  The time-dependent Ginzburg-Landau formalism is applied to analyze the vortex
states and vortex dynamics in superconducting spherical nanoshells, subjected
to mutually perpendicular strong dc and weak ac magnetic fields. We demonstrate
that nonuniformity of the shell thickness can dramatically affect the ac
magnetic response of a 3D array of superconducting nanoshells. Remarkably, this
response is strongly influenced not only by the relevant geometric and material
parameters and the ac-field frequency but also by the magnitude of the applied
dc field: by changing this field the real part of the effective ac magnetic
permeability can be tuned from positive values significantly larger than one
down to negative values.
