Visualization of Global Trade-Offs in Aerodynamic Problems by ARMOGAs

Trade-offs is one of important elements for engineering design problems characterized by multiple conflicting design objectives to be simultaneously improved. In many design problems such as aerodynamic design, due to computational reasons, only a limited number of evaluations can be allowed for industrial use. Efficient MOEAs, Adaptive Range Multi-Objective Genetic Algorithms (ARMOGAs), to identify trade-offs using a small number of function evaluations have been developed. In this study, ARMOGAs are applied to aerodynamic designs problems to identify trade-offs efficiently. In addition to identify trade-offs, trade-off analysis is also important to obtain useful knowledge about the design problem. To analyze the high-dimensional data of aerodynamic optimization problem, Self-Organizing Maps are applied to understand the trade-offs

Eccentricity Trap: Trapping of Resonantly Interacting Planets near the Disk Inner Edge

Using orbital integration and analytical arguments, we have found a new mechanism (an "eccentricity trap") to halt type I migration of planets near the inner edge of a protoplanetary disk. Because asymmetric eccentricity damping due to disk-planet interaction on the innermost planet at the disk edge plays a crucial role in the trap, this mechanism requires continuous eccentricity excitation and hence works for a resonantly interacting convoy of planets. This trap is so strong that the edge torque exerted on the innermost planet can completely halt type I migrations of many outer planets through mutual resonant perturbations. Consequently, the convoy stays outside the disk edge, as a whole. We have derived semi-analytical formula for the condition for the eccentricity trap and predict how many planets are likely to be trapped. We found that several planets or more should be trapped by this mechanism in protoplanetary disks that have cavities. It can be responsible for the formation of non-resonant, multiple, close-in super-Earth systems extending beyond 0.1AU. Such systems are being revealed by radial velocity observations to be quite common around solar-type stars.Comment: 24 pages, 7 figures, accepted for publication in Ap