Spray flame dynamics with oscillating flow and droplet grouping

The co-flow laminar spray diffusion flame in an oscillating flow field is investigated. Mild slip is permitted between the droplets and their host surroundings and droplet grouping resulting from the host flow oscillations is accounted for. The spray is modelled using the sectional approach and a perturbation analysis using a small sectional Stokes number is utilised for solving the liquid phase governing equations. The effect of droplet grouping is described through a specially constructed model for the vaporisation Damkohler number. The large chemical Damkohler number assumption is adopted and a formal analytical solution is developed for Schwab-Zeldovitch parameters through which the dynamics of the spray flame front shapes and thermal fields are deduced. Computed results based on the solutions demonstrate how the phenomenon of droplet grouping can lead to the existence of multiple flame sheets as a result of the dynamic change in the type of the main homogeneous flame from under- to over-ventilated as the flow field oscillates. Concomitant fluctuating thermal fields are also shown to be present indicating a potential impact on undesirable pollutants production.     

Near affine Hjelmslev planes

A study is made of two generalizations of affine Hjelmslev planes in which the parallel axiom is not required to hold. Integer invariants are obtained for the finite planes in these new classes. Formulas are derived which enable one to compute the cardinalities of certain subsets of points and lines in terms of the invariants, and results are obtained on the nonexistence of planes with certain sets of invariants.     

An iteration scheme for boundary value/alternative problems

Numerische Mathematik - A coupled iteration scheme for approximating the solution of nonlinear boundary value problems framed in the context of alternative problems (i.e. auxiliary equation and...     

Index four orientable embeddings and case zero of the Heawood conjecture

By imposing a special symmetry, we are able to construct index four triangular embeddings of graphs in compact orientable 2-manifolds. Because of the complexity of the current graphs required, such embeddings have heretofore been unattainable, but the imposed symmetry reduces the problem to constructing a special kind of index two current graph. We illustrate the method with a solution for case zero of the Heawood conjecture, using an abelian group, thus completing a constructive proof of the Heawood map color theorem, and eliminating the need for Galois field theory and nonabelian groups in its solution. The method has also been used in the determination of the genus of K_n,n,n,n.     

Modeling of MIG/MAG welding with experimental validation using an active contour algorithm applied on high speed movies

This paper investigates some issues in physical modeling of metal inert gas/metal active gas (MIG/MAG) welding process in the short arc mode. In this mode, a metal supply is molten in the arc state and then transferred to the weld pool during the short-circuit state. A hybrid model having two distinct continuous states whose switchings are controlled by two guard conditions is proposed. Due to the complexity of the physical phenomena involved in the welding process, simplifications are used to obtain a model accounting for the main physical contributions but simple enough to yield an efficient, fast and numerically tractable simulator which can be used intensively for evaluating different control strategies. In an attempt to validate the proposed model, different measurements have been made including supply voltage and current sampled synchronously with high speed digital video. In order to extract some relevant quantities representative of the metal transfer from image sequences, an active contour algorithm is developed and tested. The effectiveness of the proposed model in the prediction of major tendencies of a welding process, especially in the arc state, is shown using experimental data. Some limitations of the model during the metal transfer are also stressed and possible remedies are then proposed.     

All directed BIBDs with k = 3 exist

A directed BIBD with parameters ($\text{υ, b, r, k, λ}{}^1$) is a BIBD with parameters ($\text{υ, b, r, k, 2λ}{}^1$) in which each ordered pair of varieties occurs together in exactly $\text{λ}{}^1$ blocks. It is shown that $\text{λ}{}^1\text{υ(υ ? 1) ≡ 0}$ (mod 3) is a necessary and sufficient condition for the existence of a directed ($\text{υ, b, r, k, λ}{}^1$) BIBD with k = 3.     

A Nanometer Aerosol Size Analyzer (nASA) for Rapid Measurement of High-concentration Size Distributions

We have developed a fast-response nanometer aerosol size analyzer (nASA) that is capable of scanning 30 size channels between 3 and 100 nm in a total time of 3 s. The analyzer includes a bipolar charger (Po²¹⁰), an extended-length nanometer differential mobility analyzer (Nano-DMA), and an electrometer (TSI 3068). This combination of components provides particle size spectra at a scan rate of 0.1 s per channel free of uncertainties caused by response-time-induced smearing. The nASA thus offers a fast response for aerosol size distribution measurements in high-concentration conditions and also eliminates the need for applying a de-smearing algorithm to resulting data. In addition, because of its thermodynamically stable means of particle detection, the nASA is useful for applications requiring measurements over a broad range of sample pressures and temperatures. Indeed, experimental transfer functions determined for the extended-length Nano-DMA using the tandem differential mobility analyzer (TDMA) technique indicate the nASA provides good size resolution at pressures as low as 200 Torr. Also, as was demonstrated in tests to characterize the soot emissions from the J85-GE engine of a T-38 aircraft, the broad dynamic concentration range of the nASA makes it particularly suitable for studies of combustion or particle formation processes. Further details of the nASA performance as well as results from calibrations, laboratory tests and field applications are presented below.