  We study pinning and unpinning of superfluid vortices in the inner crust of a
neutron star using 3-dimensional dynamical simulations. Strong pinning occurs
for certain lattice orientations of an idealized, body-centered cubic lattice,
and occurs generally in an amorphous or impure nuclear lattice. The pinning
force per unit length is $\sim 10^{16}$ dyn cm$^{-1}$ for a vortex-nucleus
interaction that is repulsive, and $\sim 10^{17}$ dyn cm$^{-1}$ for an
attractive interaction. The pinning force is strong enough to account for
observed spin jumps (glitches). Vortices forced through the lattice move with a
slip-stick character; for a range of superfluid velocities, the vortex can be
in either a cold, pinned state or a hot unpinned state, with strong excitation
of Kelvin waves on the vortex. This two-state nature of vortex motion sets the
stage for large-scale vortex movement that creates an observable spin glitch.
We argue that the vortex array is likely to become tangled as a result of
repeated unpinnings and repinnings. We conjecture that during a glitch, the
Kelvin-wave excitation spreads rapidly along the direction of the mean
superfluid vorticity and slower in the direction perpendicular to it, akin to
an anisotropic deflagration.
