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)