An Exactly Solvable Model for Nonlinear Resonant Scattering

This work analyzes the effects of cubic nonlinearities on certain resonant scattering anomalies associated with the dissolution of an embedded eigenvalue of a linear scattering system. These sharp peak-dip anomalies in the frequency domain are often called Fano resonances. We study a simple model that incorporates the essential features of this kind of resonance. It features a linear scatterer attached to a transmission line with a point-mass defect and coupled to a nonlinear oscillator. We prove two power laws in the small coupling \to 0 and small nonlinearity \to 0 regime. The asymptotic relation ~ C^4 characterizes the emergence of a small frequency interval of triple harmonic solutions near the resonant frequency of the oscillator. As the nonlinearity grows or the coupling diminishes, this interval widens and, at the relation ~ C^2, merges with another evolving frequency interval of triple harmonic solutions that extends to infinity. Our model allows rigorous computation of stability in the small and limit. In the regime of triple harmonic solutions, those with largest and smallest response of the oscillator are linearly stable and the solution with intermediate response is unstable

Simulator systems integration

The implementation of available wind shear data into general aviation flight training simulators is discussed. Currently, there are 11 simulators with wind shear models installed involving some 9 different aircraft models. Retrofits to other systems that were put out earlier are currently underway, and all the new simulators will have wind shear available for the instructors to use for demonstrations and training. There are three types of computer systems involved, and two different types of instructor stations. Most of the systems with wind shear are the CRT-type displays. The integration of wind shear models in flight simulators is discussed in detail