Metamaterials and Topological Mechanics Lecture 03 by Tom Lubensky

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Infosys-ICTS Chandrasekhar Lectures • Metamaterials and Topological Mechanics • Speaker: Tom Lubensky (University of Pennsylvania, Pennsylvania) • Date: 24 June 2019, 16:00 to 18:00 • Venue: Ramanujan lecture hall, ICTS campus • • • Lecture 1 : Metamaterials and Topological Mechanics • Date Time : Monday, 24 June 2019, 16:00 • Abstract : Metamaterials are engineered to have properties not found in nature, such as a negative optical index of refraction, one-way light or vibration waves, or exotic elastic behavior. Made-to-order structures at length scales as short as a micron can now be fabricated with advanced materials processing like 3D printing. Topology is a unifying mathematical concept related to properties that do not change under continuous changes in parameters. Topological mechanical materials, like topological insulators, have bulk excitation spectra characterized by topological invariants, associated with the opening of bandgaps, that determine physical properties like the Hall conductivity or the nature of edge excitations. This talk will discuss mechanical metamaterials with topologically protected zero-energy edge states in an idealized limit. These states exist at every wavenumber on a surface so that any surface shape distortion costs no energy. Changing the topological class of the material causes one or more zero modes per wavenumber to move from one side of a sample to the opposite creating rigid and supersoft edges. • • Lecture 2 : From classical elasticity to topological mechanics • Date Time : Tuesday, 25 June 2019, 14:30 • • Lecture 3: From classical elasticity to topological mechanics • Date Time : Wednesday, 26 June 2019, 14:30 • • Lecture 4 : From classical elasticity to topological mechanics • Date Time : Thursday, 27 June 2019, 14:30 • • Lecture 5 : From classical elasticity to topological mechanics • Date Time : Friday, 28 June 2019, 14:30 • • This lecture series is part of the program Bangalore School on Statistical Physics - X • Table of Contents (powered by https://videoken.com) • 0:00:00 Metamaterials and Topological Mechanics (Lecture - 03) • 0:00:31 Phonons and Surface Phonons • 0:01:27 Fourier Transform • 0:02:31 Newton's Law • 0:09:01 Surface Rayleigh Waves • 0:32:25 Free energy density equations • 0:36:08 For Example • 0:37:52 Affine Response • 0:46:14 Lattice Models • 1:07:37 Continuum Limit • 1:13:48 Maxwell Lattice • 1:29:27 Q A

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