Predicting turbulent flow in a staggered tube bundle

This paper presents the results of calculations performed for the turbulent, incompressible flow around a staggered array of tubes for which carefully obtained experimental results are available as part of an established ERCOFTAC-IAHR test case. The Reynolds-averaged Navier–Stokes equations are solved using a pressure-based finite volume algorithm, using collocated cell vertex store on an unstructured and adaptive mesh of tetrahedra. Turbulence closure is obtained with a truncated form of a low-Reynolds number k– model developed by Yang and Shih. The computational domain covers all seven rows of tubes used in the experimental study and periodic flow is allowed to develop naturally. The results of the computations are surprisingly good and compare favourably with results obtained by others using a wide range of alternative k– models for a single cylinder with periodic inflow and outflow boundaries on structured meshes.     

Delayed bifurcations and negative hysteresis in semiconductor lasers: the role of initial conditions

The dynamical intensity response of a semiconductor laser under the influence of injection current modulation, and the resulting hysteresis behavior, is investigated experimentally and theoretically. We report the first experimental observation, in a semiconductor laser, of the transition from a negative to a positive hysteresis as the modulation frequency of the injection current is varied. The theoretical work isolates the initial conditions on the intrinsic laser parameters as the sole determinant in influencing the kind of hysteresis one observes.     

Carbon papers with conductive polymer coatings for use in solid-state supercapacitors

Conductive polymer-coated carbon papers have been fabricated through polymerisation of pyrrole-based monomers oxidised with various heteropolyacids. Smooth surfaces are obtained when multiple coatings are applied to the carbon surface and give good contact with the Nafion^® electrolyte. Cyclic voltammetry was used to study the electrodes and a.c. impedance and charge / discharge cycling was used to study membrane electrode assemblies (MEA). MEAs were fabricated using a hot-press technique.     

Molecular mechanics‐based measures of steric effects: Customized code to compute Ligand repulsive energies

Ligand repulsive energies, E_R, have been demonstrated to provide reliable steric parameters for ligands in organometallic systems. To date, ligand repulsive energies have been computed manually using commercially available molecular mechanics code. We report a customized code, ERCODE, that calculates ligand repulsive energies. Some reported E_R values differ from those in the literature due to a modified conformational search strategy presented. Updated ligand repulsive energies for 100 phosphines, 12 phosphites, 26 amines, and 54 alcohols, ethers, and sulfides are presented. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 239–246, 2000     

Permutations with roots

We prove that the probability p₂(n) that a random permutation of length n has a square root is monotonically nonincreasing in n. More generally, we prove that the probability p_r(n) that a random permutation of length n has an rth root, r prime, is monotonically nonincreasing in n. We also show for all r≥2 that p_r(n)→0 as n→∞. While doing this, we combinatorially prove that p_r(n)=p_r(n+1) for r prime and for all n not congruent to −1 mod r, and we construct several bijections for sets of permutations defined by modular class restrictions on the cycle lengths. We also include a simple probabilistic proof that, for r≥2, p_r(n)→0 as n→∞. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 17: 157–167, 2000