Reduced-Basis Methods for PDE-Constrained Elliptic Optimal Control Problems with Uncertain Coefficients

This thesis covers a convex optimal control problem, which possesses an elliptic PDE subjected to uncertainty as constraint.It will be shown that with the help of the projected stochastic gradient method an optimal control over a discrete random space can be computed faster than with the projected gradient method. The determination of the necessary finite element (FE) solutions can be speeded-up by use of the reduced basis (RB) method. For the error between the FE and the reduced-order solution a-posteriori error estimates can be denoted for the state and the adjoint equation. The convergence behaviour between the FE and the reduced-order solution will be studied. The numerical results confirm the theoretical results of the convergence behaviour. Furthermore the difference between the optimal solution with and without the RB method can be bounded. The optimization with the projected stochastic gradient method and the RB method turns out to be a more efficient method.publishe

Recent Advances in Microwave-Assisted Polymer Synthesis.

In the past few years the use of microwave irradiation in polymer science has become a well-established technique to drive and promote chemical reactions. The main advantages of microwave heating are a strong reduction in reaction time and a high potential to contribute to green and sustainable chemistry. This article provides a short review of recent examples in the field of microwave-assisted polymer synthesis with special emphasis on radical polymerizations, step-growth polymerizations, ring-opening polymerizations, and polymer modifications

Reversible addition fragmentation chain transfer (RAFT) and hetero-Diels-Alder chemistry as a convenient conjugation tool for access to complex macromolecular designs

The combination of RAFT chemistry and the hetero-Diels-Alder (HDA) cycloaddition was successfully utilized in the synthesis of poly(styrene) (PS) star polymers with up to 4 arms. This variant of the "coupling onto" method of star polymer synthesis was investigated for two different RAFT end groups (diethoxyphosphoryldithioformate and pyridin-2-yldithioformate) and coupling agents bearing 2, 3, or 4 diene functional groups. When a diethoxyphosphoryldithioformate terminated polymer was reacted with the 2-, 3-, and 4-fold functionalized coupling agents, the yields of 2-arm star, 3-arm star, and 4-arm star polymers were 81%, 77%, and 65%, respectively, and when a pyridin-2-yldithioformate terminated polymer was reacted with the same coupling agents, the yields of 2-arm star, 3-arm star and 4-arm star polymers were 91%, 86% and 82% respectively. The HDA coupling reaction was monitored via UV/vis spectroscopy from the perspective of the RAFT end group as well as by 1H NMR spectroscopy from the perspective of the diene functionality. The results of these investigations indicated that the phosphoryldiethoxydithioformate terminated polymer achieves 92% conversion within a 24 h time frame and the pyridin-2-yldithioformate terminated polymer achieves 96% conversion in 10 h. The 4-arm star polymers were also subjected to high-temperature environments, and GPC measurements indicated that complete cleavage of all 4 arms from the core was achieved in 24 h at 160 °C. © 2008 American Chemical Society

A study into the stability of 3,6-dihydro-2H-thiopyran rings: Key linkages in the RAFT hetero-Diels-Alder click concept

The combination of RAFT chemistry and hetero-Diels-Alder (HDA) cycloaddition provides a convenient conjugation tool for the construction of macromolecular architectures. The actual conjugation linkage, which is formed in the RAFT HDA approach, consists of a 3,6-dihydro-2H-thiopyran ring. Herein, a careful study into the stability of polymer linked by 3,6-dihydro-2H-thiopyran rings under different thermal and pH conditions is performed. As polymeric model system, a 3,6-dihydro-2H-thiopyran functionalized poly(ethylene glycol) (PEG) obtained after a HDA cycloaddition between a diene functionalized PEG and 1-phenylethyl (diethoxyphosphoryl)dithioformate or 1-phenylethyl pyridin-2-yldithioformate is used. Electrospray ionization mass spectrometry (ESI-MS) is employed to map the generated products. The stability tests under thermal conditions showed for the diethoxyphosphoryl derivative the preservation of the polymer end-groups after 24 h at temperatures up to 80°C. At higher temperatures degradation reactions of the 3,6-dihydro-2H-thiopyran ring including the retro HDA reaction occurred. A complete fragmentation was observed after 24 h at 160°C. The pyridinyl derivative was found to be slightly more temperature stable since its structure was unaffected at conditions up to 24 h at 120°C and full cleavage was only observed after 24 h at 180°C. In this case the fragmentation mechanism occurred exclusively via the retro HDA reaction and the resulting diene functionalized polymer was the only detected product species. Both conjugates showed an excellent stability toward hydrolysis in aqueous media under strong acidic (0.1 and 1 M HCL) and strong basic (0.1 and 1 M NaOH) conditions. © 2008 American Chemical Society