  We present an extensive study of Mott insulator (MI) and superfluid (SF)
shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic
traps. For this we develop an inhomogeneous mean-field theory. Our results for
the BH model with one type of spinless bosons agrees quantitatively with
quantum Monte Carlo (QMC) simulations. Our approach is numerically less
intensive than such simulations, so we are able to perform calculation on
experimentally realistic, large 3D systems, explore a wide range of parameter
values, and make direct contact with a variety of experimental measurements. We
also generalize our inhomogeneous mean-field theory to study BH models with
harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two
species of bosons we obtain rich phase diagrams with a variety of SF and MI
phases and associated shells, when we include a quadratic confining potential.
For the spin-1 BH model we show, in a representative case, that the system can
display alternating shells of polar SF and MI phases; and we make interesting
predictions for experiments in such systems.
