Downwind Gauß-Seidel Smoothing for Convection Dominated Problems

In the case of convection dominated problems, multigrid methods require an appropriate smoothing to ensure robustness. As a first approach we discuss a Gauss–Seidel smoothing with a correct numbering of the unknowns and if necessary a special block partitioning. Numerical experiments show that, in the case of general convection directions, the multigrid algorithms obtained in this way have the same properties as in the model situation. If the graph arising from the convection part is acyclic, we describe a numbering algorithm which is valid for all spatial dimensions. Cycles give rise to special blocks for a blockwise Gauss–Seidel smoothing. We describe an algorithm for the two-dimensional case. The proposed algorithm requires a computational work of optimal order (linear in the size of the problem). © 1997 by John Wiley & Sons, Ltd.     

Intelligent driving in traffic systems with partial lane discipline

It is a most common notion in traffic theory that driving in lanes and keeping lane changes to a minimum leads to smooth and laminar traffic flow, and hence to increased traffic capacity. On the other hand, there exist persistent vehicular traffic systems that are characterised by habitual disregarding of lane markings, and partial or complete loss of laminar traffic flow. Here, we explore the stability of such systems through a microscopic traffic flow model, where the degree of lane-discipline is taken as a variable, represented by the fraction of drivers that disregard lane markings completely. The results show that lane-free traffic may win over completely ordered traffic at high densities, and that partially ordered traffic leads to the poorest overall flow, while not considering the crash probability. Partial order in a lane-free system is similar to partial disorder in a lane-disciplined system in that both lead to decreased traffic capacity. This could explain the reason why standard enforcement methods, which rely on continuous increase of order, often fail to incur order to lane-free traffic systems. The results also provide an insight into the cooperative phenomena in open systems with self-driven particles.     

Novel silver‐tubing method for quantitative introduction of water into high‐temperature conversion systems for stable hydrogen and oxygen isotopic measurements

A new method to seal water in silver tubes for use in a TC/EA (thermal conversion/elemental analyzer) reduction unit using a semi‐automated sealing apparatus can yield reproducibilities (1 standard deviation) of δ²H and δ¹⁸O measurements of 1.0‰ and 0.06‰, respectively. These silver tubes containing reference waters may be preferred for the calibration of H‐ and O‐bearing materials analyzed with a TC/EA reduction unit. The new sealing apparatus employs a computer‐controlled stepping motor to produce silver tubes identical in length. The reproducibility of the mass of water sealed in tubes (in a range of 200–400 µg) can be as good as 1%. Approximately 99% of the sealed silver tubes are satisfactory (leak free). Although silver tubes sealed with reference waters are robust and can be shaken or heated to 110°C with no loss of integrity, they should not be frozen because the expansion during the phase transition of water to ice will break the cold seals and all the water will be lost. The tubes should be shipped in insulated containers. This new method eliminates air inclusions and isotopic fractionation of water associated with the loading of water into capsules using a syringe. The method is also more than an order of magnitude faster than preparing water samples in ordinary Ag capsules. Nevertheless, some laboratories may prefer loading water into silver capsules because expensive equipment is not needed, but users of this method are cautioned to apply the necessary corrections for evaporation, back exchange with laboratory atmospheric moisture, and blanks. Copyright © 2010 John Wiley & Sons, Ltd.     

Determination of metal additives and bromine in recycled thermoplasts from electronic waste by TXRF analysis

A new method for analysis of metal additives in recycled thermoplasts from electronic waste was developed, based on dissolving the samples in an organic solvent and subsequent analysis of the corresponding solutions or suspensions by total-reflection X-ray fluorescence spectroscopy (TXRF). The procedure proved to be considerably less time consuming than the conventional digestion of the polymer matrix. Additives containing Ti, Zn, Br, Cd, Sn, Sb, and Pb were analyzed in a hundred randomly selected samples from recycling, which provided an overview of the range of elemental concentrations in thermoplasts utilized for consumer electronics. The results were validated independently by instrumental neutron activation analysis (INAA), subsequent regression analysis confirmed the trueness of the chosen approach. Received: 7 February 2000 / Revised: 25 February 2000 / Accepted: 1 March 2000     

Microstructure morphology transitions at mesoscopic epitaxial surfaces

Spiral surface growth is well understood in the limit where motion of the spiral ridge is controlled by the local supersaturation of adatoms in its surrounding. In liquid epitaxial growth, however, spirals can form governed by both, transport of heat as well as solute. We propose for the first time a two-scale model of epitaxial growth which takes into account all of these transport processes. This new model assumes a separation of length scales for the transport of heat compared to that of the solutal field. It allows for the first time numerical simulations of extended surface regions by at the same time taking into account microstructure evolution and microstructure interaction. We apply this model successfully to extend the scaling relation for the step spacing given by the BCF theory [Phil. Trans. R. Soc. London, Ser. A 243, 299 (1951)] to microstructure evolution governed by heat and solute diffusion. Further applications to understand the mechanisms and consequences of spiral interaction at epitaxial surfaces, in particular the resulting morphology transitions, are discussed.     

Monte Carlo Simulations of Observation Time-Dependent Self-Diffusion in Porous Media Models

Observation time-dependent self-diffusion coefficients can be used to obtain microstructural information of porous media. This paper presents two different kinds of Monte Carlo simulations of the self diffusion process of fluids like water in porous systems, a lattice-free method and a lattice-based method. The results for simple porous media model geometries agree well with each other and with published analytical as well as semi-analytical equations. The use of these equations, which are important for the interpretation of Pulsed Field Gradient-Nuclear Magnetic Resonance (PFG-NMR) time-dependent diffusion data with respect to properties of porous media, is discussed.     

Phase field model simulations of hydrogel dynamics under chemical stimulation

Two decades ago, it has been observed experimentally that hydrogels immersed in a bath solution swells or shrinks under external stimulations (Ric?ka et al., Macromolecules 17:2916?C2921, 1984). Recently, this fact has received renewed interest, since understanding the precise mechanisms underlying that kind of behavior has the potential to tailor most sensitive drug delivery systems based on hydrogels (Segalman and Witkowski, Mater Sci Eng C 2:243?C249, 1995). Here we contribute to a precise understanding of the mechanisms responsible for the hydrogels?? swelling kinetics as well as dynamics by proposing for the first time a model approach that can resolve the inherent short-range correlation effects along the hydrogel?Csolution interface jointly with the long-range ionic transport fields. To that end, we investigate the swelling dynamics of hydrogels, which is a moving boundary problem, by a phase field model, which couples the Nernst?CPlanck equation for the concentration of mobile ions, Poisson equation for the electric potential, mechanical equation for the displacement, and an equation for the phase field variable. Simulation for two-dimensional case reveals that under the chemical stimulation, the hydrogel will swell or shrink if the concentration of mobile ions inside bath solution decreases or increases. This is in agreement with the experimental results qualitatively and validates our new model approach.