The lift on an aerofoil in starting flow
An analysis is given of the initial development of the lift on an aerofoil in inviscid starting flow. It is shown that because of the spiral shape of the vortex sheet shed initially from the trailing edge the lift and drag are both singular at the start of impulsive motion. This result is in contrast with the prediction of finite forces by methods that assume the vortex sheet to be initially planar. The effect of a steady rate of change of incidence following the sudden onset of transverse (heaving) motion of an aerofoil in a steady stream is also discussed.
In this paper, we study the asymptotical optimal solutions for the general airline revenue management problem, considering both customer cancelations and no-shows. We study a simple case where there is only one fare-class; the management controls the opening and closing of the fare-class, with the objective of maximizing the total revenue. We first develop a fluid control problem, where the customer arrival and cancelation processes are treated as deterministic, whereas the no. of no-shows is random. The optimal fluid solution is shown to have a simple structure of accepting up to a single time point t* and rejecting afterwards. We show that this policy acts as an upper bound for the MDP problem. Applying the optimal fluid solution to the stochastic environment, we show that this policy is asymptotically optimal on the fluid scaling.