Atmospheric chemistry of diazomethane – an experimental and theoretical study

The kinetics of the O₃, OH and NO₃ radical reactions with diazomethane were studied in smog chamber experiments employing long-path FTIR and PTR-ToF-MS detection. The rate coefficients were determined to be k _CH2NN+O3?=?(3.2?±?0.4)?×?10^?17 and k _CH2NN+OH?=?(1.68?±?0.12)?×?10^?10 cm³ molecule^?1 s^?1 at 295?±?3?K and 1013?±?30 hPa, whereas the CH₂NN?+?NO₃ reaction was too fast to be determined in the static smog chamber experiments. Formaldehyde was the sole product observed in all the reactions. The experimental results are supported by CCSD(T*)-F12a/aug-cc-pVTZ//M062X/aug-cc-pVTZ calculations showing the reactions to proceed exclusively via addition to the carbon atom. The atmospheric fate of diazomethane is discussed.     

Adaptive application of operators in standard representation

Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55. This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1.     

Design and Cold Tests of Asymmetric Quasioptical Resonators

This paper presents the design and test of asymmetric quasioptical resonators for gyrotron applications, where most of the diffraction output coupling comes from the smaller of two mirrors. A computer code based on scalar diffraction theory is used to calculate the resonator losses and the electric field near the mirrors. Resonators with mirror separations approaching confocal have reduced side lobes in the diffraction patterns, which should allow for better power transmission and focusing. Cold tests have been performed at 94 and 141 GHz to measure the quality factor of the asymmetric resonators as a function of mirror separation and mirror misalignment. Typical resonator parameters include 65 cm mirror separation, 1-3% output coupling and 85% of the losses from the small mirror. A half-symmetric resonator with one flat and one curved mirror has also been investigated. The calculated values of Q are in reasonably good agreement with the cold test measurements.     

Planting in his Neighbor's Garden: David Hilbert and Early Göttingen Quantum Physics

David Hilbert (1862-1943) played an important role in establishing quantum physics in Göttingen. I analyze the ways in which his influence was decisive by comparison with Woldemar Voigt (1850-1919). Voigt was the leading Göttingen theoretical physicist before the arrival of Peter Debye (1884-1966), who was appointed to a new professorship in 1914 at Hilbert's instigation. I portray the Göttingen mathematicians, above all Hermann Minkowski (1864-1909) and David Hilbert, as planting the seeds for the blossoming of quantum physics under their student Max Born (1882-1970) in the 1920s.     

Mapping properties of wave and scattering operators for two-body Schrödinger operators

The modified wave and scattering operators are shown to be bounded between weighted L ²-spaces for two-body Schrödinger operators with long range potentials.     

PROTEIN STRUCI'URE MODELLING OF THE BACTERIAL LIGHT-HARVESTING COMPLEX

Abstract Protein structure modelling offers a method of obtaining 3-dimensional information that can be tested and used to plan mutagenesis experiments when a crystallographically determined structure is not available. At its simplest a model may consist of little more than a secondary structure prediction coupled with a determination of the likely regions of transmembrane/membrane surface/globular configuration. These methods can yield an interesting topology map of the protein, which places the residues in their likely positions with respect to, for example, the membrane interface. If it is a member of a large family of related proteins then aligned protein sequences can be used to predict the residues that have an important function as these. will be largely conserved in the alignments. Using all these methods a model can be constructed (using for example, the Nicholson Molecular Modelling Kit) to visualize the proposed structure in three dimensions following the premise of good design, that is, avoiding obvious steric clashes, packing of helices in a realistic manner, observing the correct H-bond lengths, etc . In this latter exercise the review of Chothia ( Annu. Rev. Biochem . 53 , 537–572, 1984) of the principles of protein structure is particularly helpful as it clearly sets out how proteins pack and their preferred configuration. There is a wealth of information about individual amino acid conformational preferences and observed frequencies of occurrence in known protein structures, which can help decide how the residues in the model can be oriented.
In this article we have collated the various protein models of the bacterial light-harvesting complexes and present our own model, which is a synthesis of the available biophysical data and theoretical predictions, and show its performance in explaining recent results of site-directed mutants of the LHI and LH2 light-harvesting complexes of Rhodobacter sphaeroides .     

Kinetic determination of magnesium and calcium by stopped-flow injection analysis

A kinetic method for the simultaneous determination of magnesium and calcium ions in solution is described. The method is based on the dissociation reactions of cryptand (2.2.2) complexes; a stopped-flow injection technique is used with spectrophotometric monitoring of the phthalein complexone complexes of the released metal ions. Analyses were done at a rate of 80 h^?1, with injected sample volumes of 80 μl. A microcomputer system for data acquisition and control of the system is described.