Asymptotic dynamics of attractive-repulsive swarms

We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel's first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady-state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly-supported population has edges that behave like traveling waves whose speed, density and slope we calculate. For the contracting case, the dynamics of the cumulative density approach those of Burgers' equation. We derive an analytical upper bound for the finite blow-up time after which the solution forms one or more $\delta$-functions.Comment: 23 pages, 10 figures; revised version updates the analysis in sec. 2.1 and 2.2, and contains enhanced discussion of the admissible class of social interaction force

Improving biocontrol using antagonist mixtures with heat and/or sodium bicarbonate to control postharvest decay of apple fruit

Abstract 'Golden Delicious' apples were wound-inoculated with either Colletotrichum acutatum or Penicillium expansum and then treated with various combinations of heat (38 • C) for 4 days, 2% sodium bicarbonate, and two biocontrol agents alone or combined. The fruit were stored for 4 months at 1 • C and then at 20 • C for 2 weeks. Either heat or the antagonists reduced decay caused by C. acutatum, but a combination of the two was required to completely eliminate decay caused by this pathogen in most cases. Sodium bicarbonate alone or in combination with the antagonists had little effect on C. acutatum. The antagonists alone reduced decay caused by P. expansum but tended to be more effective when combined. Sodium bicarbonate increased the effectiveness of decay control by each antagonist alone or in combination. All of the treatments that included heat virtually eliminated decay caused by this pathogen. The proper combination of alternative control measures can provide an effective strategy to reduce postharvest decay of apple fruit. Published by Elsevier B.V