Topology in Nonlinear Mechanical Systems

Po Wei Lo, Christian D. Santangelo, Bryan Gin Ge Chen, Chao Ming Jian, Krishanu Roychowdhury, Michael J. Lawler

Research output: Contribution to journalArticlepeer-review

Abstract

Many advancements have been made in the field of topological mechanics. The majority of the work, however, concerns the topological invariant in a linear theory. In this Letter, we present a generic prescription to define topological indices that accommodates nonlinear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a Z-valued quantity in terms of a topological index in differential geometry known as the Poincaré-Hopf index, which features the topological invariant of nonlinear zero modes (ZMs), is predicted. We further identify one type of topologically protected solitons that are robust to disorders. Our prescription constitutes a new direction of searching for novel topologically protected nonlinear ZMs in the future.

Original languageEnglish (US)
Article number076802
JournalPhysical Review Letters
Volume127
Issue number7
DOIs
StatePublished - Aug 13 2021

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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