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Dilatancy Transition in a Granular Model

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Abstract

We introduce a model of granular matter and use a volume/strain ensemble to analyze infinitesimal shearing. Monte Carlo simulation suggests the model exhibits a second order phase transition associated with the onset of dilatancy.

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References

  1. Rao, K.K., Nott, P.R.: An Introduction to Granular Flow. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  2. Reynolds, O.: Phil. Mag. Series 5 20, 469 (1885)

    Google Scholar 

  3. Aharonov, E., Sparks, D.: Phys. Rev. E 60, 6890 (1999)

    Article  ADS  Google Scholar 

  4. Piccioni, M., Loreto, V., Roux, S.: Phys. Rev. E 61, 2813 (2000)

    Article  ADS  Google Scholar 

  5. Tillemans, H.-J., Herrmann, J.: Physica A 217, 261 (1995)

    Article  ADS  Google Scholar 

  6. Coniglio, A., Herrmann, H.J.: Physica A 225, 1 (1996)

    Article  ADS  Google Scholar 

  7. Nowak, E.R., Knight, J.B., Ben-Naim, E., Jaeger, H.M., Nagel, S.R.: Phys. Rev. E 57, 1971 (1998)

    Article  ADS  Google Scholar 

  8. Schröter, M., Nägle, S., Radin, C., Swinney, H.L.: Europhys. Lett. 78, 44004 (2007)

    Article  ADS  Google Scholar 

  9. Edwards, S.F., Oakeshott, R.B.S.: Physica A 157, 1080 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  10. de Gennes, P.-G.: Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca (1979)

    Google Scholar 

  11. Barrat, A., Kurchan, J., Loreto, V., Sellitto, M.: Phys. Rev. Lett. 85, 5034 (2000)

    Article  ADS  Google Scholar 

  12. Chakraborty, B.: Soft Matter 6, 2884 (2010)

    Article  ADS  Google Scholar 

  13. Edwards, S.F., Grinev, D.V.: Adv. Phys. 51, 1669 (2002)

    Article  ADS  Google Scholar 

  14. Herrmann, H.J.: Physica A 263, 51 (1999)

    Article  ADS  Google Scholar 

  15. Hoover, W.G., Hoover, C.G., Bannerman, M.N.: J. Stat. Phys. 136, 715 (2009)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. Bi, D., Chakraborty, B.: Philos. Trans. R. Soc. Lond. 367, 5073 (2009)

    Article  MATH  ADS  Google Scholar 

  17. Blumenfeld, R., Edwards, S.F.: J. Phys. Chem. B 113, 3981 (2009)

    Article  Google Scholar 

  18. Parrinello, M., Rahman, A.: J. Chem. Phys. 76, 2662 (1982)

    Article  ADS  Google Scholar 

  19. MacDonald, I.R.: Mol. Phys. 100, 95 (2002)

    Article  ADS  Google Scholar 

  20. Aristoff, D., Radin, C.: J. Stat. Phys. 135, 1 (2009)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. Radin, C.: J. Stat. Phys. 131, 567 (2008)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. Aristoff, D., Radin, C.: J. Math. Phys. 51, 113302 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  23. Scott, G.D., Kilgour, D.M.: Br. J. Appl. Phys. 2, 863 (1969)

    ADS  Google Scholar 

  24. Scott, G.D., Charlesworth, A.M., Mak, M.K.: J. Chem. Phys. 40, 611 (1964)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, University of Texas, Austin, TX, 78712, USA

    David Aristoff & Charles Radin

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  1. David Aristoff
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  2. Charles Radin
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Correspondence to Charles Radin.

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Aristoff, D., Radin, C. Dilatancy Transition in a Granular Model. J Stat Phys 143, 215–225 (2011). https://doi.org/10.1007/s10955-011-0180-4

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  • DOI: https://doi.org/10.1007/s10955-011-0180-4

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