High-order Boundary Integral Method for Surface Diffusions on 
Elastically Stressed Axisymmetric Rods
  
Abstract:

Many applications in materials involve surface diffusion of elastically 
stressed solids. Study of singularity formation and long-time behavior 
of such solid surfaces requires accurate simulations in both space and 
time. Here we present a high-order boundary integral method for an 
elastically stressed solid with axi-symmetry due to surface diffusions.
Using the high-order boundary integral method, we demonstrate that
in absence of elasticity the cylinder surface pinches in a finite time 
at the axis of the symmetry and the universal cone angle of the 
pinching is found to be consistent with the previous studies based on 
a self-similar assumption. In the presence of elastic stress, 
we show that a finite-time, geometrical singularity occurs well 
before the cylindrical solid collapses onto the axis of symmetry, 
and the angle of the corner singularity 
on the cylinder surface is also estimated.