Two-dimensional mobile breather scattering in a hexagonal crystal lattice

Jānis Bajārs; J. Chris Eilbeck; Benedict Leimkuhler

doi:10.1103/PhysRevE.103.022212

Two-dimensional mobile breather scattering in a hexagonal crystal lattice

Jānis Bajārs^*
, J. Chris Eilbeck
, Benedict Leimkuhler

^*Corresponding author for this work

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

15 Citations (Scopus)

37 Downloads (Pure)

Abstract

We describe the full two-dimensional scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an "egg-box"harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated with the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two-dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained energy density function in time for a set of randomly excited mobile breather solutions. Certain collisions lead to 60∘ scattering, and collisions of mobile and stationary breathers can generate a rich variety of states.

Original language	English
Article number	022212
Journal	Physical Review E
Volume	103
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevE.103.022212
Publication status	Published - 18 Feb 2021

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Condensed Matter Physics

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©2021 American Physical Society Phys. Rev. E 103, 022212
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title = "Two-dimensional mobile breather scattering in a hexagonal crystal lattice",

abstract = "We describe the full two-dimensional scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an {"}egg-box{"}harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated with the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two-dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained energy density function in time for a set of randomly excited mobile breather solutions. Certain collisions lead to 60∘ scattering, and collisions of mobile and stationary breathers can generate a rich variety of states.",

author = "Jānis Bajārs and Eilbeck, \{J. Chris\} and Benedict Leimkuhler",

note = "Funding Information: J.B., during his postdoctoral research at the University of Edinburgh, and B.L. acknowledge the support of the UK Research and Innovation organization which has funded this work as part of the EPSRC Science and Innovation grant for the Numerical Algorithms and Intelligent Software Centre under Grant No. EP/G036136/1. J.B. also acknowledges support from PostDocLatvia grant No. 1.1.1.2/VIAA/4/20/617. J.C.E. thanks M. Russell for many useful conversations. We are most grateful to an anonymous referee for many helpful comments and corrections. Publisher Copyright: {\textcopyright} 2021 American Physical Society. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

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N2 - We describe the full two-dimensional scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an "egg-box"harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated with the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two-dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained energy density function in time for a set of randomly excited mobile breather solutions. Certain collisions lead to 60∘ scattering, and collisions of mobile and stationary breathers can generate a rich variety of states.

AB - We describe the full two-dimensional scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an "egg-box"harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated with the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two-dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained energy density function in time for a set of randomly excited mobile breather solutions. Certain collisions lead to 60∘ scattering, and collisions of mobile and stationary breathers can generate a rich variety of states.

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Two-dimensional mobile breather scattering in a hexagonal crystal lattice

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