  We study the mechanics and statistical physics of dislocations interacting on
cylinders, motivated by the elongation of rod-shaped bacterial cell walls and
cylindrical assemblies of colloidal particles subject to external stresses. The
interaction energy and forces between dislocations are solved analytically, and
analyzed asymptotically. The results of continuum elastic theory agree well
with numerical simulations on finite lattices even for relatively small
systems. Isolated dislocations on a cylinder act like grain boundaries. With
colloidal crystals in mind, we show that saddle points are created by a
Peach-Koehler force on the dislocations in the circumferential direction,
causing dislocation pairs to unbind. The thermal nucleation rate of dislocation
unbinding is calculated, for an arbitrary mobility tensor and external stress,
including the case of a twist-induced Peach-Koehler force along the cylinder
axis. Surprisingly rich phenomena arise for dislocations on cylinders, despite
their vanishing Gaussian curvature.
