Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization

Manda, Bertin Many; Chaunsali, Rajesh; Theocharis, Georgios; Skokos, Charalampos

doi:10.48550/arxiv.2112.12997

Cited by 1 publication

(1 citation statement)

References 78 publications

(157 reference statements)

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“…dimensional (2D) topological Maxwell lattices, the study of nonlinear effects have been so far limited to perturbation theories (23). This is an important gap, as nonlinear systems do not obey superposition and, as such, support an ability to control the spatiotemporal allocation of energy in materials that vastly exceeds their linear counterparts (32)(33)(34) through phenomena such as self-localization (35,36), frequency conversion and dynamic tunability (37,38), and chaos (39), as well as rich interplay with finite-frequency topological states (2,23,(40)(41)(42)(43)(44)(45). As already suggested for Maxwell lattices in the linear regime, we envision that combining nonlinear responses with the strong localization, non-reciprocity, and the robust nature of topological protection will lead to an important expansion of the ability to tailor spatiotemporal stress, deformation, and energy fields, with application areas demonstrated for nonlinear dynamical systems ranging from impact mitigation (46) to neuromorphic (47) and ultrafast mechanoacoustic computation (48,49).…”

Section: Introductionmentioning

confidence: 99%

Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial

Xiu¹,

Frankel²,

Liu³

et al. 2022

Preprint

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Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, non-reciprocal, onedimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a new regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials, and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly exceeding conventional elasticity.

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