Multiscale modelling of dendrite growth during vacuum arc remelting

Vacuum Arc Remelting (VAR) is the accepted method for producing homogeneous, fine microstructures that are free of inclusions required for rotating grade applications. However, as ingot sizes are increasing INCONEL 718 becomes increasingly susceptible to defects such as freckles, tree rings, and white spots increases for large diameter billets. Therefore, predictive models of these defects are required to allow optimization of process parameters. In this paper, a multiscale and multi-physics model is presented to predict the development of microstructures in the VAR ingot during solidification. At the microscale, a combined stochastic nucleation approach and finite difference solution of the solute diffusion is applied in the semi-solid zone of the VAR ingot. The micromodel is coupled with a solution of the macroscale heat transfer, fluid flow and electromagnetism in the VAR process through the temperature, pressure and fluid flow fields. The main objective of this study is to achieve a better understanding of the formation of the defects in VAR by quantifying the influence of VAR processing parameters on grain nucleation and dendrite growth. In particular, the effect of different ingot growth velocities on the microstructure formation was investigated. It was found that reducing the velocity produces significantly more coarse grains.

Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak

Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host's intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic.