Using multi-agent negotiation techniques for the autonomous resolution of air traffic conflicts

The National Airspace System in its current incarnation is nearing its maximum capacity. The Free Flight initiative, which would alter the current system by allowing pilots to select more direct routes to their destinations, has been proposed as a solution to this problem. However, allowing pilots to fly anywhere, as opposed to being restricted to planned jetways, greatly complicates the problem of ensuring separation between aircraft. In this thesis I propose using cooperative, multi-agent negotiation techniques in order to efficiently and pseudo-optimally resolve air traffic conflicts. The system makes use of software agents running in each aircraft that negotiate with one another to determine a safe and acceptable solution when a potential air traffic conflict is detected. The agents negotiate using the Monotonic Concession Protocol and communicate using aircraft to aircraft data links, or possibly the ADS-B signal. There are many benefits to using such a system to handle the resolution of air traffic conflicts. Automating CD&R will improve safety by reducing the workloads of air traffic controllers. Additionally, the robustness of the system is improved as the decentralization provided by software agents running in each aircraft reduces the dependence on a single ground based system to coordinate all aircraft movements. The pilots, passengers, and carriers benefit as well due to the increased efficiency of the solutions reached by negotiation

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

Applications of linear hyperbolic partial differential equations: predator-prey systems and gravitational instability of nebulae

AbstractExisting mathematical models and linear stability analyses of their appropriate exact solutions relevant to the paradox of enrichment and Jeans' criterion, respectively, are reviewed. The former is concerned with the outcome of a laboratory predator-prey mite system on oranges, in which a stable limit-cycle situation was destabilized upon tripling the food supply of the herbivorous mite, resulting in the extinction of both mite species due to overexploitation; while the latter can be used to predict the mean distance between adjacent condensations for chains of gravitational instabilities occurring in the outer regions of spiral nebulae. Each problem involves a linear hyperbolic partial differential equation: a first-order McKendrick-Von Foerster equation for the ecological phenomenon and a second-order wave-type equation for the cosmological one. The results of both analyses are then compared with observables of the phenomena under examination. Finally, the chronological development of the mathematical models and the global implications of linear stability theory in these two instances are discussed

A vegetative pattern formation aridity classification scheme along a rainfall gradient: an example of desertification control.

A classification scheme for vegetative patterning along a rainfall gradient in an arid flat environment is developed from an interaction-diffusion plant-surface water model

A one-dimensional nonlinear stablity analysis of vegetative pattern formation for an interaction-diffusion plant-surface water model system in an arid flat environment

Washington State University Department of MathematicsKealy, B. J. & Wollkind, D. (2010, March 26). A one-dimensional nonlinear stablity analysis of vegetative pattern formation for an interaction-diffusion plant-surface water model system in an arid flat environment. Poster presented at the Washington State University Academic Showcase, Pullman, WA