Redox mediation enabled by immobilised centres in the pores of a metal-organic framework grown by liquid phase epitaxy

A layer of a metal-organic framework (SURMOF) was prepared on a thiol monolayer on Au. Charge transport across the insulating membrane could be established by using ferrocene as an immobilised redox mediator. Reversibility of the immobilisation and its role in the electrode kinetics are discussed.     

A mathematical investigation of the Car-Parrinello method

The Car-Parrinello method for ab-initio molecular dynamics avoids the explicit minimization of energy functionals given by functional density theory in the context of the quantum adiabatic approximation (time-dependent Born-Oppenheimer approximation). Instead, it introduces a fictitious classical dynamics for the electronic orbitals. For many realistic systems this concept allowed first-principle computer simulations for the first time. In this paper we study the quantitative influence of the involved parameter , the fictitious electronic mass of the method. In particular, we prove by use of a carefully chosen two-time-scale asymptotics that the deviation of the Car-Parrinello method from the adiabatic model is of order – provided one starts in the ground state of the electronic system and the electronic excitation spectrum satisfies a certain non-degeneracy condition. Analyzing a two-level model problem we prove that our result cannot be improved in general. Received June 14, 1996     

Modelling and Optimization of Cogeneration Plants

Cogeneration plants have a long tradition in Germany and are used to transfrom a given energy into various destination energies, e.g. natural gas into mechanical, electrical and heat energy. In this paper a cogeneration plant composed of several components like gas turbines, waste heat boilers, steam turbines, etc, is modelled in steady state. The thermo-dynamic behaviour of the plant is determined by a set of measured data, which is used to adopt the mathematical model to the real plant. By defining a suitable objective function incorporating e.g. emission trading, an appropriate NLP-solver can be used to solve the generated model which includes several nonlinear constraints. Solutions for different environmental and business conditions are presented, to demonstrate the enormous potential of the proposed method for energy suppliers. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Real-Time Solution of Bi-Level Optimal Control Problems

Bi-level optimal control problems are presented as an extension to classical optimal control problems. Hereby, additional constraints for the primary problem are considered, which depend on the optimal solution of a secondary optimal control problem. A demanding problem is the numerical complexity, since at any point in time the solution of the optimal control problem as well as a complete solution of the secondary problem have to be determined. Hence we deal with two dependent variables in time. The numerical solution of the bi-level problem is illustrated by an application of a container crane. Jerk and energy optimal trajectories with free final time are calculated under the terminal condition that the crane system comes to be at rest at a predefined location. In enlargement additional constraints are investigated to ensure that the crane system can be brought to a rest position by a safety stop at a free but admissible location in minimal time from any state of the trajectory. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weakly Nonlinear Time-Adiabatic Theory

We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations, that is to nonlinear Schrödinger equations in which either the nonlinear coupling constant or, equivalently, the solution is asymptotically small. To this end, a notion of criticality is introduced at which the linear bound states stay adiabatically stable, but nonlinear effects start to show up at leading order in the form of a slowly varying nonlinear phase modulation. In addition, we prove that in the same regime a class of nonlinear bound states also stays adiabatically stable, at least in terms of spectral projections.     

SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control

Parametric nonlinear optimal control problems subject to control and state constraints are studied. Two discretization methods are discussed that transcribe optimal control problems into nonlinear programming problems for which SQP-methods provide efficient solution methods. It is shown that SQP-methods can be used also for a check of second-order sufficient conditions and for a postoptimal calculation of adjoint variables. In addition, SQP-methods lead to a robust computation of sensitivity differentials of optimal solutions with respect to perturbation parameters. Numerical sensitivity analysis is the basis for real-time control approximations of perturbed solutions which are obtained by evaluating a first-order Taylor expansion with respect to the parameter. The proposed numerical methods are illustrated by the optimal control of a low-thrust satellite transfer to geosynchronous orbit and a complex control problem from aquanautics. The examples illustrate the robustness, accuracy and efficiency of the proposed numerical algorithms.     

Sensitivity Analysis for a Class of H 0 1 ${{H_{0}^{1}}}$ -Elliptic Variational Inequalities of the Second Kind

Set-Valued and Variational Analysis - We study the stability of solutions to ${H_{0}^{1}}$ -elliptic variational inequalities of the second kind that contain a non-differentiable Nemytskii...