While traditional materials can often be modeled as networks of masses interacting by springs, highly unusual behavior arises when the masses of such a network are replaced by rapidly spinning tops (gyroscopes). In particular, these networks can exhibit band gaps and uni-directional wave propagation on the network’s edges. Since these behaviors are protected by topological properties of the structures, the waves traverse sharp corners and persist despite impurities in the material.
To our surprise, we found that not only can topological matter have some disorder, but networks with topological band structure can be constructed in a completely amorphous structure. See our recent paper for more info.
We also demonstrated the ability to create a topological switch using a gyroscopic metamaterial in an experiment. By introducing a patterned magnetic field at every site that interacts with each gyroscope, we break the inversion symmetry (the symmetry under looking at the mirror image) of the network. Once the inversion symmetry breaking is large enough, the edge modes bleed into bulk modes, and the topological waves are shut off. We can control this transition in real time, enabling the use of topological waves for information storage and readout. Read our paper here. Another paper on other topological phase transitions in these systems is here.
Fracture in sheets draped on curved surfaces
In recent decades, a deeper understanding of fracture has led to novel tools for controlling cracks. Collaborators and I have uncovered how Gaussian curvature guides material failure in otherwise unstructured or modified elastic sheets. We find that draping an elastic sheet over a curved substrate can trigger or prevent crack growth, direct crack paths, and even arrest cracks. This complex behavior obeys robust geometric principles which should apply to a wide range of systems spanning many scales, from nanoparticle membranes to macroscopic structures. Check out the paper here.
Fracture and deformation in nanoparticle sheets
A useful regime to study the deformation of sheets conformed to curved surfaces is on the nanoscale. Nanoparticle monolayer sheets are ultrathin inorganic–organic hybrid materials with broad applications. They combine highly controllable optical and electrical properties with mechanical flexibility and remarkable strength. Like other thin sheets, their low bending rigidity allows them to easily roll into or conform to cylindrical geometries. More important still, they can also cope with strain through local particle rearrangement and plastic deformation. This means that, unlike thin sheets such as paper or graphene, nanoparticle sheets can much more easily conform to surfaces with complex topography characterized by non-zero Gaussian curvature, like spherical caps or saddles. We investigated the limits of nanoparticle monolayers’ ability to conform to substrates with Gaussian curvature by stamping nanoparticle sheets onto lattices of larger polystyrene spheres. We found that tuning the size of the spheres reproducibly changes the behavior of the sheet, and we propose a theoretical account of this behavior that is supported by simulations.
Read the paper here.
Evolution of dwarf galaxies
During my undergraduate years, I worked on a fundamental question in astrophysics: How are nearby dwarf galaxies evolving as new stars are born? Since these small galaxies are less evolved than larger galaxies like the Milky Way, understanding their histories could shed light on the evolution of galaxies formed in the early universe. With Dr. Kristen McQuinn and Prof Evan Skillman, I looked at bursts of star formation activity in nearby ‘starburst’ dwarf galaxies, examining their star formation activity with data from Hubble (visible light), MIPS (IR), GALEX (UV), and Chandra (x-ray). By examining the same galaxies through a variety of wavelengths, we measured the rates of star formation in these galaxies and the spatial distribution of galactic superwinds. Our papers from this work can be found here, and here, and here.