Convergence to Global Equilibrium for Spatially Inhomogeneous Kinetic Models of Non-Micro-Reversible Processes

We study the long-time asymptotics of linear kinetic models with periodic boundary conditions or in a rectangular box with specular reflection boundary conditions. An entropy dissipation approach is used to prove decay to the global equilibrium under some additional assumptions on the equilibrium distribution of the mass preserving scattering operator. We prove convergence at an algebraic rate depending on the smoothness of the solution. This result is compared to the optimal result derived by spectral methods in a simple one dimensional example.     

Existence and Convergence to Equilibrium of a Kinetic Model for Cometary Flows

A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on moments of the distribution function. An earlier existence result is extended to bounded domains with reflecting boundaries and to initial conditions permitting vacuum regions. The long time behaviour is investigated. Convergence on compact time intervals (shifted to infinity) to the set of equilibrium solutions is proven. The set of smooth equilibrium solutions is computed.     

Casimir force on a surface with shallow nanoscale corrugations: geometry and finite conductivity effects

We measure the Casimir force between a gold sphere and a silicon plate with nanoscale, rectangular corrugations with a depth comparable to the separation between the surfaces. In the proximity force approximation (PFA), both the top and bottom surfaces of the corrugations contribute to the force, leading to a distance dependence that is distinct from a flat surface. The measured Casimir force is found to deviate from the PFA by up to 10%, in good agreement with calculations based on scattering theory that includes both geometry effects and the optical properties of the material.     

Controlling the phase delay of light transmitted through double-layer metallic subwavelength slit arrays

We demonstrate that the phase of light transmitted through double-layer subwavelength metallic slit arrays can be controlled through lateral shift of the two layers. Our samples consist of two aluminum layers, each of which contains an array of subwavelength slits. The two layers are placed in sufficient proximity to allow coupling of the evanescent fields at resonance. By changing the lateral shift between the layers from zero to half the period, the phase of the transmitted electromagnetic field is increased by pi, while the transmitted intensity remains high. Such a controllable phase delay could open new capabilities for nanophotonic devices that cannot be achieved with single-layer structures.     

Über die Homogenisierbarkeit von Rechenprogrammen

Ohne Zusammenfassung     

Online SAXS investigations of polymeric hollow fibre membranes

Polymeric membranes are used in industrial and analytical separation techniques. In this study small-angle X-ray scattering (SAXS) with synchrotron radiation has been applied for in-situ characterisation during formation of polymeric membranes. The spinning of a polyetherimide (PEI) hollow fibre membrane was chosen for investigation of dynamic aggregation processes during membrane formation, because it allows the measurement of the dynamic equilibrium at different distances from the spinning nozzle. With this system it is possible to resolve structural changes in the nm-size range which occur during membrane formation on the time-scale of milliseconds. Integral structural parameters, like radius of gyration and pair-distance distribution, were determined. Depending on the chosen spinning parameters, e.g. the flow ratio between polymer solution and coagulant water, significant changes in the scattering curves have been observed. The data are correlated with the distance from the spinning nozzle in order to get information about the kinetics of membrane formation which has fundamental influence on structure and properties of the membrane.     

Das System Gd/Co/B: Darstellung und röntgenographische Charakterisierung von GdCo4B,Gd3Co11B4, GdCoB4 und GdCo12B6

The System Gd/Co/B: Preparation and Characterization by X‐ray Diffraction of GdCo₄B, Gd₃Co₁₁B₄, GdCoB₄, and GdCo₁₂B₆ The compounds GdCo₄B, Gd₃Co₁₁B₄, GdCoB₄, and GdCo₁₂B₆ were characterized by X‐ray investigations of single crystals. GdCo₄B (P 6/mmm, a = 505.9(1) pm, c = 690.1(1) pm) crystallizes with the CeCo₄B structure type; Gd₃Co₁₁B₄ (P 6/mmm, a = 508.7(1) pm, c = 982.9(9) pm) with the Ce₃Co₁₁B₄ stucture type; GdCo₁₂B₆ ( , a = 949.5(1) pm, c = 747.4(1) pm) with the SrNi₁₂B₆ structure type and GdCoB₄ (P bam, a = 591.3(9) pm, b = 1145.1(6) pm, c = 346.2(3) pm) with the YbCoB₄ structure type.