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 dr...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2021-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/abdb6f |
| _version_ | 1797750301321592832 |
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| author | Christopher Chong Yifan Wang Donovan Maréchal Efstathios G Charalampidis Miguel Molerón Alejandro J Martínez Mason A Porter Panayotis G Kevrekidis Chiara Daraio |
| author_facet | Christopher Chong Yifan Wang Donovan Maréchal Efstathios G Charalampidis Miguel Molerón Alejandro J Martínez Mason A Porter Panayotis G Kevrekidis Chiara Daraio |
| author_sort | Christopher Chong |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:31:43Z |
| format | Article |
| id | doaj.art-9ed4fd16cec6402686e9870094201aa6 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:31:43Z |
| publishDate | 2021-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-9ed4fd16cec6402686e9870094201aa62023-08-08T15:28:45ZengIOP PublishingNew Journal of Physics1367-26302021-01-0123404300810.1088/1367-2630/abdb6fNonlinear localized modes in two-dimensional hexagonally-packed magnetic latticesChristopher Chong0https://orcid.org/0000-0002-4908-3252Yifan Wang1https://orcid.org/0000-0003-2284-520XDonovan Maréchal2Efstathios G Charalampidis3https://orcid.org/0000-0002-5417-4431Miguel Molerón4Alejandro J Martínez5Mason A Porter6https://orcid.org/0000-0002-5166-0717Panayotis G Kevrekidis7https://orcid.org/0000-0002-7714-3689Chiara Daraio8Department of Mathematics , Bowdoin College, Brunswick, ME 04011, United States of AmericaDivision of Engineering and Applied Science California Institute of Technology Pasadena , CA 91125, United States of America; School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, Singapore 639798Division of Engineering and Applied Science California Institute of Technology Pasadena , CA 91125, United States of AmericaMathematics Department, California Polytechnic State University , San Luis Obispo, CA 93407-0403, United States of AmericaInstitute of Geophysics , Department of Earth Sciences, ETH Zurich, 8092 Zurich, SwitzerlandComputational Biology Laboratory , Fundación Ciencia & Vida, Santiago, 7780272, Chile; Universidad San Sebastian , Santiago, 7510156, ChileDepartment of Mathematics, University of California , Los Angeles, CA 90095, United States of AmericaDepartment of Mathematics and Statistics, University of Massachusetts , Amherst, MA, 01003, United States of AmericaDivision of Engineering and Applied Science California Institute of Technology Pasadena , CA 91125, United States of AmericaWe 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.https://doi.org/10.1088/1367-2630/abdb6fbreatherFermi–Pasta–Ulam–Tsingou latticemagnetic latticehexagonal latticenonlinear localized mode |
| spellingShingle | Christopher Chong Yifan Wang Donovan Maréchal Efstathios G Charalampidis Miguel Molerón Alejandro J Martínez Mason A Porter Panayotis G Kevrekidis Chiara Daraio Nonlinear localized modes in two-dimensional hexagonally-packed magnetic lattices New Journal of Physics breather Fermi–Pasta–Ulam–Tsingou lattice magnetic lattice hexagonal lattice nonlinear localized mode |
| title | Nonlinear localized modes in two-dimensional hexagonally-packed magnetic lattices |
| title_full | Nonlinear localized modes in two-dimensional hexagonally-packed magnetic lattices |
| title_fullStr | Nonlinear localized modes in two-dimensional hexagonally-packed magnetic lattices |
| title_full_unstemmed | Nonlinear localized modes in two-dimensional hexagonally-packed magnetic lattices |
| title_short | Nonlinear localized modes in two-dimensional hexagonally-packed magnetic lattices |
| title_sort | nonlinear localized modes in two dimensional hexagonally packed magnetic lattices |
| topic | breather Fermi–Pasta–Ulam–Tsingou lattice magnetic lattice hexagonal lattice nonlinear localized mode |
| url | https://doi.org/10.1088/1367-2630/abdb6f |
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