Stochastic Quantization for the Fractional Edwards Measure

For a class of generalized Choquard equations with perturbation terms, we establish the existence of bound and ground states by virtue of the method of Nehari manifold.     

An integrated tabu search algorithm for the lot streaming problem in job shops

In this paper, we focus on solving the lot streaming problem in a job shop environment, where consistent sublots are considered. The presented three-phase algorithm incorporates the predetermination of sublot sizes, the determination of schedules based on tabu search and the variation of sublot sizes. With regard to tabu search implementation, a constructive multi-level neighbourhood is developed, which effectively connects three isolated neighbourhood functions. Moreover, enhancements of the basic version of tabu search are conducted. Combined with the procedure for varying sublot sizes, the algorithm further exploits the improvement potential. All tested instances show a rapid convergence to their lower bounds. The well-known difficult benchmark problems also achieve substantial makespan reduction. In addition, the performance of specific components is intensively examined in our study.     

A finite element approach for modelling hip joint contact

In this contribution a finite element model for the three dimensional investigation of hip joint contact is described. A shell-like interface element with variable thickness is developed for modelling fluid flow in the synovial gap. For this purpose the Taylor-Hood element is extended in order to take a spatial thickness distribution and local thickness changes into account. The interaction between the synovial fluid and the cartilage layers is solved by a staggered iteration using an artificial compressibility method. Cartilage is modelled using the theory of porous media and three dimensional geometries are reconstructed from medical imaging data. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nitridation of Niobium Pentoxide Films in Ammonia by Rapid Thermal Processing

The feasibility of niobium oxynitride formation through nitridation of niobium pentoxide films in ammonia by rapid thermal processing (RTP) was investigated. Niobium films 200 and 500 nm thick were deposited by sputtering on Si(100) wafers covered by a 100 nm thick thermally grown SiO₂ layer. These as‐deposited films exhibited distinct texture effects. They were processed in three steps using an RTP system. The as‐deposited niobium films were first nitridated in an ammonia atmosphere at 1000 °C for 1 min and then oxidised in molecular oxygen at temperatures ranging from 400 to 600 °C. Those samples in which a single Nb₂O₅ phase was determined after oxidation were additionally nitridated in ammonia at 1000 °C for 1 min. Investigations show that surface roughness of the samples after oxidation of niobium films first nitridated in ammonia is lower than after direct oxidation of as‐deposited films in oxygen, although the niobium pentoxide phase formed after annealing was the same in both cases. We explain this result as being due to the large expansion of the niobium lattice during the direct oxidation of the niobium film in molecular oxygen and also to the high oxidation rate of the as‐deposited niobium film in oxygen. By incorporation of oxygen in the crystal lattice of niobium and rapid formation of niobium pentoxide, substantial intrinsic stress was built up in the film, frequently resulting in delamination of the film from the substrate. Nitrogen hinders the diffusion of oxygen in nitridated films, which leads to a decrease of the oxidation rate and thus slower formation of Nb₂O₅. Nitridation of the completely oxidised niobium films in ammonia leads to the formation of niobium oxynitride and niobium nitride phases.     

Differentiable evaluation of objective functions in sampling design with variance-covariance matrices

In this short note we consider the differentiable evaluation of the objective function of the sampling design optimization problem based on the inverse of the Fisher information matrix, and where the integer design variables have been converted into real variables using a relaxation technique. To ensure differentiability and cover the full range of the variables, and thus improve the convergence behavior of derivative-based optimization algorithms, we propose applying a Cholesky decomposition on the Fisher information matrix, but using a special higher precision floating point arithmetic to ensure stability. While each evalu-ation of the functional becomes slower, the algorithm is much simpler, amenable to be used with automatic differentiation directly, and can be shown to be very stable. For many practical situations, this is a valuable trade-off. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reaktionen der Digalliumverbindung R2Ga–GaR2 [R = CH(SiMe3)2] mit Wasser und Carbonsäuren – Synthese von μ‐Hydroxo‐μ‐carboxylatodigallium‐Verbindungen unter Erhalt der Ga–Ga‐Bindungen

Treatment of the digallium compound R₂Ga–GaR₂ [ 1 , R = CH(SiMe₃)₂] with a broad variety of functionalized carboxylic acids in the presence of water yielded μ‐hydroxo‐μ‐carboxylatodigallium compounds ( 2 – 10 ) containing intact Ga–Ga bonds in high to moderate yields. The compounds form dimeric formula units in which the unsupported Ga–Ga bonds are bridged by two hydroxo and two carboxylato ligands. Each gallium atom is terminally coordinated by a bulky alkyl group. NMR spectroscopy revealed mixtures of two isomeric compounds in solution in all cases. The second component may show a different bridging mode with each Ga–Ga bond bridged by a bidentate carboxylato ligand to form Ga₂O₂C five‐membered heterocycles.     

Infrared spectroscopy of large ammonia clusters as a function of size

We have measured the vibrational spectra of large ammonia (NH3)n clusters by photofragment spectroscopy in the spectral range from 3150 to 3450 cm(-1) for the average sizes n = 29, 80, 212, 447, and 989 and by depletion spectroscopy for n=8. The spectra are dominated by peaks around 3385 cm(-1) which are attributed to the asymmetric nu3 NH-stretch mode. Two further peaks between 3200 and 3260 cm(-1) have about equal intensity for n = 8 and 29, but only about 0.40 of the intensity of the nu3 peak for the larger sizes. The spectra for the smallest and largest size agree with those obtained by Fourier transform infrared spectroscopy in slit jet expansion and collision cells, respectively. By accompanying calculation we demonstrate that the energetic order of the spectral features originating from the bending overtone 2nu4 and the symmetric NH-stretch nu1 in the range from 3150 to 3450 cm(-1) is changed between n = 10 and 100, while the asymmetric NH-stretch nu3 only exhibits a moderate redshift. The reason is the coupling of the ground state modes to the overtones.