More Like this

1. Geometric control of topological dynamics in a singing saw

   https://doi.org/10.1073/pnas.2117241119  

   Shankar, Suraj; Bryde, Petur; Mahadevan, L. (April 2022, Proceedings of the National Academy of Sciences)

   Significance The ability to sustain notes or vibrations underlies the design of most acoustic devices, ranging from musical instruments to nanomechanical resonators. Inspired by the singing saw that acquires its musical quality from its blade being unusually bent, we ask how geometry can be used to trap and insulate acoustic modes from dissipative decay in a continuum elastic medium. By using experiments and theoretical and numerical analysis, we demonstrate that spatially varying curvature in a thin shell can localize topologically protected modes at inflection lines, akin to exotic edge states in topological insulators. A key feature is the ability to geometrically control both spatial localization and the dynamics of oscillations in thin shells. Our work uncovers an unusual mechanism for designing robust, yet reconfigurable, high-quality resonators across scales. 

   more » « less
2. Flexoelectricity-driven periodic buckling in multilayer graphene bonded to compliant substrate

   https://doi.org/10.1557/s43579-022-00239-9  

   Kothari, Mrityunjay; Kim, Kyung-Suk (September 2022, MRS Communications)

   Advincula, Rigoberto C. (Ed.)

   Flexoelectricity in multilayer graphene (MLG) buckling can stimulate kink-shaped crinkle formation. In the process, the bifurcation becomes subcritical and the suspended-MLG’s crinkle curvature is localized to a narrow band of ∼2𝑛𝑚 width. We extend the study to flexoelectric layers bonded to a soft elastic substrate. Elastic substrates can guide the morphology of MLG and produce periodic patterns. We show that MLG’s flexoelectricity together with substrate elasticity can produce periodic crinkles, which qualitatively explains the grade-dependent mosaic spreading in highly oriented pyrolytic graphite (HOPG). Experimental measurements of HOPG’s surface-slope variations indeed confirm curvature localization at the crinkle valleys and ridges. 

   more » « less
3. Uniqueness of convex ancient solutions to mean curvature flow in R^3.

   https://doi.org/10.1007/s00222-019-00859-4  

   Brendle, Simon; Choi, Kyeongsu (July 2019, Inventiones mathematicae)

   A well-known question of Perelman concerns the classification of noncompact ancient solutions to the Ricci flow in dimension 3 which have positive sectional curvature and are κ-noncollapsed. In this paper, we solve the analogous problem for mean curvature flow in R^3, and prove that the rotationally symmetric bowl soliton is the only noncompact ancient solution of mean curvature flow in R^3 which is strictly convex and noncollapsed. 

   more » « less
4. Evolution of the Josephine Peridotite Shear Zones: 1. Compositional Variation and Shear Initiation

   https://doi.org/10.1029/2019GC008399  

   Kumamoto, Kathryn M.; Warren, Jessica M.; Hauri, Erik H. (December 2019, Geochemistry, Geophysics, Geosystems)

   Abstract Shear localization in the upper mantle, a necessity for plate tectonics, can have a number of causes, including shear heating, the presence of melt, the development of a strong crystal preferred orientation, and the presence of water. The Josephine Peridotite of southwestern Oregon contains shear zones that provide an excellent opportunity to examine the initiation of shear localization. These shear zones are relatively small scale and low strain compared to many shear zones in peridotite massifs, which typically have extreme grain size reduction indicating extensive deformation. We use major, trace, and volatile element analyses of a large suite of harzburgites from the Fresno Bench shear zones to evaluate the mechanisms leading to shear localization. Lithological evidence and geochemical transects across three shear zones show a complex history of melting, melt addition, and melt‐rock interaction. The distribution of aluminum and heavy rare earth elements across the shear zones suggest that melt flow was focused in the centers of the studied shear zones. Water concentrations in orthopyroxene grains of 180–334 ppm H₂O indicate a comparatively high degree of hydration for nominally anhydrous minerals. The correlation of water with aluminum and ytterbium in orthopyroxene is consistent with a melt source for this hydration, suggesting that water equilibrated between the melt and peridotite. The presence of melt and hydration of the host rock provide mechanisms for initial weakening that lead to localized deformation. 

   more » « less
5. Corner states in a second-order mechanical topological insulator

   https://doi.org/10.1038/s43246-021-00170-x  

   Chen, Chun-Wei; Chaunsali, Rajesh; Christensen, Johan; Theocharis, Georgios; Yang, Jinkyu (December 2021, Communications Materials)

   null (Ed.)

   Abstract Demonstration of topological boundary modes in elastic systems has attracted a great deal of attention over the past few years due to its unique protection characteristic. Recently, second-order topological insulators have been proposed in manipulating the topologically protected localized states emerging only at corners. Here, we numerically and experimentally study corner states in a two-dimensional phononic crystal, namely a continuous elastic plate with embedded bolts in a hexagonal pattern. We create interfacial corners by adjoining trivial and non-trivial topological configurations. Due to the rich interaction between the bolts and the continuous elastic plate, we find a variety of corner states of and devoid of topological origin. Strikingly, some of the corner states are not only highly-localized but also tunable. Taking advantage of this property, we experimentally demonstrate asymmetric corner localization in a Z-shaped domain wall. This finding could create interest in exploration of tunable corner states for the use of advanced control of wave localization. 

   more » « less