Matrix representation of three-dimensional astigmatic resonators

Three-dimensional astigmatic resonators, typical examples of which are the resonators bounded by cylindrical-spherical mirrors and cylindrical-cylindrical mirrors oriented at an arbitrary crossed angle, are investigated in detail by using a complex curvature tensor concept and generalized tensor ABCD law. Computerized numerical calculations illustrate some interesting characteristics of these astigmatic resonators.     

Aerodynamics of ski jumping: experiments and CFD simulations

The aerodynamic behaviour of a model ski jumper is investigated experimentally at full-scale Reynolds numbers and computationally applying a standard RANS code. In particular we focus on the influence of different postures on aerodynamic forces in a wide range of angles of attack. The experimental results proved to be in good agreement with full-scale measurements with athletes in much larger wind tunnels, and form a reliable basis for further predictions of the effects of position changes on the performance. The comparison of CFD results with the experiments shows poor agreement, but enables a clear outline of simulation potentials and limits when accurate predictions of effects from small variations are required.     

Analysis of fragrance compounds in blood samples of mice by gas chromatography, mass spectrometry, GC/FTIR and GC/AES after inhalation of sandalwood oil.

After inhalation experiments with sandalwood oil and the pure fragrance compounds coumarin and alpha-terpineol, substances were detected and measured in the blood samples of test animals (mice) using gas chromatography/mass spectrometry (GC/MS) (MID) in connection with GC/FTIR (SWC), GC/AES (carbon and oxygen trace) and flame ionization detection/gas chromatography. Using tiglinic acid benzyl ester as the internal standard the following concentrations in serum could be found: alpha-santalol 6.1 ng/mL, beta-santalol 5.3 ng/mL and alpha-santalene 0.5 ng/mL. In separate inhalation experiments with coumarin and with alpha-terpineol the corresponding concentrations were 7.7 ng/mL and 6.9 ng/mL, respectively.     

Ungleichungen für elementare Mittelwerte

Ohne Zusammenfassung     

Polynomial-time approximation schemes for packing and piercing fat objects

We consider two problems: given a collection of n fat objects in a fixed dimension, (1) ( packing) find the maximum subcollection of pairwise disjoint objects, and (2) ( piercing) find the minimum point set that intersects every object. Recently, Erlebach, Jansen, and Seidel gave a polynomial-time approximation scheme (PTAS) for the packing problem, based on a shifted hierarchical subdivision method. Using shifted quadtrees, we describe a similar algorithm for packing but with a smaller time bound. Erlebach et al.'s algorithm requires polynomial space. We describe a different algorithm, based on geometric separators, that requires only linear space. This algorithm can also be applied to piercing, yielding the first PTAS for that problem.     

Domain size equilibration in sphere‐forming block copolymers

The kinetics of domain size equilibration were studied for asymmetric poly(ethylene‐alt‐propylene)‐b‐poly(dimethyl siloxane) (EPDMS) and polyisoprene‐b‐poly(dimethyl siloxane) (IDMS) block copolymers in the body‐centered cubic ordered phase. Small‐angle X‐ray scattering measurements of the principal peak position (q*) were made as a function of time after temperature jumps within the ordered state. The equilibration times were remarkably long, especially on cooling and for temperatures below 100 °C. For example, after a quench to 40 °C, q* for EPDMS had not fully equilibrated even after several weeks of annealing; IDMS required several days to equilibrate at the same temperature. In contrast, a lamella‐forming EPDMS sample was able to adjust q* within the timescale of the measurements (i.e., minutes) with both heating and cooling over the same temperature range. Measurements of tracer diffusion indicated that chain mobility was not the rate‐limiting step, although differences in mobility did account for the differences between EPDMS and IDMS. Rather, the limiting step was the required reduction in the number density of spheres on cooling; the disappearance of spheres, either by evaporation or by fusion, provided a large kinetic barrier. Lamellae, however, could adjust domain dimensions simply by local displacements of individual chains. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 715–724, 2003     

Complex morphology of melt-spun nylon-6 fibres investigated by 1H double-quantum-filtered NMR spin-diffusion experiments.

The complex morphology of high-speed melt-spun nylon-6 fibres hydrated with D2O was investigated using 1H double-quantum-filtered spin-diffusion NMR experiments. The magnetisation exchange from selected crystalline domains along the fibrils and interfibrils was simulated with the help of a three-dimensional solution of a spin-diffusion equation approximated by a product of one-dimensional analytical NMR signals, which correspond to a lamellar morphology. This allows to measure the sizes of crystalline and less-mobile amorphous domains along the fibrils, as well as the diameter of the fibrils and interfibril distances. A series of nylon-6 fibres with extreme values of winding speed and draw ratio was investigated. The changes detected in the domain size along the fibrils and interfibrils show the same trend in the data obtained from wide-angle X-ray diffraction and small-angle X-ray scattering.     

Decentered twisted Gaussian Schell-model beams and their propagation through a misaligned first-order optical system

The propagation properties of decentered twisted Gaussian Schell-model (DTGSM) beams passing through a misaligned first-order optical system are studied. The explicit expressions for the cross-spectral density function and Wigner distribution function of the output beam are derived, which retain their form unchanged. It is shown that the DTGSM beams preserve their closed property. The second-order moments matrix and the Wigner distribution function evolve with the usual laws, whereas the first-order moments matrix varies, as if a ray passes through such system. The propagation of DTGSM beams through an aligned first-order optical system is treated as the limiting case that corresponds to the vanishing misalignment parameters.