On c‐Bhaskar Rao designs with block size 4

Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λ_min=?λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ ? 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ?c ≠ 2 for c > 0 and whenever c ? λ_min≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10009     

Asymptotic packing via a branching process

It is shown that under certain side conditions the natural random greedy algorithm almost always provides an asymptotically optimal packing of disjoint hyperedges from a hypergraph H.     

Fabrication of material-independent morphology gradients for high-throughput applications

Gradient surfaces allow rapid, high-throughput investigations and systematic studies in many disparate fields, including biology, tribology and adhesion. We describe a novel method for the fabrication of material-independent morphology gradients, involving a two-step process of particle erosion followed by a chemical polishing procedure that preferentially removes features with a small radius of curvature as a function of time. Gradients are fabricated on aluminium surfaces, but they may be readily transferred to other materials via a replication technique, which allows for the production of identical roughness gradient samples with any chosen surface chemistry. The gradients have been characterized by means of scanning electron microscopy and optical profilometry. Standard roughness parameters (Ra, Rq, Rz, Sm and Sk) were calculated from optical profilometry data. The roughness has also been assessed over different wavelength windows by means of a fast Fourier transformation approach.     

Can you feel the double jump?

When p = c/n and c goes from less than one to greater than one, the random graph G(n, p) experiences the double jump. The first order language is too weak to recognize this change while there are properties expressable in the second order monadic language for which the change is clear. © 1994 John Wiley & Sons, Inc.     

The decisive role of calorimetric measurements in equilibrium phase diagram calculations

In this paper, examples are given of how calorimetric values can give greater certainty to phase equilibria calculated from thermodynamic data. Errors that may arise when phase diagram evaluations are carried out largely from the basis of Gibbs energy information only are illustrated by reference to recent evaluations of the Ti?Si system and the resulting calculated oxidation behaviour of titanium silicides. The importance of calorimetric values for calculation of metastable phase equilibria is demonstrated by results of work on the AlN?TiN hard-metal coating system. Finally, suggestions are made with regard to areas of work where calorimetric data are urgently needed.     

Sulfur adsorption on Fe(1 1 0): a DFT study

The adsorption of atomic S on the Fe(1 1 0) surface is examined using density functional theory (DFT). Three different adsorption sites are considered, including the atop, hollow and bridge sites and the S is adsorbed at a quarter monolayer coverage in a p(2 × 2) arrangement. The hollow site is found to be the most stable, followed by the bridge and atop sites. At all three sites, S adsorption results in relatively minor surface reconstruction, with the most significant being that for the hollow site, with lateral displacements of 0.09 Å. Comparisons between S-adsorbed and pure Fe surfaces revealed reductions in the magnetic moments of surface-layer Fe atoms in the vicinity of the S. At the hollow site, the presence of S causes an increase in the surface Fe d-orbital density of states between 4 and 5 eV. However, S adsorption has no significant effect on the structure and magnetic properties of the lower substrate layers.     

A method for investigating the orientational behaviour of fibrous particles in gaseous flow

A method is described by which the angular orientation distribution of fibrous particles carried in a gaseous stream may be investigated. The method is based upon the interpretation of the spatial intensity distribution or scattering profile of laser light scattered by individual fibres. The scattering instrument used to capture the profiles is described, and the mathematical computation required to ascertain the orientation of each particle at the measurement point is detailed. Illustrative results are given for a study of airborne micromachined silicon particles of 12 μm length and 1.0 μm by 1.5 μm cross-section. The method is currently being employed by the authors to investigate ways of improving the orientation control over nonspherical particles in systems such as aerodynamic particle sizers and particle shape classifiers, since lack of particle orientation control is known to adversely affect the measurement accuracy of both these types of instrument.