Topology in non-linear mechanical systems
Soft Condensed Matter
2021-08-18 v1
Abstract
Many advancements have been made in the field of topological mechanics. The majority of the works, however, concerns the topological invariant in a linear theory. We, in this work, present a generic prescription of defining topological indices which accommodates non-linear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a Z-valued quantity in terms of the Poincare-Hopf index, that features the topological invariant of non-linear 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 non-linear ZMs in the future.
Cite
@article{arxiv.2104.12778,
title = {Topology in non-linear mechanical systems},
author = {Po-Wei Lo and Krishanu Roychowdhury and Bryan Gin-ge Chen and Christian D. Santangelo and Chao-Ming Jian and Michael J. Lawler},
journal= {arXiv preprint arXiv:2104.12778},
year = {2021}
}