Binary collision approximation for solitary waves in a Y-shaped granular chain

doi:10.1088/1674-1056/22/1/014501

Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (1): 14501-014501.doi: 10.1088/1674-1056/22/1/014501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Binary collision approximation for solitary waves in a Y-shaped granular chain

陈琼^a, 杨先清^a, 赵新印^a, 王振辉^a, 赵跃民^b

a College of Science, China University of Mining and Technology, Xuzhou 221116, China;
b School of Chemical Engineering & Technology, China University of Mining and Technology, Xuzhou 221116, China

收稿日期:2012-06-03 修回日期:2012-07-07 出版日期:2012-12-01 发布日期:2012-12-01
基金资助:
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 of China (Grant No. 2010LKWL09).

Binary collision approximation for solitary waves in a Y-shaped granular chain

Chen Qiong (陈琼)^a, Yang Xian-Qing (杨先清)^a, Zhao Xin-Yin (赵新印)^a, Wang Zhen-Hui (王振辉)^a, Zhao Yue-Min (赵跃民)^b

a College of Science, China University of Mining and Technology, Xuzhou 221116, China;
b School of Chemical Engineering & Technology, China University of Mining and Technology, Xuzhou 221116, China

Received:2012-06-03 Revised:2012-07-07 Online:2012-12-01 Published:2012-12-01
Contact: Yang Xian-Qing E-mail:xianqyang@163.com
Supported by:
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 of China (Grant No. 2010LKWL09).

摘要/Abstract

摘要： We implement a binary collision approximation to study solitary wave propagation in a two-dimensional double Y-shaped granular chain. The solitary wave was transmitted and reflected when it met the interface of the bifurcated branches of the Y-shaped granular chains. We obtain analytic results of the ratios of the transmitted and reflected speeds to the incident speed of the solitary wave, the maximum force between two neighbor beads in solitary wave, and the total time took by the pulse to pass through each branch. All of the analytic results are in good agreement with experimental observations by Daraio et al. [Phys. Rev. E 82 036603 (2010)]. Moreover, we also discuss the delay effects on the arrival of split pulses, and predict the recombination of the split waves traveling in branches in the final stem of asymmetric systems. The prediction of pulse recombination is verified by our numerical results.

关键词: Y-shaped granule chain, solitary wave, binary collision approximation

Abstract: We implement a binary collision approximation to study solitary wave propagation in a two-dimensional double Y-shaped granular chain. The solitary wave was transmitted and reflected when it met the interface of the bifurcated branches of the Y-shaped granular chains. We obtain analytic results of the ratios of the transmitted and reflected speeds to the incident speed of the solitary wave, the maximum force between two neighbor beads in solitary wave, and the total time took by the pulse to pass through each branch. All of the analytic results are in good agreement with experimental observations by Daraio et al. [Phys. Rev. E 82 036603 (2010)]. Moreover, we also discuss the delay effects on the arrival of split pulses, and predict the recombination of the split waves traveling in branches in the final stem of asymmetric systems. The prediction of pulse recombination is verified by our numerical results.

Key words: Y-shaped granule chain, solitary wave, binary collision approximation

中图分类号: (Granular systems)

45.70.-n

46.40.Cd (Mechanical wave propagation (including diffraction, scattering, and dispersion))

陈琼, 杨先清, 赵新印, 王振辉, 赵跃民. Binary collision approximation for solitary waves in a Y-shaped granular chain[J]. Chin. Phys. B, 2013, 22(1): 14501-014501.

Chen Qiong (陈琼), Yang Xian-Qing (杨先清), Zhao Xin-Yin (赵新印), Wang Zhen-Hui (王振辉), Zhao Yue-Min (赵跃民). Binary collision approximation for solitary waves in a Y-shaped granular chain[J]. Chin. Phys. B, 2013, 22(1): 14501-014501.

参考文献 23

[1]	Sen S, Hong J, Bang J, Acalos E and Doney R 2008 Phys. Rep. 462 21
[2]	Carretero-Gonález R, Khatri D, Porter M A, Kevrekidis P G and Daraio C 2009 Phys. Rev. Lett. 102 024102
[3]	Hong J 2002 Physica A 315 187
[4]	Wang P J, Xia J H, Liu C S, Liu H and Yan L 2011 Acta Phys. Sin. 60 014501 (in Chinese)
[5]	Hong J 2005 Phys. Rev. Lett. 94 108001
[6]	Daraio C, Nesterenko V F, Herbold E B and Jin S 2006 Phys. Rev. Lett. 96 058002
[7]	Doney R and Sen S 2006 Phys. Rev. Lett. 97 155502
[8]	Vergara L 2006 Phys. Rev. E 73 066623
[9]	Wang P J, Xia J H, Li Y D and Liu C S 2007 Phys. Rev. E 76 041305
[10]	Khatri D, Daraio C and Rizzo P 2008 Proc. SPIE 7292 69340U
[11]	Daraio C, Nesterenko V F, Herbold E B and Jin S 2005 Phys. Rev. E 72 016603
[12]	Nesterenko V F, Daraio C, Herbold E B and Jin S 2005 Phys. Rev. Lett. 95 158702
[13]	Daraio C, Ngo D, Nesterenko V F and Fraternali F 2010 Phys. Rev. E 82 036603
[14]	Rosas A and Lindenberg K 2004 Phys. Rev. E 69 037601
[15]	Hascoet E and Herrmann H J 2000 Eur. Phys. J. B 14 183
[16]	Daraio C and Nesterenko V F 2006 Phys. Rev. E 73 026612
[17]	Chen Q, Yang X Q, Wang Z H and Zhao X Y 2012 Chin. Phys. Lett. 29 014501
[18]	Harbola U, Rosas A, Esposito M and Lindenberg K 2009 Phys. Rev. E 80 031303
[19]	Harbola U, Rosas A, Romero A H, Esposito M and Lindenberg K 2009 Phys. Rev. E 80 051302
[20]	Harbola U, Rosas A, Romero A H and Lindenberg K 2010 Phys. Rev. E 82 011306
[21]	Chen Q, Yang X Q, Zhao X Y, Wang Z H and Zhao Y M 2012 Acta Phys. Sin. 61 044501 (in Chinese)
[22]	Pinto I L D and Rosas A 2010 Phys. Rev. E 82 031308
[23]	Chatterjee A 1999 Phys. Rev. E 59 5912

Binary collision approximation for solitary waves in a Y-shaped granular chain

Binary collision approximation for solitary waves in a Y-shaped granular chain

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