Design and Experimental Characterization of Low‐Volume PM10/2.5/1.0 Trichotomous Sampler Inlet

This paper presents the development and laboratory evaluation of a PM10/2.5/1.0 trichotomous sampling inlet that consists of two main parts: a previously designed PM10 size‐selective inlet part and a PM2.5/1.0 two‐stage virtual impactor, which was newly fabricated and attached serially to the PM10 size selective inlet part. Particles are collected in three locations through the trichotomous sampling inlet to provide for not only particle concentration measurements of PM10, PM2.5 and PM1.0, but also those of PM2.5–10 and PM1.0–2.5.     

Improved bounds for sampling contingency tables

We study the problem of sampling contingency tables (nonnegative integer matrices with specified row and column sums) uniformly at random. We give an algorithm which runs in polynomial time provided that the row sums r_i and the column sums c_j satisfy r_i = Ω(n^3/2m log m), and c_j = Ω(m^3/2n log n). This algorithm is based on a reduction to continuous sampling from a convex set. The same approach was taken by Dyer, Kannan, and Mount in previous work. However, the algorithm we present is simpler and has weaker requirements on the row and column sums. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 135–146, 2002     

Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow

Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical–numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd.     

A simple and realistic triton wave function

We propose a simple triton wave function that consists of a product of three correlation operators operating on a three-body spin-isospin state. This wave function is formally similar to that used in the recent variational theories of nuclear matter, the main difference being in the long-range behavior of the correlation operators. Variational calculations are carried out with the Reid potential, using this wave function in the so-called “symmetrized product” and “independent pair” forms. The triton energy and density distributions obtained with the symmetrized product wave function agree with those obtained in Faddeev and other variational calculations using harmonic oscillator states. The proposed wave function and calculational methods can be easily generalized to treat the four-nucleon α-particle.     

Assessment of thermal expansion coefficient of methylsilsesquioxane thin film

For the methylsilsesquioxane film whose optical birefringence is almost zero, it was recently reported that its vertical thermal expansion coefficient (CTE) was approximately one order of magnitude larger than the lateral CTE. Though the birefringence is not an absolute predictor of anisotropic behavior, the discrepancy in both the CTEs was so remarkable that it was essential to investigate whether the anisotropy was intrinsic property or not. If the effect of Poisson's ratio is considered in the calculation of the vertical CTE and when elastic modulus measured by surface acoustic wave spectroscopy is used in the assessment of the lateral CTE, both the CTEs are coincident with each other. Therefore, it can be concluded that the discrepancy in the CTEs can be attributed to a higher in‐plane polymer chain orientation but it can also arise from the misleadingly assumed modulus and Poisson's ratio. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3109–3120, 2006     

OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

On disjoint configurations in infinite graphs

For a graph A and a positive integer n, let nA denote the union of n disjoint copies of A; similarly, the union of ?₀ disjoint copies of A is referred to as ?₀A. It is shown that there exist (connected) graphs A and G such that nA is a minor of G for all n??, but ?₀A is not a minor of G. This supplements previous examples showing that analogous statements are true if, instead of minors, isomorphic embeddings or topological minors are considered. The construction of A and G is based on the fact that there exist (infinite) graphs G₁, G₂,… such that G_i is not a minor of G_j for all i ≠ j. In contrast to previous examples concerning isomorphic embeddings and topological minors, the graphs A and G presented here are not locally finite. The following conjecture is suggested: for each locally finite connected graph A and each graph G, if nA is a minor of G for all n ? ?, then ?₀A is a minor of G, too. If true, this would be a far‐reaching generalization of a classical result of R. Halin on families of disjoint one‐way infinite paths in graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 222–229, 2002; DOI 10.1002/jgt.10016