  We study properties of the strongly repulsive Bose gas on one-dimensional
incommensurate optical lattices with a harmonic trap, which can be deal with by
using the exact numerical method through the Bose-Fermi mapping. We first
exploit the phase transition of the hard-core bosons in the optical lattices
from superfluid-to-Bose-glass phase as the strength of the incommensurate
potential increases. Then we study the dynamical properties of the system after
suddenly switching off the harmonic trap. We calculate the one-particle density
matrices, momentum distributions, the natural orbitals and their occupations
for both the static and dynamic systems. Our results indicate that the
Bose-glass phase and superfluid phase display quite different properties and
expansion dynamics.
