Multicorrelation analysis and state space reconstruction

Constructing a mathematical model of a nonlinear system involves developing methods for determining a set of nonlinear differential equations. Based on Floris Takens\u27 theory, the delayed-time space with a given time-series is created, where the first inflection of multicorrelation function is an approximation of the optimal delay time. The multicorrelation function is the generalization of the autocorrelation function into a higher dimension of the system. The standard Grassberger-Proccia algorithm computes the correlation dimension of an artificially generated data set, which involves measuring the distances between all pairs of points, and estimates the dimensionality of the nonlinear system. Finally, the governing differential equations are generated by using a polynomial least squares method. The generated state equations provide the possibility of predicting the system. The practical aspects of attractor reconstruction is discussed in this investigation, by using nonlinear ordinary differential equations with low degrees of freedom as examples

The Edge supersonic transport

As intercontinental business and tourism volumes continue their rapid expansion, the need to reduce travel times becomes increasingly acute. The Edge Supersonic Transport Aircraft is designed to meet this demand by the year 2015. With a maximum range of 5750 nm, a payload of 294 passengers and a cruising speed of M = 2.4, The Edge will cut current international flight durations in half, while maintaining competitive first class, business class, and economy class comfort levels. Moreover, this transport will render a minimal impact upon the environment, and will meet all Federal Aviation Administration Part 36, Stage III noise requirements. The cornerstone of The Edge's superior flight performance is its aerodynamically efficient, dual-configuration design incorporating variable-geometry wingtips. This arrangement combines the benefits of a high aspect ratio wing at takeoff and low cruising speeds with the high performance of an arrow-wing in supersonic cruise. And while the structural weight concerns relating to swinging wingtips are substantial, The Edge looks to ever-advancing material technologies to further increase its viability. Heeding well the lessons of the past, The Edge design holds economic feasibility as its primary focus. Therefore, in addition to its inherently superior aerodynamic performance, The Edge uses a lightweight, largely windowless configuration, relying on a synthetic vision system for outside viewing by both pilot and passengers. Additionally, a fly-by-light flight control system is incorporated to address aircraft supersonic cruise instability. The Edge will be produced at an estimated volume of 400 aircraft and will be offered to airlines in 2015 at $167 million per transport (1992 dollars)