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Published April 2021 | Submitted + Published
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Nonlinear localized modes in two-dimensional hexagonally-packed magnetic lattices


We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal configuration with a light-mass defect, and we harmonically drive the center of the chain with a tunable excitation frequency, amplitude, and angle. We use a damped, driven variant of a vector Fermi–Pasta–Ulam–Tsingou lattice to model our experimental setup. Despite the idealized nature of this model, we obtain good qualitative agreement between theory and experiments for a variety of dynamical behaviors. We find that the spatial decay is direction-dependent and that drive amplitudes along fundamental displacement axes lead to nonlinear resonant peaks in frequency continuations that are similar to those that occur in one-dimensional damped, driven lattices. However, we observe numerically that driving along other directions results in asymmetric NLMs that bifurcate from the main solution branch, which consists of symmetric NLMs. We also demonstrate both experimentally and numerically that solutions that appear to be time-quasiperiodic bifurcate from the branch of symmetric time-periodic NLMs.

Additional Information

© 2021 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 17 September 2020. Revised 29 December 2020. Accepted 13 January 2021. Published 5 April 2021. The present paper is based on work that was supported by the US National Science Foundation under Grant Nos. DMS-1615037 (CC), DMS-1809074 (PGK), and EFRI-1741565 (CD). AJM acknowledges support from the Agencia Nacional de Investigación y Desarrollo de Chile (ANID) under Grant No. 3190906. EGC thanks Bowdoin College, where the initial stages of this work were carried out, for their kind hospitality. PGK also acknowledges support from the Leverhulme Trust via a Visiting Fellowship and thanks the Mathematical Institute of the University of Oxford for its hospitality during part of this work. We give special thanks to Bowdoin undergraduates Ariel Gonzales, Patrycja Pekala, Anam Shah, and Steven Xu for help with simulations and data management. Data-availability statement. The data that support the findings of this study are available upon reasonable request from the authors.

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Published - Chong_2021_New_J._Phys._23_043008.pdf

Submitted - 2009.10300.pdf


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August 20, 2023
October 23, 2023