  Three kinds of the response mechanisms to the external pressure have been
found for double-walled carbon nanotube (DWNT) bundle, depending strongly on
their average radius and symmetry. The small-diameter DWNT bundle undergoes a
small discontinuous volume change, and then deform continuously. The
intermediate-diameter DWNT bundle collapses completely after a structure phase
transition (SPT). Significantly, two SPTs exist for the larger-diameter DWNT
bundle if the outer tube has no $C_{6}$ or $C_{3}$ symmetry. It would be
interesting to search for signatures of these different structural
transformations by experimentally investigating mechanical, optical and thermal
response functions of DWNT bundle.
