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On the occurrence of polygon-shaped patterns in vibrated cylindrical granular beds

  • G. LuEmail author
  • J. R. Third
  • M. H. Köhl
  • C. R. Müller
Regular Article

Abstract

We report experimental observations of polygon-shaped patterns formed in a vertically vibrated bed of circular cross-section. A phase map is determined, showing that the polygon pattern is established for Γ = A(2πf)2/g ≳ 10 . The sensitivity of the polygon structure to bed parameters was tested by studying beds of different particle sizes and fill levels. It was hypothesized that the polygon pattern observed in cylindrical beds is the corresponding pattern to the formation of arches in square-shaped beds. The close relationship between these two patterns was demonstrated by two observations: i) the radii of the arches of a corresponding square bed and the inner radius of the cylindrical bed were found to be very similar and ii) the boundary lengths of the two patterns were in good agreement.

Keywords

Flowing matter: Nonlinear Physics 

References

  1. 1.
    H.M. Jaeger, S.R. Nagel, R.P. Behringer, Rev. Mod. Phys. 68, 1259 (1996).ADSCrossRefGoogle Scholar
  2. 2.
    I.S. Aranson, L.S. Tsimring, Rev. Mod. Phys. 78, 641 (2006).ADSCrossRefGoogle Scholar
  3. 3.
    J.M. Ottino, D.V. Khakhar, Annu. Rev. Fluid Mech. 32, 55 (2000).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    G. Seiden, P.J. Thomas, Rev. Mod. Phys. 83, 1323 (2011).ADSCrossRefGoogle Scholar
  5. 5.
    Z.H. Jiang, Y.Y. Wang, J. Wu, Europhys. Lett. 74, 417 (2006).ADSCrossRefGoogle Scholar
  6. 6.
    P.F. Stadelr, J.M. Luck, A. Mehta, Europhys. Lett. 57, 46 (2001).ADSCrossRefGoogle Scholar
  7. 7.
    P.M. Reis, G. Ehrhardt, A. Stephenson, T. Mullin, Europhys. Lett. 66, 357 (2004).ADSCrossRefGoogle Scholar
  8. 8.
    C.P. Clement, H.A. Pacheco-martinez, M.R. Swift, P.J. King, Europhys. Lett. 91, 54001 (2010).ADSCrossRefGoogle Scholar
  9. 9.
    L. Trujillo, M. Alam, H.J. Herrmann, Europhys. Lett. 64, 190 (2003).ADSCrossRefGoogle Scholar
  10. 10.
    M. Bose, P.R. Nott, V. Kumaran, Europhys. Lett. 68, 508 (2004).ADSCrossRefGoogle Scholar
  11. 11.
    G. Gutiérrez, O. Pozo, L.I. Reyes, V.R. Paredes, J.F. Draek, E. Ott, Europhys. Lett. 67, 369 (2004).ADSCrossRefGoogle Scholar
  12. 12.
    D.A. Sanders, M.R. Swift, R.M. Bowley, P.J. King, Europhys. Lett. 73, 349 (2006).ADSCrossRefGoogle Scholar
  13. 13.
    J.S. Olafsen, J.S. Urbach, Phys. Rev. Lett. 81, 4369 (1998).ADSCrossRefGoogle Scholar
  14. 14.
    E. Clement, J. Duran, J. Rajchenbach, Phys. Rev. Lett. 69, 1189 (1992).ADSCrossRefGoogle Scholar
  15. 15.
    C.R. Wassgren, C.E. Brennen, M.L. Hunt, J. Appl. Mech. 63, 712 (1996).ADSCrossRefGoogle Scholar
  16. 16.
    O. Sano, Phys. Rev. E 72, 051302 (2005).ADSCrossRefGoogle Scholar
  17. 17.
    F. Melo, P.B. Umbanhowar, H.L. Swinney, Phys. Rev. Lett. 75, 3838 (1995).ADSCrossRefGoogle Scholar
  18. 18.
    P.B. Umbanhowar, F. Melo, H.L. Swinney, Nature 382, 793 (1996).ADSCrossRefGoogle Scholar
  19. 19.
    C. Bizon, M.D. Shattuck, J.B. Swift, W.D. Mccormick, H.L. Swinney, Phys. Rev. Lett. 80, 57 (1998).ADSCrossRefGoogle Scholar
  20. 20.
    F.X. Villarruel, B.E. Lauderdale, D.M. Mueth, H.M. Jaeger, Phys. Rev. E 61, 6914 (2000).ADSCrossRefGoogle Scholar
  21. 21.
    V. Narayan, N. Menon, S. Ramaswamy, J. Stat. Mech. 01, P01005 (2006).CrossRefGoogle Scholar
  22. 22.
    D.L. Blair, T. Neicu, A. Kudrolli, Phys. Rev. E 67, 031303 (2003).ADSCrossRefGoogle Scholar
  23. 23.
    I.S. Aranson, D. Volfson, L.S. Tsimring, Phys. Rev. E 75, 051301 (2007).ADSCrossRefGoogle Scholar
  24. 24.
    V. Narayan, S. Ramaswamy, N. Menon, Science 317, 105 (2007).ADSCrossRefGoogle Scholar
  25. 25.
    V. Narayan, S. Ramaswamy, N. Menon, Science 320, 612 (2008).ADSCrossRefGoogle Scholar
  26. 26.
    J.B. Knight, H.M. Jaeger, S.R. Nagel, Phys. Rev. Lett. 70, 3728 (1993).ADSCrossRefGoogle Scholar
  27. 27.
    S. Douady, S. Fauve, C. Laroche, Europhys. Lett. 8, 621 (1989).ADSCrossRefGoogle Scholar
  28. 28.
    R.J. Milburn, M.A. Naylor, A.J. Smith, M.C. Leaper, K. Good, M.R. Swift, P.J. King, Phys. Rev. E 71, 011308 (2005).ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • G. Lu
    • 1
    Email author
  • J. R. Third
    • 1
  • M. H. Köhl
    • 1
  • C. R. Müller
    • 1
  1. 1.ETH ZürichZürichSwitzerland

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