Scattering of shock wave by impurities in a viscoelastic granular chain

  • Tao LiangEmail author
  • Wen-Shan DuanEmail author
Regular Article


The transmission and the reflection of a shock wave by one or several impurities in viscoelastic bead chains is studied in the present paper. There is only one reflected wave for a single impurity. The amplitude of the beads oscillation increases as the initial velocity of the boundaries beads increases, while it decreases as the viscosity coefficient increases. Two reflected waves will be produced if the impurity number is larger than a critical value. This critical value depends on both the initial velocity and the viscosity coefficient. In addition, the maximum amplitude of reflected wave is a constant, when the viscosity coefficient is large enough.

Graphical abstract


Flowing Matter: Granular Materials 


  1. 1.
    V.F. Nesterenko, Dynamics of Heterogeneous Materials (Springer-Verlag, New York, 2001)CrossRefGoogle Scholar
  2. 2.
    Shu Jia, Wenjie Wan, Jason W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    M. van Hecke, J. Phys.: Condens. Matter 22, 033101 (2010)ADSGoogle Scholar
  4. 4.
    Siet van den Wildenberg, Rogier van Loo, Martin van Hecke, Phys. Rev. Lett. 111, 218003 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    V. Karpman, Nonlinear Waves in Dispersive Media (Pergamon Press, New York, 1975)CrossRefGoogle Scholar
  6. 6.
    A. Souslov, A.J. Liu, T.C. Lubensky, Phys. Rev. Lett. 103, 205503 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    A. Mehta, Granular Physics (Cambridge University Press, Cambridge, 2007)Google Scholar
  8. 8.
    S. Sen, J. Hong, J. Bang, E. Avalos, R. Doney, Phys. Rep. 462, 21 (2008)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Shi Wei Liu, Yang Yang Yang, Wen Shan Duan, Lei Yang, Phys. Rev. E 92, 013202 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    D.I. Goldman, P. Umbanhowar, Phys. Rev. E 77, 021308 (2008)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Y. Takehara, S. Fujimoto, K. Okumura, EPL 92, 44003 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    A.H. Clark, L. Kondic, R.P. Behringer, Phys. Rev. Lett. 109, 238302 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    A.H. Clark, R.P. Behringer, EPL 101, 64001 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    A.H. Clark, L. Kondic, R.P. Behringer, Granular impact dynamics: Fluctuations at short time-scales, in Proceedings of the International Conference on Powders and Grains, Vol. 1542 (AIP, Melville, NY, 2013) pp. 445--448Google Scholar
  15. 15.
    M.P. Ciamarra, A.H. Lara, A.T. Lee et al., Phys. Rev. Lett. 92, 194301 (2004)ADSCrossRefGoogle Scholar
  16. 16.
    Wen-Shan Duan, Zhen-Bin Zhang, Lei Yang, Phys. Rev. E 94, 052906 (2016)ADSCrossRefGoogle Scholar
  17. 17.
    A.H. Clark, A.J. Petersen, R.P. Behringer, Phys. Rev. E 89, 012201 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    G.E. Duvall, R. Manvi, S.C. Lowell, J. Appl. Phys. 40, 3771 (1969)ADSCrossRefGoogle Scholar
  19. 19.
    C. Brunhuber, F.G. Mertens, Y. Gaididei, Phys. Rev. E 73, 016614 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    E. Arevalo, Y. Gaididei, F.G. Mertens, Eur. Phys. J. B 27, 63 (2002)ADSCrossRefGoogle Scholar
  21. 21.
    R. Ramírez, T. Pöschel, N.V. Brilliantov, T. Schwager, Phys. Rev. E 60, 4465 (1999)ADSCrossRefGoogle Scholar
  22. 22.
    M. Manciu, S. Sen, A.J. Hurd, Physica D 157, 226 (2001)ADSCrossRefGoogle Scholar
  23. 23.
    A. Rosas, A.H. Romero, V.F. Nesterenko, K. Lindenberg, Phys. Rev. Lett. 98, 164301 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    E.B. Herbold, V.F. Nesterenko, Phys. Rev. E 75, 021304 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    A. Rosas, J. Buceta, K. Lindenberg, Phys. Rev. E 68, 021303 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    A.M. Tichler, L.R. Gómez, N. Upadhyaya, X. Campman, V.F. Nesterenko, V. Vitelli, Phys. Rev. Lett. 111, 048001 (2013)ADSCrossRefGoogle Scholar
  27. 27.
    V.F. Nesterenko, C. Daraio, E.B. Herbold, S. Jin, Phys. Rev. Lett. 95, 158702 (2005)ADSCrossRefGoogle Scholar
  28. 28.
    C. Daraio, V.F. Nesterenko, E.B. Herbold, S. Jin, Phys. Rev. Lett. 96, 058002 (2006)ADSCrossRefGoogle Scholar
  29. 29.
    C. Hoogeboom, G. Theocharis, P.G. Kevrekidis, Phys. Rev. E 82, 061303 (2010)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    S. Job, F. Melo, S. Sen, A. Sokolow, Phys. Rev. Lett. 94, 178002 (2005)ADSCrossRefGoogle Scholar
  31. 31.
    Y. Tsuji, T. Tanaka, T. Ishida, Powder Technol. 71, 239 (1992)CrossRefGoogle Scholar
  32. 32.
    D. Antypov, J.A. Elliott, EPL 94, 50004 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    Tao Liang, Xiao-Lu Zhu, Zhao-Cang Meng, Wen-Shan Duan, Lei Yang, J. Phys. Soc. Jpn. 88, 034002 (2019)ADSCrossRefGoogle Scholar
  34. 34.
    P.F. Navarro, D.J. Benson, V.F. Nesterenko, Phys. Rev. E 94, 033002 (2016)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CASNorthwest Normal UniversityLanzhouChina

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