We describe and analyze a ‘screened refuge’ technique for indefinitely sustaining control of insect pests using transgenic pesticidal crops or an applied pesticide, even when resistance is not recessive. The screen is a physical barrier that restricts pest movement. In a deterministic discrete-time model of the use of this technique, we obtain asymptotic analytical formulas for the two important equilibria of the system in terms of the refuge size and the pest fitnesses, mutation rates, and mobility out of and into the refuge. One of the equilibria is stable and is the point at which the pest population is controlled. The other is a saddle whose stable manifold bounds the basin of attraction of the former: its location provides a measure of the tolerance of the control mechanism to perturbations in the resistant allele density.

A relatively simple mechanistic model for the combustion of an aluminum particle in air is presented. The model assumes combustion to occur in two stages. In the first stage, phase transition and heterogeneous surface reactions take place until the melting temperature of the oxide is reached. In the second stage, a quasi-steady state diffusion flame is established allowing for the use of commonly employed flame sheet approximations. Modified Ranz-Marshall and standard drag correlations for a sphere are used to describe the unsteady heating, mass loss rate, and drag of the particle, with the surrounding gas. A system of non-linear ordinary differential equations are formulated and numerically integrated in time for predictions of particle mass, temperature and velocity with, and without, the effects of heterogeneous combustion. Results indicate that, within the assumptions of the current model, the effects of heterogeneous combustion have a significant impact on the overall particle burn time and temperature history for gas temperatures ranging from 1500 to 2500 K. At higher particle Reynolds number, and for temperatures greater than 2500 K, the effects of heterogeneous combustion are not as important and an ignition criterion based on the oxide melting temperature may be sufficient.

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