Surface Fluctuations and the Stability of Metal Nanowires
  The surface dynamics and thermodynamics of metal nanowires are investigated in a continuum model. Competition between surface tension and electron-shell effects leads to a rich stability diagram, with fingers of stability extending to extremely high temperatures for certain magic conductance values. The linearized dynamics of the nanowire's surface are investigated, including both acoustic surface phonons and surface self-diffusion of atoms. On the stability boundary, the surface exhibits critical fluctuations, and the nanowire becomes inhomogeneous. Some stability fingers coalesce at higher temperatures, or exhibit overhangs, leading to reentrant behavior. The nonlinear surface dynamics of unstable nanowires are also investigated in a single-mode approximation. We find evidence that some unstable nanowires do not break, but rather neck down to the next stable radius. 
C. H. Zhang, F. Kassubek, and C. A. Stafford