start out with presupernova models from stellar evolutionary calculations and include a microphysical finite-temperature nuclear equation of state, an approximate scheme for electron capture during collapse and neutrino pressure effects. Based on the results of these calculations, I obtain the to-date most realistic estimates for the gravitational wave signal from collapse, bounce and the early postbounce phase of core collapse supernovae. I supplement my {3+1} GR hydrodynamic simulations with 2D Newtonian neutrino radiation-hydrodynamic supernova calculations focussing on (1) the late postbounce gravitational wave emission owing to convective overturn, anisotropic neutrino emission and protoneutron star pulsations, and (2) on the gravitational wave signature of accretion-induced collapse of white dwarfs to neutron stars.