Optimality relationships forp-cyclic SOR

Summary The optimality question for blockp-cyclic SOR iterations discussed in Young and Varga is answered under natural conditions on the spectrum of the block Jacobi matrix. In particular, it is shown that repartitioning a blockp-cyclic matrix into a blockq-cyclic form,q, results in asymptotically faster SOR convergence for the same amount of work per iteration. As a consequence block 2-cyclic SOR is optimal under these conditions.Research supported in part by the US Air Force under Grant no. AFOSR-88-0285 and the National Science Foundation under grant no. DMS-85-21154 Present address: Boeing Computer Services, P.O. Box 24346, MS 7L-21, Seattle, WA 98124-0346, USA     

Measurement of surface topography by RGB Shadow-Moiré with direct phase demodulation

In this paper we present the application of a direct demodulation method for the measurement of surface topography by means of Shadow-Moiré. In our set-up, we use three LEDs (with green, red and blue peak wavelengths) to illuminate the grating. Due to the different position of these light sources, a polychromatic Shadow-Moiré fringe pattern is produced, which can be described as the superposition of three monochromatic (red, green and blue) fringe patterns. Taking the image of this polychromatic fringe pattern with a RGB CCD camera, we get a monochromatic fringe pattern stored at each RGB channel of the CCD. The direct demodulation algorithm employed uses these fringe patterns to calculate the wrapped phase map. After unwrapping the phase map using a standard multi-grid technique, we implemented an automatic procedure to detect the area of interest of the phase map by removing low modulation zones and to calculate the absolute value of the phase. In this way it is possible to determine the topography of a surface with a single RGB snapshot maintaining a simple experimental set-up, which is an important feature, especially for the study of dynamic phenomena such as deformations. We present the experimental results obtained after measuring different objects with both smooth and rough surface textures.     

Cyclic cohomology and algebra extensions

We construct a spectral sequence to study cyclic cohomology for an extension A = R/I of algebras. When R is a free algebra we describe the cyclic cohomology of A in terms of traces defined on R or powers of I. Explicit cyclic cocycles representing the cyclic cohomology class belonging to the trace are constructed as analogues of Chern character and Chern-Simons forms.Dedicated to Alexander Grothendieck     

Quantitative and high mass ToF-SIMS studies of siloxane segregation in hydrogel polymers using cryogenic sample handling techniques

This paper examines the capabilities of cryogenic sample handling to examine composition and structure of hydrogel materials where siloxane components are central to the analysis. XPS analysis of multicomponent polymers with cryogenic sample handling following exposure to aqueous environments has revealed the composition and kinetics of near surface reorganization for siloxane and fluorocarbon containing polymers. In this study we report results from a ToF-SIMS protocol for cryogenic sample handling applied to the analysis of surface changes upon hydration/dehydration of hydrogel polymers. Comparison of results from angle dependent XPS and ToF-SIMS are discussed for a range of commercial soft contact lens materials. Both methods detected changes in surface chemistry between the hydrated (frozen) and dehydrated surfaces. Analysis of the hydrated surfaces detected polymer components indicative of the commercial formulation as well as ice clusters. Analysis of the dehydrated materials detected changes in surface chemistry relative to the hydrated surface in addition to loss of water due to sample dehydration. A quantitative standard additions method for ToF-SIMS data was used to determine submonolayer amounts of PDMS impurities at the surface of the hydrogels. ToF-SIMS analysis of a series of seven poly (allyl methacrylate-g-dimethylsiloxane), AMA-g-DMS, graft copolymers in the hydrated state revealed high mass oligomeric ion distributions for systems with bulk PDMS content greater than 25 wt.%. This marks the first time that detection of high mass oligomeric ion distributions from hydrated (frozen) surfaces has been reported. Analysis of the dehydrated surface detected formation of high mass oligomeric ion distributions for systems with PDMS bulk content greater than 15 wt.%, but only detected these ion distributions in wet (frozen) samples when the bulk concentration was greater than 25 wt.%.     

Gas-phase thermal decomposition of peroxy-N-butyryl nitrate

The gas-phase thermal decomposition rate of peroxy-n-butyryl nitrate (n-C₃H₇C(O)OONO₂, PnBN) has been measured at ambient temperature (296 K) and 1 atm of air relative to that of peroxyacetyl nitrate (CH₃C(O)OONO₂, PAN) using mixtures of PAN (14–19 ppb), PnBN (22–46 ppb), and nitric oxide (1.35–1.90 ppm). The PnBN/PAN decomposition rate ratio was 0.773 ± 0.030. This ratio, together with a literature value of 3.0 × 10^?4 s^?1 for the thermal decomposition rate of PAN at 296 K, yields a PnBN thermal decomposition rate of (2.32 ± 0.09) × 10^?4 s^?1. The results are briefly discussed by comparison with data for other peroxyacyl nitrates and with respect to the atmospheric persistence of PnBN. © 1994 John Wiley & Sons, Inc.     

Decay of confined,two-dimensional,spatially periodic arrays of vortices: A numerical investigation

The disarrangement of a perturbed lattice of vortices was studied numerically. The basic state is an exponentially decaying, exact solution of the Navier-Stokes equations. Square arrays of vortices with even numbers of vortex cells along each side were perturbed and their evolution was investigated. Whether the energy in the perturbation grows somewhat before it decays or decays monotonically depends on the initial strength of the vortices of the basic state, the extent of lateral confinement and the structure of the perturbation. The critical condition for temporally local instability, i.e. the critical amplitude of the basic state that must be exceeded to allow energy transfer from the basic state to the perturbation, is discussed. In the strongly confined case of a square lattice of four vortices the appearance of enchancement of global rotation is the result of energy transfer from the basic state to a temporally local unstable mode. Energy is transferred from the basic state to larger-scaled structures (inverse cascade) only if the scales of the larger structures are inherently contained in the initial structure of the perturbation. The initial structure of the double array of vortices is not maintained except for a very special form of perturbation. The facts that large scales decay more slowly than small scales and that, when non-linearities are sufficiently strong, energy is transferred from one scale to another explain the differences in the disarrangement process for different initial strengths of the vortices of the basic state. The stronger vortices, i.e. the vortices perturbed in a manner that increases their strength, tend to dominate the weaker vortices. The pairing and subsequent merging (or capture) of vortices of like sense into larger-scale vortices are described in terms of peaks in the evolution of the square root of the palinstrophy divided by the enstrophy.     

Modélisation du champ des vitesses de l'urine dans un bolus urétéralModelling of urine flow in an ureteral bolus

Urine transport is made from the kidney to the bladder through the ureter by isolated pockets called bolus. To determine the urine flow in a bolus, we use an adherence condition on the interface urine/wall. It gives us an infinite linear system verified by a set of parameters. An iterative and convergent algorithm allows us to solve this system and to determine analytically the components of the velocity vector in the bolus. To cite this article: A. Vogel et al., C. R. Mecanique 332 (2004).     

Effect of nanotube functionalization on the properties of single‐walled carbon nanotube/polyurethane composites

A commercially available aliphatic thermoplastic polyurethane formulated with a methylene bis(cyclohexyl) diisocyanate hard segment and a poly(tetramethylene oxide) soft segment and chain‐extended with 1,4‐butanediol was dissolved in dimethylformamide and mixed with dispersed single‐walled carbon nanotubes. The properties of composites made with unfunctionalized nanotubes were compared with the properties of composites made with nanotubes functionalized to contain hydroxyl groups. Functionalization almost eliminated the conductivity of the tubes according to the conductivity of the composites above the percolation threshold. In most cases, functionalized and unfunctionalized tubes yielded composites with statistically identical mechanical properties. However, composites made with functionalized tubes did have a slightly higher modulus in the rubbery plateau region at higher nanotube fractions. Small‐angle X‐ray scattering patterns indicated that the dispersion reached a plateau in the unfunctionalized composites that was consistent with the plateau in the rubbery plateau region. The room‐temperature modulus and tensile strength increase was proportionally higher than almost all increases seen previously in thermoplastic polyurethanes; however, the increase was still an order of magnitude below what has been reported for the best nanotube–polymer systems. Nanotube addition increased the hard‐segment glass transition temperature slightly, whereas the soft‐segment glass transition was so diffuse that no conclusions could be drawn. Unfunctionalized tubes suppressed the crystallization of the hard segment; whereas functionalized tubes had no effect. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 490–501, 2007