American Institute of Mathematical Sciences

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October  2011, 4(5): 1107-1118. doi: 10.3934/dcdss.2011.4.1107

Breathers and kinks in a simulated crystal experiment

Qingxu Dou 1, , Jesús Cuevas 2, , J. C. Eilbeck 3, and  Francis Michael Russell 4,

1. 

School of Engineering and Physical Sciences, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, United Kingdom
2. 

Grupo de Física No Lineal. Departamento de Física Aplicada I., Escuela Politécnica Superior. Universidad de Sevilla, C/ Virgen de África, 7, 41011-Sevilla
3. 

Maxwell Institute and Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, United Kingdom
4. 

Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, United Kingdom

Received  September 2009 Revised  December 2009 Published  December 2010

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 by 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 mode, and multiple ejections at both incoming and distant surfaces. In addition, the effect of a heavier surface layer is modelled, which can lead to internal reflections of breathers or kinks at the crystal surface.
Keywords: Nonlinear vibrational modes, coupled oscillators..
Mathematics Subject Classification: Primary: 70Kxx; Secondary: 70Fxx, 34C15, 34C6.
Citation: Qingxu Dou, Jesús Cuevas, J. C. Eilbeck, Francis Michael Russell. Breathers and kinks in a simulated crystal experiment. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1107-1118. doi: 10.3934/dcdss.2011.4.1107
References:
[1]

J. Cuevas, J. F. R. Archilla, B. Sánchez-Rey and F. R. Romero, Interaction of moving discrete breathers with vacancies,, Physica D, 216 (2006).  doi: 10.1016/j.physd.2005.12.022.  Google Scholar

[2]

J. Cuevas, C. Katerji, J. F. R. Archilla, J. C. Eilbeck and F. M. Russell, Influence of moving breathers on vacancies migration,, Phys. Lett., 315 (2003), 364.  doi: 10.1016/S0375-9601(03)01097-1.  Google Scholar

[3]

J. Cuevas, B. Sánchez-Rey, J. C. Eilbeck and F. M. Russell, Interaction of moving discrete breathers with simulated interstitial defects,, in these proceedings, (2009).   Google Scholar

[4]

S. Flach, Conditions on the existence of localized excitations in nonlinear discrete systems,, Phys. Rev. E, 50 (1994).  doi: 10.1103/PhysRevE.50.3134.  Google Scholar

[5]

S. Flach and A. Gorbach, Discrete breathers - Advances in theory and applications,, Phys. Rep., 267 (2008).  doi: 10.1016/j.physrep.2008.05.002.  Google Scholar

[6]

J. L. Marín, J. C. Eilbeck and F. M. Russell, Localized moving breathers in a 2-D hexagonal lattice,, Phys. Letts. A, 248 (1998), 225.   Google Scholar

[7]

F. M. Russell and J. C. Eilbeck, Evidence for moving breathers in a layered crystal insulator at 300K,, Europhysics Letters, 78 (2007).  doi: 10.1209/0295-5075/78/10004.  Google Scholar

[8]

F. M. Russell and J. C. Eilbeck, Persistent mobile lattice excitations in a crystalline insulator,, in these proceedings, (2009).   Google Scholar

[9]

X. Yi, J. A. D. Wattis, H. Susanto and L. J. Cummings, Discrete breathers in a two-dimensional spring-mass lattice,, J. Phys. A: Math. and Theor., 42 (2009).  doi: 10.1088/1751-8113/42/35/355207.  Google Scholar

show all references

References:
[1]

J. Cuevas, J. F. R. Archilla, B. Sánchez-Rey and F. R. Romero, Interaction of moving discrete breathers with vacancies,, Physica D, 216 (2006).  doi: 10.1016/j.physd.2005.12.022.  Google Scholar

[2]

J. Cuevas, C. Katerji, J. F. R. Archilla, J. C. Eilbeck and F. M. Russell, Influence of moving breathers on vacancies migration,, Phys. Lett., 315 (2003), 364.  doi: 10.1016/S0375-9601(03)01097-1.  Google Scholar

[3]

J. Cuevas, B. Sánchez-Rey, J. C. Eilbeck and F. M. Russell, Interaction of moving discrete breathers with simulated interstitial defects,, in these proceedings, (2009).   Google Scholar

[4]

S. Flach, Conditions on the existence of localized excitations in nonlinear discrete systems,, Phys. Rev. E, 50 (1994).  doi: 10.1103/PhysRevE.50.3134.  Google Scholar

[5]

S. Flach and A. Gorbach, Discrete breathers - Advances in theory and applications,, Phys. Rep., 267 (2008).  doi: 10.1016/j.physrep.2008.05.002.  Google Scholar

[6]

J. L. Marín, J. C. Eilbeck and F. M. Russell, Localized moving breathers in a 2-D hexagonal lattice,, Phys. Letts. A, 248 (1998), 225.   Google Scholar

[7]

F. M. Russell and J. C. Eilbeck, Evidence for moving breathers in a layered crystal insulator at 300K,, Europhysics Letters, 78 (2007).  doi: 10.1209/0295-5075/78/10004.  Google Scholar

[8]

F. M. Russell and J. C. Eilbeck, Persistent mobile lattice excitations in a crystalline insulator,, in these proceedings, (2009).   Google Scholar

[9]

X. Yi, J. A. D. Wattis, H. Susanto and L. J. Cummings, Discrete breathers in a two-dimensional spring-mass lattice,, J. Phys. A: Math. and Theor., 42 (2009).  doi: 10.1088/1751-8113/42/35/355207.  Google Scholar

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