The statistical properties of this symbol string are then analyzed for multi-step correlations. Our current interests concern the detection of symbolic precursors of instabilities. Here the dynamics of the system is weakly non-stationary in time. The symbolic data is sampled in moving windows and the statistical properties of the symbols in different windows is compared. In the figure at right we show a cross correlation plot comparing the symbolic behavior of a dynamical system with the noise driving it.
Early times are at the upper left and later times at the lower right.
The instability occurs along the right edge. Short wavelength asymptotics has become a well-developed area of mathematical physics and applications can be found in all branches of physics. My efforts in this area have concentrated on situations where the WKB approximation breaks down. This work is carried out in collaboration with Prof. Allan N. Kaufman of UC Berkeley and the plasma theory group at Lawrence Berkeley National Lab. This is a resonance phenomena, much like the coupling of two oscillators, and it leads to a significant exchange of energy, momentum, and action between the various wave modes.