University of Paderborn

About: University of Paderborn is a education organization based out in Paderborn, Nordrhein-Westfalen, Germany. It is known for research contribution in the topics: Computer science & Context (language use). The organization has 6684 authors who have published 16929 publications receiving 323154 citations.

The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems

Abstract: In a given dynamical system there are essentially two different types of information which could be of practical interest: on the one hand there is the need to describe the behavior of single trajectories in detail This information is helpful for the analysis of transient behavior and also in the investigation of geometric properties of dynamical systems On the other hand, if the underlying invariant set is generated by complicated dynamics then the computation of single trajectories may give misleading results In this case there still exists important set related information covering both topological and statistical aspects of the underlying dynamical behavior Within the DFG-Schwerpunkt we have focussed on the development of set oriented methods for the numerical approximation of invariant sets (eg invariant manifolds, global attractors, chain recurrent sets) (natural) invariant measures almost invariant sets

Fast Nucleation and Growth of ZIF‐8 Nanocrystals Monitored by Time‐Resolved In Situ Small‐Angle and Wide‐Angle X‐Ray Scattering

Abstract: Prenucleation clusters: in situ synchrotron X-ray scattering with a one-second time resolution revealed the occurrence of nano-sized clusters during the nucleation and early growth of nanocrystals of a zeolitic imidazolate framework (ZIF). The complex crystallization process exhibits similarities with crystallization processes of zeolites from solution. Hmim= 2-methylimidazole.

Discrete mechanics and optimal control: an analysis ∗

Abstract: The optimal control of a mechanical system is of crucial importance in many application areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. The approach proposed in this paper is to directly discretize the variational description of the system's motion. The resulting optimization algorithm lets the discrete solution directly inherit characteristic structural properties from the continuous one like symmetries and integrals of the motion. We show that the DMOC (Discrete Mechanics and Optimal Control) approach is equivalent to a finite difference discretization of Hamilton's equations by a symplectic partitioned Runge-Kutta scheme and employ this fact in order to give a proof of convergence. The numerical performance of DMOC and its relationship to other existing optimal control methods are investigated.