  We use classical molecular dynamics simulations to study the collapse of
single (SWNT) and double-walled (DWNT) carbon nanotube bundles under
hydrostatic pressure. The collapse pressure (pc) varies as 1/R^3, where R is
the SWNT radius or the DWNT effective radius. The bundles show ~ 30% hysteresis
and the hexagonally close packed lattice is completely restored on
decompression. The pc of DWNT is found to be close to the sum of its values for
the inner and the outer tubes considered separately as SWNT, demonstrating that
the inner tube supports the outer tube and that the effective bending stiffness
of DWNT, D(DWNT) ~ 2D(SWNT) . We use an elastica formulation to derive the
scaling and the collapse behavior of DWNT and multi-walled carbon nanotubes.
