Tethered membranes far from equilibrium: Buckling dynamics

We study the dynamics of the classical Euler buckling of compressed solid m embranes. We relate the membrane buckling dynamics to phase ordering phenom ena. Membranes develop a wavelike pattern whose wavelength grows, via coars ening, as a power of time. We find that evolving membranes are similar to g rowing surfaces ("growing interfaces") whose transverse width grows as a po wer of time. The morphology of the evolving membranes is characterized by t he presence of a network of growing ridges where the elastic energy is most ly localized. We used this fact to develop a scaling theory of the buckling dynamics that gives analytic estimates of the coarsening exponents. Our fi ndings show that the membrane buckling dynamics is characterized by a disti nct scaling behavior not found in other coarsening phenomena. [S1063-651X(9 9)04510-9].