Please wait a minute...
Chin. Phys. B, 2018, Vol. 27(1): 014501    DOI: 10.1088/1674-1056/27/1/014501
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Envelope solitary waves and their reflection and transmission due to impurities in a granular material

Wen-Qing Du(杜文青)1, Jian-An Sun(孙建安)1, Yang-Yang Yang(杨阳阳)2, Wen-Shan Duan(段文山)1
1 College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou 730070, China;
2 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
Abstract  A nonlinear Schrödinger equation in one-dimensional bead chain is first obtained and an envelope solitary wave of the system is verified numerically in this system. The reflection and the transmission of an incident envelope solitary wave due to impurities has also been investigated. It is found that the magnitudes of both the reflection and the transmission not only depend on the characters of impurity materials, the wave number, the incident wave amplitude, but also on the impurity number. This can be used to detect the character and the number of the impurity materials in the bead chain by measuring the reflection and the transmission of an incident pulse.
Keywords:  impurities      envelope solitary wave      numerical simulation  
Received:  15 May 2017      Revised:  09 September 2017      Accepted manuscript online: 
PACS:  45.05.+x (General theory of classical mechanics of discrete systems)  
  05.45.-a (Nonlinear dynamics and chaos)  
  45.70.-n (Granular systems)  
Fund: Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA01020304) and the National Natural Science Foundation of China (Grant Nos. 91026005, 11547304, 11275156, 11047010, and 61162017).
Corresponding Authors:  Wen-Shan Duan     E-mail:  duanws@nwnu.edu.cn

Cite this article: 

Wen-Qing Du(杜文青), Jian-An Sun(孙建安), Yang-Yang Yang(杨阳阳), Wen-Shan Duan(段文山) Envelope solitary waves and their reflection and transmission due to impurities in a granular material 2018 Chin. Phys. B 27 014501

[1] Christiansen P L, Sorensen M P and Scott A C 2000 Nonlinear Science at the Dawn of the 21st Century (Berlin: Springer-Verlag) p. 395
[2] Akhmediev N N and Ankiewicz A 1997 Solitons: Nonlinear Pulses and Beams (London: Chapman and Hall)
[3] Remoissenet M and Whitehead J A 1994 Amer. J. Phys. 63 381
[4] Zakharov V E and Shabat A B 1971 Zh. Eksp. Teor. Fiz. 61 118
[5] Zakharov V E 1968 J. Appl. Mech. Tech. Phys. 9 190
[6] Zakharov V E and Ostrovsky L A 2009 Physica (Amsterdam) 238D 540
[7] Lighthill M J 1965 J. Inst. Math. Appl. 1 269
[8] Whitham G B 1965 J. Fluid Mech. 22 273
[9] Bespalov V I and Talanov V I 1966 JETP Lett. 3 307
[10] Benjamin T B and Feir J E 1967 J. Fluid Mech. 27 417
[11] Benjamin T B 1967 Proc. R. Soc. A 299 59
[12] Kibler B, Chabchoub A, Gelash A, Akhmediev N and Zakharov V E 2015 Phys. Rev. X 5 041026
[13] Moslem W M, Sabry R, Ellabany S K and Shukla P K 2011 Phys. Rev. E 84 066402
[14] Sen S, Hong J, Bang J, Avalos E and Doney R 2008 Phys. Rep. 462 21
[15] Boechler N, Theocharis G and Daraio C 2011 Nat. Mater. 10 665
[16] Li F, et al. 2014 Nat. Commun. 5 5311
[17] Coste C, Falcon E and Fauve S 1997 Phys. Rev. E 56 6104
[18] Hascoet E and Herrmann H J 2000 Eur. Phys. J. B 14 183
[19] Sen S and Manciu M 2001 Phys. Rev. E 64 056605
[20] Manciu F S and Sen S 2002 Phys. Rev. E 66 016616
[21] Job S, Melo F, Sokolow A and Sen S 2005 Phys. Rev. Lett. 94 178002
[22] Vergara L 2005 Phys. Rev. Lett. 95 108002
[23] Liu S W, Yang Y Y, Duan W S and Yang L 2015 Phys. Rev. E 92 013202
[24] Li D J 2015 Int. J. Theor. Phys. 54 1316
[25] Tang B, Li D J and Tang Y 2013 Can. J. Phys. 91 788
[26] Goodman R H, Holmes P J and Weinstein M I 2004 Physica D 192 215
[27] Nesterenko V F, Daraio C, Herbold E B and Jin S 2005 Phys. Rev. Lett. 95 158702
[28] Nesterenko V F 1983 J. Appl. Mech. Tech. Phys. 5 733
[29] Friesecke G and Wattis J A D 1994 Commun. Math. Phys. 161 391
[30] Sen S and Sinkovits R S 1996 Phys. Rev. E 54 6857
[31] Sen S, Manciu M and Wright J D 1998 Phys. Rev. E 57 2386
[32] Nesterenko V F 2001 Dynamics of Heterogeneous Materialls (New York: Springer-Verlag) p. 307
[33] Nesterenko V F, Lazaridi A N and Sibiryakov E B 1995 J. Appl. Mech. Tech. Phys. 36 166
[34] Job S and Melo F 2005 Phys. Rev. Lett. 94 178002
[1] Quantitative measurement of the charge carrier concentration using dielectric force microscopy
Junqi Lai(赖君奇), Bowen Chen(陈博文), Zhiwei Xing(邢志伟), Xuefei Li(李雪飞), Shulong Lu(陆书龙), Qi Chen(陈琪), and Liwei Chen(陈立桅). Chin. Phys. B, 2023, 32(3): 037202.
[2] Micro-mechanism study of the effect of Cd-free buffer layers ZnXO (X=Mg/Sn) on the performance of flexible Cu2ZnSn(S, Se)4 solar cell
Caixia Zhang(张彩霞), Yaling Li(李雅玲), Beibei Lin(林蓓蓓), Jianlong Tang(唐建龙), Quanzhen Sun(孙全震), Weihao Xie(谢暐昊), Hui Deng(邓辉), Qiao Zheng(郑巧), and Shuying Cheng(程树英). Chin. Phys. B, 2023, 32(2): 028801.
[3] Theoretical and experimental studies on high-power laser-induced thermal blooming effect in chamber with different gases
Xiangyizheng Wu(吴祥议政), Jian Xu(徐健), Keling Gong(龚柯菱), Chongfeng Shao(邵崇峰), Yang Kou(寇洋), Yuxuan Zhang(张宇轩), Yong Bo(薄勇), and Qinjun Peng(彭钦军). Chin. Phys. B, 2022, 31(8): 086105.
[4] Spatio-spectral dynamics of soliton pulsation with breathing behavior in the anomalous dispersion fiber laser
Ying Han(韩颖), Bo Gao(高博), Jiayu Huo(霍佳雨), Chunyang Ma(马春阳), Ge Wu(吴戈),Yingying Li(李莹莹), Bingkun Chen(陈炳焜), Yubin Guo(郭玉彬), and Lie Liu(刘列). Chin. Phys. B, 2022, 31(7): 074208.
[5] Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation
Li-Jun Chang(常莉君), Yi-Fan Mo(莫一凡), Li-Ming Ling(凌黎明), and De-Lu Zeng(曾德炉). Chin. Phys. B, 2022, 31(6): 060201.
[6] Characteristics of secondary electron emission from few layer graphene on silicon (111) surface
Guo-Bao Feng(封国宝), Yun Li(李韵), Xiao-Jun Li(李小军), Gui-Bai Xie(谢贵柏), and Lu Liu(刘璐). Chin. Phys. B, 2022, 31(10): 107901.
[7] Effects of Prandtl number in two-dimensional turbulent convection
Jian-Chao He(何建超), Ming-Wei Fang(方明卫), Zhen-Yuan Gao(高振源), Shi-Di Huang(黄仕迪), and Yun Bao(包芸). Chin. Phys. B, 2021, 30(9): 094701.
[8] Evolution of melt convection in a liquid metal driven by a pulsed electric current
Yanyi Xu(徐燕祎), Yunhu Zhang(张云虎), Tianqing Zheng(郑天晴), Yongyong Gong(龚永勇), Changjiang Song(宋长江), Hongxing Zheng(郑红星), and Qijie Zhai(翟启杰). Chin. Phys. B, 2021, 30(8): 084701.
[9] Effect of pressure and space between electrodes on the deposition of SiNxHy films in a capacitively coupled plasma reactor
Meryem Grari, CifAllah Zoheir, Yasser Yousfi, and Abdelhak Benbrik. Chin. Phys. B, 2021, 30(5): 055205.
[10] Numerical simulation of super-continuum laser propagation in turbulent atmosphere
Ya-Qian Li(李雅倩), Wen-Yue Zhu (朱文越), and Xian-Mei Qian(钱仙妹). Chin. Phys. B, 2021, 30(3): 034201.
[11] Asymmetric coherent rainbows induced by liquid convection
Tingting Shi(施婷婷), Xuan Qian(钱轩), Tianjiao Sun(孙天娇), Li Cheng(程力), Runjiang Dou(窦润江), Liyuan Liu(刘力源), and Yang Ji(姬扬). Chin. Phys. B, 2021, 30(12): 124208.
[12] CO2 emission control in new CM car-following model with feedback control of the optimal estimation of velocity difference under V2X environment
Guang-Han Peng(彭光含), Rui Tang(汤瑞), Hua Kuang(邝华), Hui-Li Tan(谭惠丽), and Tao Chen(陈陶). Chin. Phys. B, 2021, 30(10): 108901.
[13] Numerical simulation of chorus-driving acceleration of relativistic electrons at extremely low L-shell during geomagnetic storms
Zhen-Xia Zhang(张振霞), Ruo-Xian Zhou(周若贤), Man Hua(花漫), Xin-Qiao Li(李新乔), Bin-Bin Ni(倪彬彬), and Ju-Tao Yang(杨巨涛). Chin. Phys. B, 2021, 30(10): 109401.
[14] Numerical research on effect of overlap ratio on thermal-stress behaviors of the high-speed laser cladding coating
Xiaoxi Qiao(乔小溪), Tongling Xia(夏同领), and Ping Chen(陈平). Chin. Phys. B, 2021, 30(1): 018104.
[15] Synchronization mechanism of clapping rhythms in mutual interacting individuals
Shi-Lan Su(苏世兰), Jing-Hua Xiao(肖井华), Wei-Qing Liu(刘维清), and Ye Wu(吴晔). Chin. Phys. B, 2021, 30(1): 010505.
No Suggested Reading articles found!