Skip to main content

Ratchet rotation of a 3D dimer on a vibrating plate

Abstract.

This work studies the dynamics of a 3D dimer bouncing upon a horizontal plate undergoing a vertical harmonic vibration. Despite complex interactions within the system due to impacts and friction, numerical simulation shows that, under certain conditions prescribed for the dynamics, the center of mass of the dimer, when projected onto a horizontal plane, will follow a circular orbit. The phenomenon is like a particle under Coulomb friction performing a ratchet motion that rotates around. Investigations further reveal that the dimer dynamics bear some typical characteristics of a nonlinear system, including sensitivity to the initial conditions and bifurcation behaviors related to the physical parameters of the dynamics. Our results indicate that the coefficient of restitution and the plate's vibration intensity play critical roles in exciting the circular orbit, while the dimer's geometry and the vibration frequency mainly influence the trajectory characteristics. These findings may help understand transport mechanisms underlying systems of granular matter with anisotropic particles.

Graphical abstract

This is a preview of subscription content, access via your institution.

References

  1. Z.A. Daya, E. Ben-Naim, R.E. Ecke, Eur. Phys. J. E 21, 1 (2006)

    Article  Google Scholar 

  2. V. Yadav, A. Kudrolli, Eur. Phys. J. E 35, 1 (2012)

    Article  Google Scholar 

  3. T. Mullin, Phys. Rev. Lett. 84, 4741 (2000)

    ADS  Article  Google Scholar 

  4. D.L. Blair, T. Neicu, A. Kudrolli, Phys. Rev. E 67, 031303 (2003)

    ADS  Article  Google Scholar 

  5. I.J. Aranson, L.S. Tsimring, Phys. Rev. E 67, 021305 (2003)

    ADS  MathSciNet  Google Scholar 

  6. I. Goldhirsch, G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993)

    ADS  Google Scholar 

  7. James B. Knight, H.M. Jaeger, Sidney R. Nagel, Phys. Rev. Lett. 70, 3728 (1993)

    ADS  Google Scholar 

  8. Z. Farkas, P. Tegzes, A. Vukics, T. Vicsek, Phys. Rev. E 60, 7022 (1999)

    ADS  Google Scholar 

  9. M. Levanon, D.C. Rapaport, Phys. Rev. E 64, 011304 (2001)

    ADS  Google Scholar 

  10. Z. Farkas, F. Szalai, D.E. Wolf, T. Vicsek, Phys. Rev. E 65, 022301 (2002)

    ADS  Google Scholar 

  11. A.J. Bae, W.A.M. Morgado, J.J.P. Veerman, G.L. Vasconcelos, Physica A 342, 22 (2004)

    ADS  Google Scholar 

  12. S. Collins, A. Ruina, R. Tedrake, M. Wisse, Science 307, 1082 (2005)

    ADS  Google Scholar 

  13. M. Gomes, A. Ruina, Phys. Rev. E 83, 032901 (2011)

    ADS  MathSciNet  Google Scholar 

  14. K. Lynch, C.K. Black, IEEE Trans. Robot. Automat. 17, 113 (2001)

    Google Scholar 

  15. A. Mehta, J.M. Luck, Phys. Rev. Lett. 63, 393 (1990)

    ADS  MathSciNet  Google Scholar 

  16. J.J. Barroso, M.V. Carneiro, E.E.N. Macau, Phys. Rev. E 79, 026206 (2009)

    ADS  MathSciNet  Google Scholar 

  17. T. Gilet, N. Vandewalle, S. Dorbolo, Phys. Rev. E 79, 055201 (2009)

    ADS  Google Scholar 

  18. N.B. Tufillaro, T.M. Mello, Y.M. Choi, A.M. Albano, J. Phys. 47, 1477 (1986)

    Google Scholar 

  19. J.M. Luck, Anita Mehta, Phys. Rev. E 48, 3988 (1993)

    ADS  MathSciNet  Google Scholar 

  20. S. Giusepponi, F. Marchesoni, Europhys. Lett. 64, 36 (2003)

    ADS  Google Scholar 

  21. Z.J. Kowalik, M. Franaszek, P. Pieranski, Phys. Rev. A 37, 4016 (1988)

    ADS  MathSciNet  Google Scholar 

  22. M.C. Vargas, D.A. Huerta, V. Sosa, Am. J. Phys. 77, 857 (2009)

    ADS  Google Scholar 

  23. S. von Gehlen, M. Evstigneev, P. Reimann, Phys. Rev. E 79, 031114 (2009)

    ADS  Google Scholar 

  24. D. Speer, R. Eichhorn, M. Evstigneev, P. Reimann, Phys. Rev. E 85, 061132 (2012)

    ADS  Google Scholar 

  25. V. Frette, K. Christensen, A. Malthe-Sørenssen, J. Feder, T. Jøssang, P. Meakin, Nature 379, 49 (1996)

    ADS  Google Scholar 

  26. D. Volfson, A. Kudrolli, L.S. Tsimring, Phys. Rev. E 70, 051312 (2004)

    ADS  Google Scholar 

  27. S. Dorbolo, D. Volfson, L. Tsimring, A. Kudrolli, Phys. Rev. Lett. 95, 044101 (2005)

    ADS  Google Scholar 

  28. J. Atwell, J.S. Olafsen, Phys. Rev. E 71, 062301 (2005)

    ADS  Google Scholar 

  29. H.S. Wright, Michael R. Swift, P.J. King, Phys. Rev. E 74, 061309 (2006)

    ADS  Google Scholar 

  30. A. Kudrolli, G. Lumay, D. Volfson, L.S. Tsimring, Phys. Rev. Lett. 100, 058001 (2008)

    ADS  Google Scholar 

  31. S. Dorbolo, F. Ludewig, N. Vandewalle, New J. Phys. 11, 033016 (2009)

    ADS  Google Scholar 

  32. K. Harth, U. Kornek, T. Trittel, U. Strachauer, S. Höme, K. Will, R. Stannarius, Phys. Rev. Lett. 110, 144102 (2013)

    ADS  Google Scholar 

  33. H.J. Herrmann, S. Luding, Continuum Mech. Thermodyn. 10, 189 (1998)

    ADS  MATH  MathSciNet  Google Scholar 

  34. S. Luding, Phys. Rev. E 52, 4442 (1995)

    ADS  Google Scholar 

  35. E. Falcon, C. Laroche, S. Fauve, C. Coste, Eur. Phys. J. B 5, 111 (1998)

    ADS  Google Scholar 

  36. C. Liu, Z. Zhao, B. Brogliato, Proc. R. Soc. London, Ser. A 464, 3193 (2008)

    ADS  MATH  MathSciNet  Google Scholar 

  37. C. Liu, H. Zhang, Z. Zhao, B. Brogliato, Proc. R. Soc. London, Ser. A 469, 20120741 (2013)

    ADS  MATH  MathSciNet  Google Scholar 

  38. C. Liu, Z. Zhao, B. Brogliato, Proc. R. Soc. London, Ser. A 465, 1 (2009)

    ADS  MATH  MathSciNet  Google Scholar 

  39. Z. Zhao, C. Liu, B. Brogliato, Phys. Rev. E 78, 031307 (2008)

    ADS  MathSciNet  Google Scholar 

  40. H. Zhang, C. Liu, Z. Zhao, B. Brogliato, Sci. China-Phys. Mech. Astron. 56, 875 (2013)

    ADS  Google Scholar 

  41. Z. Zhao, C. Liu, B. Brogliato, Proc. R. Soc. London, Ser. A 465, 2267 (2009)

    ADS  MATH  MathSciNet  Google Scholar 

  42. J. Wang, C. Liu, Z. Zhao, Multibody Syst. Dyn. (August 2013), DOI:10.1007/s11044-013-9385-4

  43. W. J. Stronge, Impact mechanics (Cambridge University Press, 2000)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Caishan Liu.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wang, J., Liu, C., Jia, YB. et al. Ratchet rotation of a 3D dimer on a vibrating plate. Eur. Phys. J. E 37, 1 (2014). https://doi.org/10.1140/epje/i2014-14001-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2014-14001-x

Keywords

  • Flowing matter: Nonlinear Physics