Eigenvector of ILM, The Shooting Method.
Vary the mode frequency, w, by clicking the mouse on one of the
red or blue markers at the top of the
figure. The anharmonic mode eigenvector is constructed according to
the "rotating-wave" approximation (RWA). For some particular
eigenfrequency the mode eigenvector becomes localized. One may launch
a molecular-dynamics simulation (press MDS-button) and see the resulting
vibrational spectrum of the particles.
It seems that this applet
does not work properly on Mac
Within the rotating-wave approximation (RWA)  the eigenvector of the
anharmonic mode in the 1-D nonlinear chain has to satisfy the
following recurrence relations:
w2 M fn +
(fn+1 - 2 fn + fn-1) K2 +
(fn+1 - fn)3 K4 +
(fn-1 - fn)3 K4 = 0 ,
where A is the mode amplitude and fn
represent the mode eigenvector.
In order to find the intrinsic local mode eigenvector we launch
"shots"  from the mode center and trying to form the localized shape for
the mode: when its amplitude decreases with distance away from the center.
By varying the mode frequency we can go through a variety of different
eigenvectors. At some particular eigenfrequency the mode eigenvector
 W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,
Numerical Recipes in C, (Cambridge Univ. Press, 1992) p. 749.
Last modified: August 13, 1997