  We study the occurrence of non-classical rotational inertia (NCRI) arising
from superfluidity along grain boundaries in a two-dimensional bosonic system.
We make use of a standard mapping between the zero-temperature properties of
this system and the statistical mechanics of interacting vortex lines in the
mixed phase of a type-II superconductor. In the mapping, the liquid phase of
the vortex system corresponds to the superfluid bosonic phase. We consider
numerically obtained polycrystalline configurations of the vortex lines in
which the microcrystals are separated by liquid-like grain boundary regions
which widen as the vortex system temperature increases. The NCRI of the
corresponding zero-temperature bosonic systems can then be numerically
evaluated by solving the equations of superfluid hydrodynamics in the channels
near the grain boundaries. We find that the NCRI increases very abruptly as the
liquid regions in the vortex system (equivalently, superfluid regions in the
bosonic system) form a connected, system-spannig structure with one or more
closed loops. The implications of these results for experimentally observed
supersolid phenomena are discussed.
