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Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains
Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size t...
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| Published in: | New journal of physics 2022-09, Vol.24 (9), p.93003 |
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| Main Authors: | , , , |
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| container_issue | 9 |
| container_start_page | 93003 |
| container_title | New journal of physics |
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| creator | Peng, Liangtao Fu, Weicheng Zhang, Yong Zhao, Hong |
| description | Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size to observe whether they have the same behavior in different models. To this end, as illustrating examples, the instability dynamics of the
N
/2 mode in both the Fermi–Pasta–Ulam–Tsingou-
α
and -
β
chains under fixed boundary conditions are studied systematically. Applying the Floquet theory, we show that for both models the stability time
T
as a function of the perturbation strength
λ
follows the same behavior; i.e.,
T
∝
(
λ
−
λ
c
)
−
1
2
, where
λ
c
is the instability threshold. The dependence of
λ
c
on
N
is also obtained. The results of
T
and
λ
c
agree well with those obtained by the direct molecular dynamics simulations. Finally, the effect of instability dynamics on the thermalization properties of a system is briefly discussed. |
| doi_str_mv | 10.1088/1367-2630/ac8ac3 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1088_1367_2630_ac8ac3</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_4b77c1605ed04f7c8ee4c1d7ba3a772b</doaj_id><sourcerecordid>2709348436</sourcerecordid><originalsourceid>FETCH-LOGICAL-c369t-2b6a39580523be3566a0c050491d8c1214731e5a2dc922484997d5c86e7909513</originalsourceid><addsrcrecordid>eNp1UbtOAzEQPCGQCIGe8iRaQvy486NEEYFISFAkFYW153MSR3d2sC9FOv6BP-RLcDgENFQzWs3Mrnay7BKjG4yEGGPK-IgwisagBWh6lA1-Rsd_-Gl2FuMGIYwFIYPsZeZiB5VtbLfP672D1uqY-2XuvGusMxASCy00eetrE3Pr8m5t8qkJrf14e3-G5E64aKBNMI_Wrfwu12uwLp5nJ0toorn4xmG2mN7NJw-jx6f72eT2caQpk92IVAyoLAUqCa0MLRkDpFGJColroTHBBafYlEBqLQkpRCElr0stmOESyRLTYTbrc2sPG7UNtoWwVx6s-hr4sFIQOqsbo4qKc40ZKk2NiiXXwphC45pXQIFzUqWsqz5rG_zrzsRObfwuuHS-IhxJmtZTllSoV-ngYwxm-bMVI3WoQx3-rQ7_Vn0dyXLdW6zf_mb-K_8ExvONag</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2709348436</pqid></control><display><type>article</type><title>Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains</title><source>Publicly Available Content Database (Proquest) (PQ_SDU_P3)</source><creator>Peng, Liangtao ; Fu, Weicheng ; Zhang, Yong ; Zhao, Hong</creator><creatorcontrib>Peng, Liangtao ; Fu, Weicheng ; Zhang, Yong ; Zhao, Hong</creatorcontrib><description>Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size to observe whether they have the same behavior in different models. To this end, as illustrating examples, the instability dynamics of the
N
/2 mode in both the Fermi–Pasta–Ulam–Tsingou-
α
and -
β
chains under fixed boundary conditions are studied systematically. Applying the Floquet theory, we show that for both models the stability time
T
as a function of the perturbation strength
λ
follows the same behavior; i.e.,
T
∝
(
λ
−
λ
c
)
−
1
2
, where
λ
c
is the instability threshold. The dependence of
λ
c
on
N
is also obtained. The results of
T
and
λ
c
agree well with those obtained by the direct molecular dynamics simulations. Finally, the effect of instability dynamics on the thermalization properties of a system is briefly discussed.</description><identifier>ISSN: 1367-2630</identifier><identifier>EISSN: 1367-2630</identifier><identifier>DOI: 10.1088/1367-2630/ac8ac3</identifier><identifier>CODEN: NJOPFM</identifier><language>eng</language><publisher>Bristol: IOP Publishing</publisher><subject>Boundary conditions ; Chains ; Dynamic stability ; Energy ; Equilibrium ; Fermi–Pasta–Ulam–Tsingou chains ; Floquet theory ; Hamiltonian functions ; instability dynamics ; Molecular dynamics ; Nonlinear dynamics ; nonlinear normal modes ; Orbits ; Perturbation ; Physics ; Theoretical physics ; Thermalization (energy absorption)</subject><ispartof>New journal of physics, 2022-09, Vol.24 (9), p.93003</ispartof><rights>2022 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft</rights><rights>2022 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c369t-2b6a39580523be3566a0c050491d8c1214731e5a2dc922484997d5c86e7909513</cites><orcidid>0000-0001-5808-7936 ; 0000-0001-7667-1386 ; 0000-0002-5420-7985 ; 0000-0002-2102-674X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2709348436?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25753,27924,27925,37012,44590</link.rule.ids></links><search><creatorcontrib>Peng, Liangtao</creatorcontrib><creatorcontrib>Fu, Weicheng</creatorcontrib><creatorcontrib>Zhang, Yong</creatorcontrib><creatorcontrib>Zhao, Hong</creatorcontrib><title>Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains</title><title>New journal of physics</title><addtitle>NJP</addtitle><addtitle>New J. Phys</addtitle><description>Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size to observe whether they have the same behavior in different models. To this end, as illustrating examples, the instability dynamics of the
N
/2 mode in both the Fermi–Pasta–Ulam–Tsingou-
α
and -
β
chains under fixed boundary conditions are studied systematically. Applying the Floquet theory, we show that for both models the stability time
T
as a function of the perturbation strength
λ
follows the same behavior; i.e.,
T
∝
(
λ
−
λ
c
)
−
1
2
, where
λ
c
is the instability threshold. The dependence of
λ
c
on
N
is also obtained. The results of
T
and
λ
c
agree well with those obtained by the direct molecular dynamics simulations. Finally, the effect of instability dynamics on the thermalization properties of a system is briefly discussed.</description><subject>Boundary conditions</subject><subject>Chains</subject><subject>Dynamic stability</subject><subject>Energy</subject><subject>Equilibrium</subject><subject>Fermi–Pasta–Ulam–Tsingou chains</subject><subject>Floquet theory</subject><subject>Hamiltonian functions</subject><subject>instability dynamics</subject><subject>Molecular dynamics</subject><subject>Nonlinear dynamics</subject><subject>nonlinear normal modes</subject><subject>Orbits</subject><subject>Perturbation</subject><subject>Physics</subject><subject>Theoretical physics</subject><subject>Thermalization (energy absorption)</subject><issn>1367-2630</issn><issn>1367-2630</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNp1UbtOAzEQPCGQCIGe8iRaQvy486NEEYFISFAkFYW153MSR3d2sC9FOv6BP-RLcDgENFQzWs3Mrnay7BKjG4yEGGPK-IgwisagBWh6lA1-Rsd_-Gl2FuMGIYwFIYPsZeZiB5VtbLfP672D1uqY-2XuvGusMxASCy00eetrE3Pr8m5t8qkJrf14e3-G5E64aKBNMI_Wrfwu12uwLp5nJ0toorn4xmG2mN7NJw-jx6f72eT2caQpk92IVAyoLAUqCa0MLRkDpFGJColroTHBBafYlEBqLQkpRCElr0stmOESyRLTYTbrc2sPG7UNtoWwVx6s-hr4sFIQOqsbo4qKc40ZKk2NiiXXwphC45pXQIFzUqWsqz5rG_zrzsRObfwuuHS-IhxJmtZTllSoV-ngYwxm-bMVI3WoQx3-rQ7_Vn0dyXLdW6zf_mb-K_8ExvONag</recordid><startdate>20220901</startdate><enddate>20220901</enddate><creator>Peng, Liangtao</creator><creator>Fu, Weicheng</creator><creator>Zhang, Yong</creator><creator>Zhao, Hong</creator><general>IOP Publishing</general><scope>O3W</scope><scope>TSCCA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>H8D</scope><scope>L7M</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0001-5808-7936</orcidid><orcidid>https://orcid.org/0000-0001-7667-1386</orcidid><orcidid>https://orcid.org/0000-0002-5420-7985</orcidid><orcidid>https://orcid.org/0000-0002-2102-674X</orcidid></search><sort><creationdate>20220901</creationdate><title>Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains</title><author>Peng, Liangtao ; Fu, Weicheng ; Zhang, Yong ; Zhao, Hong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c369t-2b6a39580523be3566a0c050491d8c1214731e5a2dc922484997d5c86e7909513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Boundary conditions</topic><topic>Chains</topic><topic>Dynamic stability</topic><topic>Energy</topic><topic>Equilibrium</topic><topic>Fermi–Pasta–Ulam–Tsingou chains</topic><topic>Floquet theory</topic><topic>Hamiltonian functions</topic><topic>instability dynamics</topic><topic>Molecular dynamics</topic><topic>Nonlinear dynamics</topic><topic>nonlinear normal modes</topic><topic>Orbits</topic><topic>Perturbation</topic><topic>Physics</topic><topic>Theoretical physics</topic><topic>Thermalization (energy absorption)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Peng, Liangtao</creatorcontrib><creatorcontrib>Fu, Weicheng</creatorcontrib><creatorcontrib>Zhang, Yong</creatorcontrib><creatorcontrib>Zhao, Hong</creatorcontrib><collection>Open Access: IOP Publishing Free Content</collection><collection>IOPscience (Open Access)</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Publicly Available Content Database (Proquest) (PQ_SDU_P3)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>New journal of physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Peng, Liangtao</au><au>Fu, Weicheng</au><au>Zhang, Yong</au><au>Zhao, Hong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains</atitle><jtitle>New journal of physics</jtitle><stitle>NJP</stitle><addtitle>New J. Phys</addtitle><date>2022-09-01</date><risdate>2022</risdate><volume>24</volume><issue>9</issue><spage>93003</spage><pages>93003-</pages><issn>1367-2630</issn><eissn>1367-2630</eissn><coden>NJOPFM</coden><abstract>Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size to observe whether they have the same behavior in different models. To this end, as illustrating examples, the instability dynamics of the
N
/2 mode in both the Fermi–Pasta–Ulam–Tsingou-
α
and -
β
chains under fixed boundary conditions are studied systematically. Applying the Floquet theory, we show that for both models the stability time
T
as a function of the perturbation strength
λ
follows the same behavior; i.e.,
T
∝
(
λ
−
λ
c
)
−
1
2
, where
λ
c
is the instability threshold. The dependence of
λ
c
on
N
is also obtained. The results of
T
and
λ
c
agree well with those obtained by the direct molecular dynamics simulations. Finally, the effect of instability dynamics on the thermalization properties of a system is briefly discussed.</abstract><cop>Bristol</cop><pub>IOP Publishing</pub><doi>10.1088/1367-2630/ac8ac3</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0001-5808-7936</orcidid><orcidid>https://orcid.org/0000-0001-7667-1386</orcidid><orcidid>https://orcid.org/0000-0002-5420-7985</orcidid><orcidid>https://orcid.org/0000-0002-2102-674X</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Boundary conditions Chains Dynamic stability Energy Equilibrium Fermi–Pasta–Ulam–Tsingou chains Floquet theory Hamiltonian functions instability dynamics Molecular dynamics Nonlinear dynamics nonlinear normal modes Orbits Perturbation Physics Theoretical physics Thermalization (energy absorption) |
| title | Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains |
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