周期型二元颗粒链中孤波传播的二体碰撞近似分析

陈琼; 杨先清; 赵新印; 王振辉; 赵跃民

doi:10.7498/aps.61.044501

摘要

本文运用二体碰撞近似理论研究了孤波在周期型二元颗粒链中的传播. 周期型二元颗粒链由N个大球和一个小球交替排列而成, 球的材质都相同. 将小球和与之相邻的大球等效成一个球, 形成一条等效链. 采用二体碰撞近似理论, 推导了孤波在颗粒链中传播的速度、通过颗粒链时间以及小球的振荡频率. 理论分析得到小球振荡频率随着半径的增大而减小, 该结果与计算机模拟结果符合得相当好. 二体碰撞近似理论给出的波通过整条颗粒链时间, 在N 2时与计算机模拟结果符合得很好. 理论计算的误差随链长的变化不大. 但随着N的增大, 理论得到的结果相对误差变大.

关键词:

Abstract

We study solitary wave propagation in periodic dimer granular chains of beads with the same material but different sizes by binary collision approximation. This kind of chain which is called N:1 dimer consists of pairs of N big beads and one small bead. First we present a method to map the actual chain into an effective chain, then use the binary collision approximation to obtain the transmitted solitary wave speed, the total time taken by the pulse to pass through the chain, and the frequency of oscillation of the small particle. Frequency of oscillation, which increases with the decrease of the radius of the small particle, is analytically obtained. And the results are in excellent agreement with numerical results. For the total time of the pulse passing through the chain, the results of theoretical analysis is in good agreement with numerical results when N 2. The relative error seems no change with the chain length but becomes larger with the increase of the value of N.

Keywords:

作者及机构信息

1.
中国矿业大学理学院, 徐州 221116;

2.
中国矿业大学化工学院, 徐州 221116

基金项目: 国家自然科学基金创新研究群体科学基金(批准号:50921002)和中央高校基本科研业务费专项资金(批准号:2010LKWL09)资助的课题.

Authors and contacts

1.
College of Science, China University of Mining and Technology, Xuzhou 221116, China;

2.
School of Chemical Engineering & Technology, China University of Mining and Technology, Xuzhou 221116, China

Funds: Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 50921002) and the Fundamental Research Funds for the Central Universities (Grant No. 2010LKWL09).

参考文献

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[2]	Wang P J, Xia J H, Liu C S, Liu H, Yan L 2011 Acta Phys. Sin. 60 014501 (in Chinese) [王平建, 夏继宏, 刘长松, 刘会, 闫龙 2011 物理学报 60 014501]
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[4]	Carretero-Gonález R, Khatri D, Porter M A, Kevrekidis P G, Daraio C 2009 Phys. Rev. Lett. 102 024102
[5]	Hong J, Xu A 2001 Phys. Rev. E 63 061310
[6]	Hong J 2005 Phys. Rev. Lett. 94 108001
[7]	Daroio C, Nesterenko V F, Herbold E B, Jin S 2006 Phys. Rev. Lett. 96 058002
[8]	Daraio C, Ngo D, Nesterenko V F, Fraternali F 2010 Phys. Rev. E 82 036603
[9]	Job S, Santibanez F, Tapia F, Melo F 2009 Phys. Rev. E 80 025602(R)
[10]	Porter M A, Daraio C, Herbold E B, Szelengowicz I, Kevrekidis P G 2008 Phys. Rev. E 77 015601(R)
[11]	Vergara L 2006 Phys. Rev. E 73 066623
[12]	Wang P J, Xia J H, Li Y D, Liu C S 2007 Phys. Rev. E 76 041305
[13]	Wang P J, Li Y D, Xia J H, Liu C S 2008 Phys. Rev. E 77 060301(R)
[14]	Daraio C, Nesterenko V F, Herbold E B, Jin S 2005 Phys. Rev. E 72 016603
[15]	Nesterenko V F, Daraio C, Herbold E B, Jin S 2005 Phys. Rev. Lett. 95 158702
[16]	Hascoet E, Herrmann H J 2000 Eur. Phys. J. B 14 183
[17]	Daraio C, Nesterenko V F 2006 Phys. Rev. E 73 026612
[18]	Jayaprakash K R, Starosvetsky Y, Vakakis A F 2011 Phys. Rev. E 83 036606
[19]	Rosas A, Lindenberg K 2004 Phys. Rev. E 69 037601
[20]	Harbola U, Rosas A, Esposito M, Lindenberg K 2009 Phys. Rev. E 80 031303
[21]	Harbola U, Rosas A, Romero A H, Esposito M, Lindenberg K 2009 Phys. Rev. E 80 051302
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[23]	Pinto I L D, Rosas A 2010 Phys. Rev. E 82 031308
[24]	Pinto I L D, Rosas A, Lindenberg K 2009 Phys. Rev. E 79 061307

施引文献

[1]	Huang J, Sun Q C 2007 Acta Phys. Sin. 56 6124 (in Chinese) [黄晋, 孙其诚 2007 物理学报 56 6124]
[2]	Wang P J, Xia J H, Liu C S, Liu H, Yan L 2011 Acta Phys. Sin. 60 014501 (in Chinese) [王平建, 夏继宏, 刘长松, 刘会, 闫龙 2011 物理学报 60 014501]
[3]	Sen S, Hong J, Bang J, Acalos E, Doney R 2008 Phy. Rep. 462 21
[4]	Carretero-Gonález R, Khatri D, Porter M A, Kevrekidis P G, Daraio C 2009 Phys. Rev. Lett. 102 024102
[5]	Hong J, Xu A 2001 Phys. Rev. E 63 061310
[6]	Hong J 2005 Phys. Rev. Lett. 94 108001
[7]	Daroio C, Nesterenko V F, Herbold E B, Jin S 2006 Phys. Rev. Lett. 96 058002
[8]	Daraio C, Ngo D, Nesterenko V F, Fraternali F 2010 Phys. Rev. E 82 036603
[9]	Job S, Santibanez F, Tapia F, Melo F 2009 Phys. Rev. E 80 025602(R)
[10]	Porter M A, Daraio C, Herbold E B, Szelengowicz I, Kevrekidis P G 2008 Phys. Rev. E 77 015601(R)
[11]	Vergara L 2006 Phys. Rev. E 73 066623
[12]	Wang P J, Xia J H, Li Y D, Liu C S 2007 Phys. Rev. E 76 041305
[13]	Wang P J, Li Y D, Xia J H, Liu C S 2008 Phys. Rev. E 77 060301(R)
[14]	Daraio C, Nesterenko V F, Herbold E B, Jin S 2005 Phys. Rev. E 72 016603
[15]	Nesterenko V F, Daraio C, Herbold E B, Jin S 2005 Phys. Rev. Lett. 95 158702
[16]	Hascoet E, Herrmann H J 2000 Eur. Phys. J. B 14 183
[17]	Daraio C, Nesterenko V F 2006 Phys. Rev. E 73 026612
[18]	Jayaprakash K R, Starosvetsky Y, Vakakis A F 2011 Phys. Rev. E 83 036606
[19]	Rosas A, Lindenberg K 2004 Phys. Rev. E 69 037601
[20]	Harbola U, Rosas A, Esposito M, Lindenberg K 2009 Phys. Rev. E 80 031303
[21]	Harbola U, Rosas A, Romero A H, Esposito M, Lindenberg K 2009 Phys. Rev. E 80 051302
[22]	Harbola U, Rosas A, Romero A H, Lindenberg K 2010 Phys. Rev. E 82 011306
[23]	Pinto I L D, Rosas A 2010 Phys. Rev. E 82 031308
[24]	Pinto I L D, Rosas A, Lindenberg K 2009 Phys. Rev. E 79 061307

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