# Breathers and kinks in a simulated crystal experiment

@article{Dou2010BreathersAK, title={Breathers and kinks in a simulated crystal experiment}, author={Qingxu Dou and Jes{\'u}s Cuevas and John Christopher Eilbeck and F. M. Russell}, journal={Discrete and Continuous Dynamical Systems - Series S}, year={2010}, volume={4}, pages={1107-1118} }

We develop a simple 1D model for the scattering of an incoming particle hitting the surface of mica crystal, the transmission of energy through the crystal by a localized mode, and the ejection of atom(s) at the incident or distant face. This is the first attempt to model the experiment described in Russell and Eilbeck in 2007 (EPL, 78, 10004). Although very basic, the model shows many interesting features, for example a complicated energy dependent transition between breather modes and a kink… Expand

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#### References

SHOWING 1-10 OF 10 REFERENCES

Localized moving breathers in a 2D hexagonal lattice

- Physics
- 1998

Abstract We show for the first time that highly localized in-plane breathers can propagate in specific directions with minimal lateral spreading in a model 2D hexagonal nonlinear lattice. The lattice… Expand

Evidence for moving breathers in a layered crystal insulator at 300?K

- Materials Science, Physics
- 2006

We report the ejection of atoms at a crystal surface caused by energetic breathers which have travelled more than 107 unit cells in atomic chain directions. The breathers were created by bombardment… Expand

Interaction of moving discrete breathers with simulated interstitial defects

- 2008

In this paper, interstitial migration generated by scattering with a mobile breather is investigated numerically in a Frenkel-Kontorova one-dimensional lattice. In accordance with experimental… Expand

Interaction of moving discrete breathers with vacancies

- Physics
- 2006

Abstract In this paper a Frenkel–Kontorova model with a nonlinear interaction potential is used to describe a vacancy defect in a crystal. According to recent numerical results [J. Cuevas, C.… Expand

Discrete breathers in a two-dimensional spring-mass lattice

- Mathematics
- 2009

We consider a two-dimensional spring-mass lattice with square symmetry in which each particle experiences a nonlinear onsite potential and nonlinear nearest-neighbour interactions. At equilibrium,… Expand

Persistent mobile lattice excitations in a crystalline insulator

- Mathematics
- 2010

We examine tracks in crystals of muscovite of high energy charged
particles, and of mobile lattice excitations created by kinetic
atomic scattering. The mobile lattice excitations are interpreted… Expand

Influence of moving breathers on vacancies migration

- Physics
- 2003

A vacancy defect is described by a Frenkel–Kontorova model with a discommensuration. This vacancy can migrate when interacts with a moving breather. We establish that the width of the interaction… Expand

Discrete breathers — Advances in theory and applications

- Physics
- 2008

Nonlinear classical Hamiltonian lattices exhibit generic solutions — discrete breathers. They are time-periodic and (typically exponentially) localized in space. The lattices have discrete… Expand

Conditions on the existence of localized excitations in nonlinear discrete systems.

- Physics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1994

This work uses recent results that localized excitations in nonlinear Hamiltonian lattices can be viewed and described as multiple-frequency excitations as well as of multiple frequency excitations to find that the existence of localized excitation can be a generic property of nonlinear McMaster lattices in contrast to non linear Hamiltonian fields. Expand

E-mail address: qd5@hw.ac.uk E-mail address: jcuevas@us.es E-mail address: J.C.Eilbeck@hw.ac.uk E-mail address: Mica2mike@aol

- E-mail address: qd5@hw.ac.uk E-mail address: jcuevas@us.es E-mail address: J.C.Eilbeck@hw.ac.uk E-mail address: Mica2mike@aol