Experiments on the stability of an impulsively-initiated circular Couette flow

Experiments were performed to study the stability characteristics of an unsteady circular Couette flow generated by an impulsive stop of the outer cylinder; the initial condition was a state of rigid-body rotation. Instability of the unsteady basic state is manifested by Görtler vortices, which themselves become unstable to longer-wavelength disturbances, or Taylor vortices which persist indefinitely. The quantities of primary interest are the onset time of instability, the axial vortex wavelength at onset, and the time-evolution of this wavelength. A one-dimensional photodiode array is used to gather data from the flow, which is seeded with flow-visualization material. At sufficiently high values of the Reynolds number, the influence of the inner cylinder on the onset of instability is negligible, based on comparisons with previous experimental data.     

Die quantitative Analyse der Sulfochloride aromatischer K?rper

Ohne Zusammenfassung     

Regularization for semilinear elliptic optimal control problems with pointwise state and control constraints

In this paper a class of semilinear elliptic optimal control problem with pointwise state and control constraints is studied. We show that sufficient second order optimality conditions for regularized problems with small regularization parameter can be obtained from a second order sufficient condition assumed for the unregularized problem. Moreover, error estimates with respect to the regularization parameter are derived.     

A Priori Error Estimates for State-Constrained Semilinear Parabolic Optimal Control Problems

We consider the finite element discretization of semilinear parabolic optimization problems subject to pointwise in time constraints on mean values of the state variable. In order to control the feasibility violation induced by the discretization, error estimates for the semilinear partial differential equation are derived. Based upon these estimates, it can be shown that any local minimizer of the semilinear parabolic optimization problems satisfying a weak second-order sufficient condition can be approximated by the discretized problem. Rates for this convergence in terms of temporal and spatial discretization mesh sizes are provided. In contrast to other results in numerical analysis of optimization problems subject to semilinear parabolic equations, the analysis can work with a weak second-order condition, requiring growth of the Lagrangian in critical directions only. The analysis can then be conducted relying solely on the resulting quadratic growth condition of the continuous problem, without the need for similar assumptions on the discrete or time semidiscrete setting.     

Numerical simulation of isothermal nonwetting

A numerical simulation of isothermal wetting suppression in the presence of shear is considered during which wetting may be prevented when a drop approaches a moving wall. Air is driven into the passage between the solid and liquid surfaces by viscous action, preventing wetting. Silicone‐oil and water drops are investigated for different wall velocities and wall distances. The droplet dimples at the upstream side and bulges at the downstream side when nonwetting occurs. The free‐surface deformation can be enlarged by either increasing the wall velocity or decreasing the wall distance. The low‐viscosity silicone‐oil used in these calculations is much more sensitive to shear wetting suppression than is water, because the Weber number of the silicone‐oil is larger than that of water. Copyright © 2006 John Wiley & Sons, Ltd.     

Strategies for time-dependent PDE control with inequality constraints using an integrated modeling and simulation environment

In Neitzel et al. (Strategies for time-dependent PDE control using an integrated modeling and simulation environment. Part one: problems without inequality constraints. Technical Report 408, Matheon, Berlin, 2007) we have shown how time-dependent optimal control for partial differential equations can be realized in a modern high-level modeling and simulation package. In this article we extend our approach to (state) constrained problems. “Pure” state constraints in a function space setting lead to non-regular Lagrange multipliers (if they exist), i.e. the Lagrange multipliers are in general Borel measures. This will be overcome by different regularization techniques. To implement inequality constraints, active set methods and barrier methods are widely in use. We show how these techniques can be realized in a modeling and simulation package. We implement a projection method based on active sets as well as a barrier method and a Moreau Yosida regularization, and compare these methods by a program that optimizes the discrete version of the given problem. Ira Neitzel’s research was supported by the DFG Schwerpunktprogramm SPP 1253. Uwe Prüfert’s research was supported by the DFG Research Center Matheon. Thomas Slawig’s research was supported by the DFG Cluster of Excellence The Future Ocean and the DFG Schwerpunktprogramm SPP 1253. Website     

Manufacturing and Testing of Composite Materials and Structures. European Cooperative Research Examples

This article describes several European cooperative research examples in the field of polymer composite materials. The projects, which were carried out in collaboration between industrial and academic partners, were all supported by the European Union. They deal, e.g., with (a) the manufacturing and crash testing of thermoplastic composite structures, (b) the production of thermoplastic composite preforms, and (c) the energy absorption behavior of aluminum foams, and other interesting subjects.