An asymptotic preserving scheme for the Kac model of the Boltzmann equation in the diffusion limit

In this article, we propose a numerical scheme to solve the Kac model of the Boltzmann equation for multiscale rarefied gas dynamics. Formally, this scheme is shown to be uniformly stable with respect to the Knudsen number, consistent with the fluid-diffusion limit for small Knudsen numbers, and with the Kac equation in the kinetic regime. Our approach is based on the micro–macro decomposition which leads to an equivalent formulation of the Kac model that couples a kinetic equation with macroscopic ones. This method is validated with various test cases and compared to other standard methods.     

Polymorphism of sorbitol

The polymorphism of sorbitol was investigated, confirming the existence of four anhydrous crystalline phases plus the hydrate. The crystallised melt (CM), the alpha form, and the gamma form were obtained via a dry route. The CM was confirmed to be a crystalline state with a spherulite morphology. The alpha form was obtained via direct conversion from the CM, in contrast to more complicated routes previously reported, and was found to have a very high crystallinity. Gamma crystals were obtained by seeding the melt at high temperature; however, crystallinity was clearly less than for alpha crystals.     

Fluorine in optics

Fluorine occupies an original and strategic position in modern optics. The F₂ excimer lasers are unrivaled sources of deep UV light for semiconductors, microphotolithography and micromachining which has brought on the development of single crystal calcium fluoride optics. Due to the weak polarisability of the fluoride ion, fluoride materials have low refractive index suitable for thin film antireflective coatings specially in IR optics. Transparent magnesium fluoride ceramics, prepared by fine grains hot pressing, are transparent in the mid IR where the transparency windows of the atmosphere are located. They are used as IR domes for missiles guidance. Fluoride glasses when elaborated as optical fibers or channel waveguides and when doped with appropriate lanthanides, are original optical devices for laser operations lying from the mid IR to the UV region where light emission is characterized by up-conversion phenomena. The same devices have also found industrial applications in telecommunications as a new generation of optical amplifiers operating in the ultra-transparency window of the silica fiber.     

Analysis of an industrial component commonality problem

We discuss a case study of an industrial production-marketing coordination problem involving component commonality. For the product line considered, the strategic goal of the company is to move from the current low volume market to a high volume market. The marketing department believes that this can be achieved by substantially lowering the end products’ prices. However, this requires a product redesign to lower production costs in order to maintain profit margins. The redesign decision involves grouping end products into families. All products within one family use the same version of some components. This paper fits in the stream of recent literature on component commonality where the focus has shifted from inventory cost savings to production and development cost savings. Further, we consider both costs and revenues, leading to a profit maximization approach. The price elasticity of demand determines the relationship between the price level and number of units sold. Consequently, we integrate information from different functional areas such as production, marketing and accounting. We formulate the problem as a net-present-value investment decision. We propose a mixed integer nonlinear optimization model to find the optimal commonality decision. The recommendation based on our analysis has been implemented in the company. In addition, the application allows us to experimentally validate some claims made in the literature and obtain managerial insights into the trade-offs.     

Blends of carbon blacks and multiwall carbon nanotubes as reinforcing fillers for hydrocarbon rubbers

The reinforcement of a styrene‐butadiene rubber (SBR) by single fillers—carbon black (CB) or multiwall carbon nanotubes (MWNTs)—or by mixtures of CB and MWNTs, is investigated. The morphologies, mechanical and electrical properties of the composites, are analyzed. A significant improvement in the tensile properties is observed for samples containing a dual phase. Using atomic force (AFM) and transmission electron (TEM) microscopies, we demonstrate that the double loading improves the dispersion of the nanotubes in SBR. Electrical measurements show lower resistivity and a lower percolation threshhold for composites containing blends of fillers, which provides further evidence of better dispersion. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 46: 1939–1951, 2008     

Random Version of the Theorems of the Alternative

Three theorems of the alternative for abstract linear inequality systems which depend on random parameter are produced in infinite dimensions.     

Memory effects and homogenization

Dedicated to Bernard D. Coleman on his sixtieth birthday