Aircraft con ict detection and resolution is currently attracting the interest of many air transportation service providers and is concerned with the following question: Given a set of airborne aircraft and their intended trajectories, what control strategy should be followed by the pilots and the air tra c service provider to prevent the aircraft from coming too close to each other? This paper addresses this problem by presenting a distributed air-ground architecture, whereby each aircraft proposes its desired heading while a centralized air tra c control architecture resolves any con ict arising between the aircraft involved in the con ict, while minimizing the deviation between desired and con ict-free heading for each aircraft. The resolution architecture relies on a combination of convex programming and randomized searches: It is shown that a v ersion of the planar, multi-aircraft con ict resolution problem that accounts for all possible crossing patterns among aircraft might berecast as a nonconvex, quadratically constrained quadratic program. For this type of problem, there exist e cient numerical relaxations, based on semide nite programming, that provide lower bounds on the best achievable objective. These relaxations also lead to a random search technique to compute feasible, locally optimal and con ict-free strategies. This approach is demonstrated on numerical examples and discussed.

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Considering two intersecting flows of aircraft, this paper provides new stability proofs of aircraft deviation boundedness under decentralized, sequential conflict avoidance rules. In particular, proofs are provided to handle lateral displacement and offset maneuvers. Turning then towards the case of three intersecting aircraft flows using a simplified offset model, this paper provides evidence that simple decentralized conflict avoidance rules may not be closed-loop stable. However, centralized conflict resolution algorithms are proven to be stabilizing, that is, a suitable maneuver pattern is displayed that is resulting in bounded aircraft deviations.

Molecular dynamics simulation method was used to study the rarefied gaseous flows in nanochannels. A pressure-driven force was introduced to drive the gas to flow between two parallel walls. The effects of driven force magnitude and channel height were investigated. The results show that a single layer of gaseous molecules is adsorbed on the wall surface. The density of adsorption layer decreases with the increase of channel height, but doesnt vary with driven force. The velocity profile across the channel has the traditional parabolic shape. The average velocity and gas slip velocity on the wall increase linearly with the increase of pressure-driven force. The gas slip velocity decreases linearly with the increase of channel height. The ratio of slip to average velocity decreases linearly with the increase of channel height.