Approximation of Integral Operators by Variable-Order Interpolation

Summary. We employ a data-sparse, recursive matrix representation, so-called -matrices, for the efficient treatment of discretized integral operators. We obtain this format using local tensor product interpolants of the kernel function and replacing high-order approximations with piecewise lower-order ones. The scheme has optimal, i.e., linear, complexity in the memory requirement and time for the matrix-vector multiplication. We present an error analysis for integral operators of order zero. In particular, we show that the optimal convergence (h) is retained for the classical double layer potential discretized with piecewise constant functions.Corrigendum This revised version was published online in February 2005 due to typesetting mistakes in the author correction process.     

Coevolutionary dynamics: from finite to infinite populations

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly considering large populations. In particular, we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics. Moreover, differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and, depending on the population size, can even invert the direction of the evolutionary process.     

Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation

We present phase-resolved pulse propagation measurements that allow us to fully describe the transition between several light-matter interaction regimes. The complete range from linear excitation to the breakdown of the photonic bandgap on to self-induced transmission and self-phase modulation is studied on a high-quality multiple-quantum-well Bragg structure. An improved fast-scanning cross-correlation frequency-resolved optical gating setup is applied to retrieve the pulse phase with an excellent signal-to-noise ratio. Calculations using the semiconductor Maxwell-Bloch equations show qualitative agreement with the experimental findings.     

Carrier envelope phase noise in stabilized amplifier systems

At present most laser systems for generating phase-stabilized high-energy pulses are chirped pulse amplifier systems that involve the selection and subsequent amplification of pulses from a phase-stabilized seed oscillator. We investigate the effect of the picking process on the carrier envelope phase stability and how the phase noise of the picked pulse sequence can be estimated from the phase noise properties of the seed oscillator. All noise components from the original pulse train above the picking frequency are aliased into the picked pulse train and therefore cannot be neglected.     

Studies on the synthesis of 2,3-o-hydroxyalkyl ethers of cellulose

Novel 2,3-O-hydroxyethyl- and 2,3-O-hydroxypropyl cellulose products were synthesized by heterogeneous etherification of 6-O-(4-monomethoxytrityl) cellulose (MMTC). Due to the very hydrophobic character of MMTC, the reaction was successful in the presence of anionic and non-ionic detergent in the reaction mixture yielding the 2,3-O-cellulose ethers with a molar degree of substitution (MS) varying between 0.25 and 2.00 after detritylation. The products were characterized by means of (1)H and (13)C NMR spectroscopy including two-dimensional methods. The 2,3-O-hydroxypropyl cellulose samples are soluble in water at a MS as low as 0.8. The spectroscopic studies showed that the unusual solubility results from a preferred substitution of hydroxy groups of the anhydroglucose unit while the newly formed hydroxy moieties are included in the reaction to a minor extent only. In contrast, conventionally synthesized hydroxypropyl cellulose is soluble in water starting at a MS of about 4.0 because of the formation of oxyethylene side chains. (13)C DEPT 135 NMR spectrum of 2,3-O-hydroxypropyl cellulose.     

Frequency-dependent transversal flow control in centrifugal microfluidics

This work presents a novel flow switch for centrifugal microfluidic platforms which is solely controlled by the Coriolis pseudo force. This Coriolis switch consists of an inverse Y-structure with one common upstream channel and two symmetric outlets on a rotating disk. Above a certain threshold frequency, the Coriolis force becomes dominant that the entire flow is diverted into one of the outlets which is selected by the direction of rotation. The threshold frequency has been measured to be 350 rad s(-1)(approximately 55.7 Hz) for a channel width of 360 microm and a depth of 125 microm. The results are supported by extensive CFD simulations.     

A density functional study of the chemical differences between Type I and Type II MoS2-based structures in hydrotreating catalysts

Density functional theory is used to investigate the origin of the activity differences between Type I and Type II MoS2-based structures in hydrotreating catalysts. It is well known that the Type II structures, where only weak interactions with the support exist, have a higher catalytic activity than Type I structures, where Mo-O linkages to the alumina are present. The present results show that the differences in activities for MoS2 and Co-Mo-S structures can be attributed to the electronic and bonding differences introduced by the bridging O bonds. We find that the Mo-O linkages are most probably located on the (1010) S edge. The presence of oxygen linkages increases the energy required to form sulfur vacancies significantly so that almost no vacancies can be formed at these and neighboring sites. In this way, the reactivity of the S edge is reduced. In addition, the studies also show that the linkages introduce changes in the one-dimensional metallic-like brim states. Furthermore, the presence of oxygen linkages also changes the energetics of hydrogen adsorption, which becomes less exothermic on sulfur sites directly above linkages and more exothermic on sulfur sites adjacent to linkages. The present results explain previously observed differences in Type I-Type II transition temperatures for Co-Mo-S structures with different Co contents.