Scale-dependent Elastic Constants in Mutilated Sheets and Shells - Rescheduled

Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the nonlinear Foeppl-von Karman equations in 1904. However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, leading to strongly scale-dependent elastic constants, consistent with experiments that twist and bend atomically-thin free-standing graphene sheets. With thermally excited graphene sheets, one can study as well the quantum mechanics of two dimensional Dirac massless fermions in a fluctuating curved space whose dynamics resembles a simplified form of general relativity. We also describe recent measurements of a scale-dependent bending rigidity for rippled nanometer-thick cantilevers of Al_2O_3. We then move on to analyze the physics of sheets mutilated with puckers and stitches. Puckers and stitches lead to Ising-like phase transitions that strongly affect the physics of the fluctuating sheet. Thermal fluctuations also cause thin spherical shells beyond a certain critical radius to spontaneously collapse.

Speaker: David Nelson, Stanford University

This event has been rescheduled for November 19, 2024.  See our listing for Dmitir Basov on this date instead.