Explorations for alternating FPU-chains with large mass

Wilberd van der Kallen; Ferdinand Verhulst

doi:10.1016/j.ijnonlinmec.2021.103809

Explorations for alternating FPU-chains with large mass

Wilberd van der Kallen, Ferdinand Verhulst^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We show interaction between high- and low-frequency modes in periodic α-FPU chains with alternating large masses. This high-low frequency interaction is known if the number of particles N is a 4-fold, our treatment discusses the difficult case where the number of particles N=2p involves p prime. A key role is played by identifying symmetric invariant manifolds, thus reducing the dimension of the problems drastically, and a MATHEMATICA programme focused on these systems. We show explicitly high-low frequency interaction for systems with 2pn particles where 2≤p≤47 is prime and n is an arbitrary natural number. In addition we have strong arguments for interactions in arbitrary large chains.

Original language	English
Article number	103809
Pages (from-to)	1-9
Number of pages	9
Journal	International Journal of Non-Linear Mechanics
Volume	137
DOIs	https://doi.org/10.1016/j.ijnonlinmec.2021.103809
Publication status	Published - Dec 2021

Keywords

Alternating masses
FPU-chains
Invariant manifolds
Mode interaction

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1-s2.0-S0020746221001438-mainFinal published version, 1.4 MBLicence: CC BY

Cite this

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title = "Explorations for alternating FPU-chains with large mass",

abstract = "We show interaction between high- and low-frequency modes in periodic α-FPU chains with alternating large masses. This high-low frequency interaction is known if the number of particles N is a 4-fold, our treatment discusses the difficult case where the number of particles N=2p involves p prime. A key role is played by identifying symmetric invariant manifolds, thus reducing the dimension of the problems drastically, and a MATHEMATICA programme focused on these systems. We show explicitly high-low frequency interaction for systems with 2pn particles where 2≤p≤47 is prime and n is an arbitrary natural number. In addition we have strong arguments for interactions in arbitrary large chains.",

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note = "Funding Information: A useful remark by dr. J. Stienstra helped us in the discussion of permutations of quadratic terms in Section 6.2. J. Stienstra also checked the transformations to equations of motions independently. We owe Ref. [5] to one of the anonymous referees. Publisher Copyright: {\textcopyright} 2021 The Author(s)",

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AU - van der Kallen, Wilberd

AU - Verhulst, Ferdinand

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N2 - We show interaction between high- and low-frequency modes in periodic α-FPU chains with alternating large masses. This high-low frequency interaction is known if the number of particles N is a 4-fold, our treatment discusses the difficult case where the number of particles N=2p involves p prime. A key role is played by identifying symmetric invariant manifolds, thus reducing the dimension of the problems drastically, and a MATHEMATICA programme focused on these systems. We show explicitly high-low frequency interaction for systems with 2pn particles where 2≤p≤47 is prime and n is an arbitrary natural number. In addition we have strong arguments for interactions in arbitrary large chains.

AB - We show interaction between high- and low-frequency modes in periodic α-FPU chains with alternating large masses. This high-low frequency interaction is known if the number of particles N is a 4-fold, our treatment discusses the difficult case where the number of particles N=2p involves p prime. A key role is played by identifying symmetric invariant manifolds, thus reducing the dimension of the problems drastically, and a MATHEMATICA programme focused on these systems. We show explicitly high-low frequency interaction for systems with 2pn particles where 2≤p≤47 is prime and n is an arbitrary natural number. In addition we have strong arguments for interactions in arbitrary large chains.

KW - Alternating masses

KW - FPU-chains

KW - Invariant manifolds

KW - Mode interaction

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ER -

Explorations for alternating FPU-chains with large mass

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Keywords

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