Reaction-diffusion model for combustion with fuel consumption: II. Robin boundary conditions

A model, derived in a previous paper, for the reaction betweena gaseous oxidant and a solid porous fuel is analysed furtherfor general Robin boundary conditions. Numerical solutions areobtained and the effects of varying the dimensionless parameters,particularly the Frank-Kamenetskii parameter and the Lewisnumber L, are discussed in detail and compared with resultsobtained previously when Dirichlet boundary conditions are applied.Analytic solutions are obtained for the small-time developmentand for large values of . This latter solution shows the existenceof a propagating reaction-diffusion burning wave, and has featureswhich are qualitatively different to those derived earlier.     

Synthesis, Characterization, and Luminescence Properties of Anthrylpolyamines: An Experiment for an Integrated, Advanced Laboratory Course

A 10-week, open-ended experiment for a junior/senior-level integrated laboratory course is described. The project involves the synthesis and instrumental characterization of two monosubstituted and two disubstituted anthrylpolyamines of varying lengths, as well as a detailed investigation of their photophysical and photochemical properties in the presence of polyanions of biological interest. Depending on the nature of the polyanion, emission quenching of the anthracene chromophore occurs by a template-directed excimer formation, or by an energy-transfer process. A correlation between the charge of the protonated anthrylpolyamines and the degree of emission quenching is also investigated. This project is ideally suited for introducing students to different quenching mechanisms within the context of a research-oriented, integrated laboratory experience.     

A Computer Program to Calculate the Percent Total Deuteration in an Exchange Reaction

The acid-catalyzed hydrogen-deuterium exchange reaction in aliphatic ketones was modeled as a purely random process. Using a computer program, a statistically random hydrogen-deuterium exchange was simulated for a particular molecule, 2-indanone. For this molecule, there are two carbons, each providing two potential sites for exchange. The program determined the relative amounts for each of the partially deuterated species, including the total percent deuteration. A comparison with mass spectral data showed good agreement with this model.     

A NEW FLUX-CONSERVING NEWTON SCHEME FOR THE NAVIER-STOKES EQUATIONS

SUMMARY

A new numerical method is developed for the two-dimensional, steady Navier-Stokes equations. Using local polynomial expansions to represent the discrete primitive variables on each cell, we construct a scheme which has the following properties: First, the local discrete primitive variables are functional solutions of both the integral and differential forms of the Navier-Stokes equations. Second, fluxes are balanced across cell interfaces using exact functional expressions (to the order of accuracy of the local expansions). No interpolation, flux models, or flux limiters are required. Third, local and global conservation of mass, momentum, and energy are explicitly provided for. Finally, the discrete primitive variables and their derivatives are treated in a unified and consistent manner. All are treated as unknowns to be solved together for simulating the local and global flux conservation.

A general third-order formulation for the steady, compressible Navier-Stokes equations is presented. As a special case, the formulation is applied to incompressible flow, and a Newton's method scheme is developed for the solution of laminar channel flow. H is shown that, at Reynolds numbers of 100, 1000, and 2000, the developing channel flow boundary layer can be accurately resolved using as few as six to ten cells per channel width.     

The Factorization of Sparse Symmetric Indefinite Matrices

The Harwell multifrontal code MA27 is able to solve symmetricindefinite systems of linear equations such as those that arisefrom least-squares and constrained optimization algorithms,but may sometimes lead to many more arithmetic operations beingneeded to factorize the matrix than is required by other strategies.In this paper, we report on the results of our investigationof this problem. We have concentrated on seeking new strategiesthat preserve the multifrontal principle but follow the sparsitystructure more closely in the case when some of the diagonalentries are zero.     

Smooth curves linked to thick curves

In this paper we construct smooth irreducible spacecurves C which link geometrically by surfaces of minimal degree containingC to curves of generic embedding dimension three. This produces interesting behavior with respect to both C and . The curves link to smooth connected curves by surfaces of low degree butcannot link to smooth connected curves by surfaces of high degree.The curves C give counterexamples to a conjecture of Martin-Deschamps and Perrin.     

The finite difference mesh on an air-to-dielectric interface

Cognitive obstacles that arise in the teaching and learning of scalar line integrals, derived from cognitive aids provided to students when first learning about integration of single variable functions are described. A discussion of how and why the obstacles cause students problems is presented and possible strategies to overcome the obstacles are outlined.