| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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Head-on Collision of Solitary Waves Described by the Toda Lattice Model in Granular Chain |
| Qianqian Wu1, Xingyi Liu1, Tengfei Jiao1, Surajit Sen2*, and Decai Huang1* |
1Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, China
2Department of Physics, State University of New York, Buffalo 14260-1500, USA
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| Cite this article: |
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Qianqian Wu, Xingyi Liu, Tengfei Jiao et al 2020 Chin. Phys. Lett. 37 074501 |
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Abstract We study the head-on collision of two solitary waves in a precompressed granular chain using the discrete element method. Our study takes the Toda chain solution as the initial condition for the simulations. The simulation covers the dynamical evolution of the collision process from the start of the incident wave to the end of the collision. The interaction has a central collision region of about five-grain width in which two solitary waves merge completely and share only one peak. Four stages, i.e., the pre-in-phase traveling stage, lag-phase collision state, lead-phase collision state, and post-in-phase traveling stage, are identified to describe the complex collision processes. Our results may be helpful for explaining the existence of long-lived solitary waves seen in the simulations by Takato and Sen [Europhys. Lett. 100 (2012) 24003].
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Received: 18 March 2020
Published: 21 June 2020
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| Fund: Supported by the National Natural Science Foundation of China (Grant No. 11574153). |
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| [1] | Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240 |
| [2] | Schwarz U T, English L Q and Sievers A J 1999 Phys. Rev. Lett. 83 223 |
| [3] | Xie A H, van der Meer L , Hoff W and Austin R H 2000 Phys. Rev. Lett. 84 5435 |
| [4] | Fleischer J W, Segev M, Efremidis N K and Christoulids D N 2003 Nature 422 147 |
| [5] | Nesterenko V F 1983 J. Appl. Mech. Tech. Phys. 24 733 |
| [6] | Coste C, Falcon E and Fauve S 1997 Phys. Rev. E 56 6104 |
| [7] | Sokolow A, Bittle E and Sen S 2007 Europhys. Lett. 77 24002 |
| [8] | Sun D and Sen S 2013 Granul. Matter 15 157 |
| [9] | Sen S, Manciu M and Manciu F S 1999 Appl. Phys. Lett. 75 1479 |
| [10] | Vergara L 2005 Phys. Rev. Lett. 95 108002 |
| [11] | Liu X Y, Jiao T F, Ma L, Su J Y, Chen W Z, Sun Q C and Huang D C 2017 Granul. Matter 19 55 |
| [12] | Breindel A, Sun D and Sen S 2011 Appl. Phys. Lett. 99 063510 |
| [13] | Ma L, Huang D C, Chen W Z, Jiao T F, Sun M, Hu F L and Su Y J 2017 Phys. Lett. A 381 542 |
| [14] | Hertz H 1881 J. Reine U. Angew. Math. 92 156 |
| [15] | Sun D K, Daraio C and Sen S 2011 Phys. Rev. E 83 066605 |
| [16] | Herbold E B and Nesterenko V F 2007 Appl. Phys. Lett. 90 261902 |
| [17] | Toda M 1998 Theory of Nonlinear Lattices (New York: Springer-Verlag) |
| [18] | Wang F G, Yang Y Y, Han J F and Duan W S 2018 Chin. Phys. B 27 044501 |
| [19] | Shen Y, Kevrekidis P G, Sen S and Hoffman A 2014 Phys. Rev. E 90 022905 |
| [20] | Takato Y and Sen S 2012 Europhys. Lett. 100 24003 |
| [21] | Kuwabara G and Kono K 1987 Jpn. J. Appl. Phys. 26 1230 |
| [22] | Scha̋fer J, Dippel S and Wolf D E 1996 J. Phys. I 6 5 |
| [23] | Ávalos E and Sen S 2009 Phys. Rev. E 79 046607 |
| [24] | Ávalos E, Sun D K, Doney D L and Sen S 2011 Phys. Rev. E 84 046610 |
| [25] | Sen S and Manciu M 2001 Phys. Rev. E 64 056605 |
| [26] | Manciu M, Tehan V and Sen S 2000 Chaos 10 658 |
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