Scale Dependent Elasticity and Mutilated Nanosheets

Explore a physics colloquium lecture that delves into the fascinating world of elastic membrane deformations and their behavior under thermal fluctuations. Learn about the historical development from the nonlinear Foeppl-von Karman equations to modern understanding of scale-dependent elasticity in atomically-thin materials like graphene. Discover how thermal fluctuations affect the quantum mechanics of two-dimensional Dirac massless fermions in curved space, drawing parallels to simplified general relativity. Examine recent experimental findings on scale-dependent bending rigidity in Al_2O_3 nanometer-thick cantilevers, and investigate the physics of sheets with puckers and stitches, including their Ising-like phase transitions. Understand how thermal fluctuations influence the spontaneous collapse of thin spherical shells beyond critical radii. Gain insights from renowned physicist David Nelson's extensive research on collective effects in condensed matter physics, including his groundbreaking work with Bertrand I. Halperin on dislocation-mediated melting and the discovery of the hexatic phase of matter.