Stabilization strategies for some reaction–diffusion systems

A two-component reaction–diffusion system is considered. The question of stabilizing to zero one of the components of the solution via an internal control acting on a small subdomain and preserving nonnegativity of both components is investigated. Our results apply to predator–prey systems.     

On Lévy-driven vacation models with correlated busy periods and service interruptions

This paper considers queues with server vacations, but departs from the traditional setting in two ways: (i) the queueing model is driven by Lévy processes rather than just compound Poisson processes; (ii) the vacation lengths depend on the length of the server’s preceding busy period. Regarding the former point: the Lévy process active during the busy period is assumed to have no negative jumps, whereas the Lévy process active during the vacation is a subordinator. Regarding the latter point: where in a previous study (Boxma et al. in Probab. Eng. Inf. Sci. 22:537–555, 2008) the durations of the vacations were positively correlated with the length of the preceding busy period, we now introduce a dependence structure that may give rise to both positive and negative correlations. We analyze the steady-state workload of the resulting queueing (or: storage) system, by first considering the queue at embedded epochs (viz. the beginnings of busy periods). We show that this embedded process does not always have a proper stationary distribution, due to the fact that there may occur an infinite number of busy-vacation cycles in a finite time interval; we specify conditions under which the embedded process is recurrent. Fortunately, irrespective of whether the embedded process has a stationary distribution, the steady-state workload of the continuous-time storage process can be determined. In addition, a number of ramifications are presented. The theory is illustrated by several examples.     

Effect of process parameters on the EHD airflow

This work deals with the assessment by numerical investigations of the electrohydrodynamic enhancement of heat transfer in a channel. In order to get a better understanding of the phenomena, we developed an original numerical approach. The model handles the couplings between a non-isothermal turbulent flow and corona discharges from multiple wires. The typical configuration consists in a channel where air enters at a given velocity. In the channel, the ionic wind is produced by multiple coronating wires. In this study, the model is used in order to analyse the effect of some process parameters (inter-electrode distance, wire radius, applied voltage) on the flow and on the convective heat transfer enhancement. We firstly confirm that the model operates well and permits selection of the best parameters in a specific configuration. The model reveals that similar flows could be obtained with different combinations between the inter-electrode distance and the applied voltage. In a second stage, the distance between adjacent wires is discussed. Synergetic effects are obtained for close wires; they locally lead to a tenfold increase of the heat transfer enhancement.