Numerical-Asymptotic Expansion Matching for Computing a Viscous Flow Around a Sharp Expansion Corner

A computational technique which is based on a numerical-asymptotic expansion matching for computing the local singular behavior of a viscous flow around a sharp right-angle expansion corner is presented. Moffatt's (1964) asymptotic solution is extended and a matching with a time-marching finite-difference scheme of the Navier--Stokes equations is formulated. Local mesh refinement around the corner is required to meet the validity of the asymptotic solution. Flows in an expanding channel with expansion ratio D/d=3 at various Reynolds numbers 1≤Re≤700 are simulated. The results are compared with those from a standard finite-difference scheme that uses second-order forward/backward differences near the corner. It is found that the results of the standard scheme converge toward those of the present technique as the level of local refinement near the corner is increased. The time-dependent parameters of the first two terms of the asymptotic solution at the steady-state solution are also described for various cases of Re and D/d. It is demonstrated that the present method enhances the accuracy of the simulations and requires less refinements near the corners to achieve converged numerical results. Received 14 August 2000 and accepted 25 October 2001     

Flow auctions

Flow goods (like electricity) are sold through auctions in a dynamic framework. An important design question is the frequency of such auctions. We use a simple dynamic auction model in continuous time to answer this question. We focus on the relationship between the persistency of bidders’ valuations and the optimal choice of frequency. If the seller focuses on the equilibrium in which bidders follow a repeated static Nash strategy, then the frequency of auctions should typically increase when persistency declines. However, accounting for the fact that bidders can follow different equilibria that are collusive in nature, the comparative statics are reversed, forcing the seller to reduce the frequency when bidders’ valuations are less persistent. The argument builds on the fact that high frequency auctions are more conducive to collusion among bidders.     

The continuous grey pattern problem

A new location problem is formulated and solved. It is the continuous version of the grey pattern problem which is a special case of the Quadratic Assignment Problem. The problem is a minimization of a convex function subject to non-convex constraints and has infinitely many optimal solutions. We propose several mathematical programming formulations that are suitable for a multi-start heuristic algorithm. In addition to solving these formulations by the Solver in Excel and Mathematica, a special Nelder–Mead algorithm is proposed. This special algorithm provided the best results. One suggested modification may improve the performance of the Nelder–Mead algorithm for other optimization problems as well.     

Enhancement of surface wettability via the modification of microtextured titanium implant surfaces with polyelectrolytes

Micrometer- and submicrometer-scale surface roughness enhances osteoblast differentiation on titanium (Ti) substrates and increases bone-to-implant contact in vivo. However, the low surface wettability induced by surface roughness can retard initial interactions with the physiological environment. We examined chemical modifications of Ti surfaces [pretreated (PT), R(a) ≤ 0.3 μm; sand blasted/acid etched (SLA), R(a) ≥ 3.0 μm] in order to modify surface hydrophilicity. We designed coating layers of polyelectrolytes that did not alter the surface microstructure but increased surface ionic character, including chitosan (CHI), poly(L-glutamic acid) (PGA), and poly(L-lysine) (PLL). Ti disks were cleaned and sterilized. Surface chemical composition, roughness, wettability, and morphology of surfaces before and after polyelectrolyte coating were examined by X-ray photoelectron spectroscopy (XPS), contact mode profilometry, contact angle measurement, and scanning electron microscopy (SEM). High-resolution XPS spectra data validated the formation of polyelectrolyte layers on top of the Ti surface. The surface coverage of the polyelectrolyte adsorbed on Ti surfaces was evaluated with the pertinent SEM images and XPS peak intensity as a function of polyelectrolyte adsorption time on the Ti surface. PLL was coated in a uniform thin layer on the PT surface. CHI and PGA were coated evenly on PT, albeit in an incomplete monolayer. CHI, PGA, and PLL were coated on the SLA surface with complete coverage. The selected polyelectrolytes enhanced surface wettability without modifying surface roughness. These chemically modified surfaces on implant devices can contribute to the enhancement of osteoblast differentiation.     

A generalized eigenmode algorithm for reducible regular matrices over the max-plus algebra with applications to the Metro-bus public transport system in Mexico city

In this paper, an algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is applied to the Metro-bus public transport system in Mexico city. A timed event Petri net model is constructed from the data table that characterizes the transport system. A max-plus recurrence equation, with a reducible and regular matrix, is associated with the transport system timed event Petri net. Next, given the reducible and regular matrix, the problem consists of giving an algorithm which will tell us how to compute its generalized eigenmode over the max plus algebra. The solution to the problem is achieved by studying some type of recurrence equations. In fact, by transforming the reducible regular matrix into its normal form, and considering a very specific recurrence equation, an explicit mathematical characterization is obtained, upon which the algorithm is constructed. The generalized eigenmode obtained sets a timetable for the transport system.     

Application of the generalized internal reference method for the characterization of parameters causing drift in inductively-coupled plasma emission spectrometry

Drift in signals limits the performance of inductively-coupled plasma (i.c.p.) emission spectrometry. The generalized internal reference method was applied to deconvolute the drift of an i.c.p. system. The plasma parameters were correlated to the drift components and the error boundary for the method was found. In the system studied, it was found that fluctuations in the nebulizer uptake rate were responsible for short-term signal changes. Long-term signal drift was caused mainly by flow variations of both cooling gas and aerosol carrier gas. The incident power to the plasma was found to be stable compared to other sources of drift. The method was found to be adequate for evaluating the origins of i.c.p. drift.     

On the reactivity-selectivity relationship in the solvolysis of several reactive alkyl halides

In contrast to previous reports, the selectivities of four carbenium ions R⁺ towards N₃^? and H₂O (log(K_N3^?/K_H2O)) change more than the solvolytic reactivities (log K_solv) of their rather reactive precursors RCl.