The electrical conductance growth of a metallic granular packing

  • Zorica M. Jakšić
  • Milica Cvetković
  • Julija R. Šćepanović
  • Ivana Lončarević
  • Ljuba Budinski-Petković
  • Slobodan B. VrhovacEmail author
Regular Article


We report on measurements of the electrical conductivity on a two-dimensional packing of metallic disks when a stable current of ~1 mA flows through the system. At low applied currents, the conductance σ is found to increase by a pattern σ(t) = σ Δσ E α [ − (t/τ) α ], where E α denotes the Mittag-Leffler function of order α ∈ (0,1). By changing the inclination angle θ of the granular bed from horizontal, we have studied the impact of the effective gravitational acceleration g eff = gsinθ on the relaxation features of the conductance σ(t). The characteristic timescale τ is found to grow when effective gravity g eff decreases. By changing both the distance between the electrodes and the number of grains in the packing, we have shown that the long term resistance decay observed in the experiment is related to local micro-contacts rearrangements at each disk. By focusing on the electro-mechanical processes that allow both creation and breakdown of micro-contacts between two disks, we present an approach to granular conduction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the conduction dynamics of granular material at low currents, we impose that the micro-contacts at the interface switch stochastically between two possible states, “on” and “off”, characterizing the conductivity of the micro-contact. We assume that the time intervals between the consecutive changes of state are governed by a certain waiting-time distribution. It is demonstrated how the microscopic random dynamics regarding the micro-contacts leads to the macroscopic observation of slow conductance growth, described by an exact fractional kinetic equations.


Statistical and Nonlinear Physics 


  1. 1.
    R. Holm, Electric Contacts: Theory and Applications, 4th edn. (Springer-Verlag, Berlin/Heidelberg, 1967)Google Scholar
  2. 2.
    V. Da Costa, Y. Henry, F. Bardou, M. Romeo, K. Ounadjela, Eur. Phys. J. B 13, 297 (2000)ADSCrossRefGoogle Scholar
  3. 3.
    B.F. Toler, R.A. Coutu Jr., J.W. McBride, J. Micromech. Microeng. 23, 103001 (2013)ADSCrossRefGoogle Scholar
  4. 4.
    E. Branly, C. R. Acad. Sci. 280, 785 (1890)Google Scholar
  5. 5.
    S. Dorbolo, M. Ausloos, N. Vandewalle, Phys. Rev. E 67, 040302 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    E. Falcon, B. Castaing, C. Laroche, Europhys. Lett. 65, 186 (2004)ADSCrossRefGoogle Scholar
  7. 7.
    E. Falcon, B. Castaing, Am. J. Phys. 73, 302 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    S. Dorbolo, N. Vandewalle, Traffic Granul. Flow 5, 521 (2005)Google Scholar
  9. 9.
    P. Bèquin, V. Tourant, Granul. Matter 12, 375 (2010)CrossRefGoogle Scholar
  10. 10.
    M. Creyssels, S. Dorbolo, A. Merlen, C. Laroche, B. Castaing, E. Falcon, Eur. Phys. J. E 23, 255 (2007)CrossRefGoogle Scholar
  11. 11.
    E. Falcon, B. Castaing, M. Creyssels, Eur. Phys. J. B 38, 475 (2004)ADSCrossRefGoogle Scholar
  12. 12.
    N. Vandewalle, C. Lenaerts, S. Dorbolo, Europhys. Lett. 53, 197 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    D. Bonamy, L. Laurent, Ph. Claudin, J.-Ph. Bouchaud, Europhys. Lett. 51, 614 (2000)ADSCrossRefGoogle Scholar
  14. 14.
    S. Dorbolo, M. Ausloos, N. Vandewalle, M. Houssab, J. Appl. Phys. 94, 7835 (2003)ADSCrossRefGoogle Scholar
  15. 15.
    J.J. Lee, C.W. Lee, I. Yu, Y.K. Jung, J. Lee, J. Phys.: Condens. Matter 19, 356202 (2007)ADSGoogle Scholar
  16. 16.
    R. Hilfer, J. Non-Cryst. Solids 305, 122 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    M.M. Meerschaert, H.-P. Scheffler, J. Appl. Probab. 41, 623 (2004)MathSciNetCrossRefGoogle Scholar
  18. 18.
    A.A. Stanislavsky, Phys. Rev. E 61, 4752 (2000)ADSCrossRefGoogle Scholar
  19. 19.
    R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000)ADSCrossRefGoogle Scholar
  20. 20.
    G.M. Zaslavsky, Phys. Rep. 371, 461 (2002)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    T. Aste, J. Phys.: Condens. Matter 17, S2361 (2005)ADSGoogle Scholar
  22. 22.
    E.W. Weisstein, Mittag-Leffler function, From MathWorld − A Wolfram Web Resource (2017),
  23. 23.
    D. Howell, R.P. Behringer, C. Veje, Phys. Rev. Lett. 82, 5241 (1999)ADSCrossRefGoogle Scholar
  24. 24.
    M. Muthuswamy, A. Tordesillas, in Proceedings of the 10th ASCE Aerospace Division International Conference on Engineereng, Construction and Operations in Challenging Environments (Earth & Space 2006), edited by R.B. Malla, W.K. Binienda, A.K. Maji (Aerospace Division of the American Society of Civil Engineers, Reston, VA, 2006), p. 33Google Scholar
  25. 25.
    M. Muthuswamy, A. Tordesillas, JSTAT P09003 (2006)Google Scholar
  26. 26.
    A. Modaressi, S. Boufellouh, P. Evesque, Chaos 9, 523 (1999)ADSCrossRefGoogle Scholar
  27. 27.
    Z.M. Jakšić, J.R. Šćepanović, I. Lončarević, Lj. Budinski-Petković, S.B. Vrhovac, A. Belić, Phys. Rev. E 90, 062208 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    A. Janicki, A. Weron, Stat. Sci. 9, 109 (1994)CrossRefGoogle Scholar
  29. 29.
    M. Magdziarz, K. Weron, Physica A 367, 1 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    F. Mainardi, Chaos Solitons Fract. 7, 1461 (1996)ADSCrossRefGoogle Scholar
  31. 31.
    A.A. Stanislavsky, Phys. Rev. E 67, 021111 (2003)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    A.A. Stanislavsky, Chaos Solitons Fract. 34, 51 (2007), in Search of a Theory of ComplexityADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Aleksander Stanislavsky, Karina Weron, Aleksander Weron, Commun. Nonlinear Sci. Numer. Simul. 24, 117 (2015)ADSCrossRefGoogle Scholar
  34. 34.
    A.A. Stanislavsky, Acta Phys. Polonica B 34, 3649 (2003)ADSGoogle Scholar
  35. 35.
    F. Mainardi, R. Gorenflo, J. Comput. Appl. Math. 118, 283 (2000)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    R.K. Saxena, A.M. Mathai, H.J. Haubold, Physica A 344, 657 (2004)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    R. Hilfer, L. Anton, Phys. Rev. E 51, R848 (1995)ADSCrossRefGoogle Scholar
  38. 38.
    T.J. Kozubowski, S.T. Rachev, J. Comput. Anal. Appl. 1, 177 (1999)MathSciNetGoogle Scholar
  39. 39.
    D. Fulger, E. Scalas, G. Germano, Phys. Rev. E 77, 021122 (2008)ADSCrossRefGoogle Scholar
  40. 40.
    E. Heinsalu, M. Patriarca, I. Goychuk, G. Schmid, P. Hänggi, Phys. Rev. E 73, 046133 (2006)ADSCrossRefGoogle Scholar
  41. 41.
    E. Heinsalu, M. Patriarca, I. Goychuk, P. Hänggi, J. Phys.: Condens. Matter 19, 065114 (2007)ADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Zorica M. Jakšić
    • 1
  • Milica Cvetković
    • 1
  • Julija R. Šćepanović
    • 1
  • Ivana Lončarević
    • 2
  • Ljuba Budinski-Petković
    • 2
  • Slobodan B. Vrhovac
    • 1
    Email author
  1. 1.Institute of Physics Belgrade, University of BelgradeBelgradeSerbia
  2. 2.Faculty of EngineeringNovi SadSerbia

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