Tethered membranes far from equilibrium: buckling dynamics

We study the dynamics of the classical Euler buckling of compressed solid membranes. We relate the membrane buckling dynamics to phase ordering phenomena. Membranes develop a wavelike pattern whose wavelength grows, via coarsening, as a power of time. We find that evolving membranes are similar to growing surfaces ("growing interfaces") whose transverse width grows as a power of time. The morphology of the evolving membranes is characterized by the presence of a network of growing ridges where the elastic energy is mostly localized. We used this fact to develop a scaling theory of the buckling dynamics that gives analytic estimates of the coarsening exponents. Our findings show that the membrane buckling dynamics is characterized by a distinct scaling behavior not found in other coarsening phenomena.