Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns

An asymptotic interface equation for directional solidification near the absolute stabiliy limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts destabilizing on a planar interface. Moreover, linear stability analysis suggests that the morphology diagram is modified by the flow near the onset of the Mullins-Sekerka instability. Via numerical analysis, the bifurcation structure of the system is shown to change. Besides the known hexagonal cells, structures consisting of stripes arise. Due to its symmetry-breaking properties, the flow term induces a lateral drift of the whole pattern, once the instability has become active. The drift velocity is measured numerically and described analytically in the framework of a linear analysis. At large flow strength, the linear description breaks down, which is accompanied by a transition to flow-dominated morphologies, described in a companion paper. Small and intermediate flows lead to increased order in the lattice structure of the pattern, facilitating the elimination of defects. Locally oscillating structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review

Merging and Spacing of Heterogeneous Aircraft in Support of NextGen

© AIAA. The definitive version is available at: http://arc.aiaa.org/doi/abs/10.2514/1.54076DOI:10.2514/1.54076FAA’s NextGen program aims to increase the capacity of the national airspace, while ensuring the safety of aircraft. This paper provides a distributed merging and spacing algorithm that maximizes the throughput at the terminal phase of flight, using infor- mation communicated between neighboring aircraft through the ADS-B framework. Aircraft belonging to a mixed fleet negotiate with each other and use dual decomposi- tion to reach an agreement on optimal merging times, with respect to a pairwise cost, while ensuring proper inter-aircraft spacing for the respective aircraft types. A set of sufficient conditions on the geometry and operating conditions of merging forks are provided to identify when proper inter-aircraft spacing can always be achieved using the proposed algorithm for any combination of merging aircraft. Also, optimal de- centralized controllers are derived for merging air traffic when operating under such conditions. The performance of the presented algorithm is verified through computer simulations