  We studied the appearance of Mott insulator domains of hard sphere bosons on
quasi one-dimensional optical lattices when an harmonic trap was superimposed
along the main axis of the system. Instead of the standard approximation
represented by the Bose-Hubbard model, we described those arrangements by
continuous Hamiltonians that depended on the same parameters as the
experimental setups. We found that for a given trap the optical potential
depth, $V_0$, needed to create a single connected Mott domain decreased with
the number of atoms loaded on the lattice. If the confinement was large enough,
it reached a minimum when, in absence of any optical lattice, the atom density
at the center of the trap was the equivalent of one particle per optical well.
For larger densities, the creation of that single domain proceeded via an
intermediate shell structure in which Mott domains alternated with superfluid
ones.
