Constructing slow modes of
from free modes of
Xi
1. Make an independent set
of free modes of
(dR1,ÉdR5).
These create gaps (only)
at the 5 contacts
2. Construct trial modes (dR*1,ÉdR*5) from (dR1,ÉdR5) to close these gaps
E g, displacement of
particle i for mode 1
L
dR*1,i = dR1,i sin(2pXi/L)
3. Select (dR1,ÉdR5) so that (dR*1,ÉdR*5) are orthogonal.
4. Trial modes have low energy,
hence low average frequency w(L)~1/L
Éabout as low as lowest acoustic modes of these particles
Thus there are 5 normal modes of with average
frequency < w(L)
