Stability of cylindrical bodies in the theory of surface diffusion

Perturbation arguments and finite element calculations are employed to study the nonlinear partial differential equations governing morphological changes induced by curvature-driven diffusion of mass in the surface of an axially symmetric body. Isotropy of surface properties is assumed. Second- and higher-order perturbation analyses indicate that the familiar result of the linear theory of small amplitude longitudinal perturbations of a cylinder to the effect that a long cylinder is stable against all perturbations with spatial Fourier spectra containing only wavelengths less than the circumference of the cylinder does not hold in the full nonlinear theory. The perturbation analyses yield criteria for determining when longitudinal perturbations with high wave-number spectra grow in amplitude, after an initial decay followed by an incubation time, and result in break-up of the body into a necklace of beads. The principal conclusions of the formal perturbation analyses are found to be in good accord with numerical solutions obtained by finite element methods.