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Annual Review of Condensed Matter Physics

Volume 6, 2015

The Statistical Physics of Athermal Materials

Abstract

At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends on only a few macroscopic parameters, such as temperature, pressure, volume, and energy. In this review, we discuss recent advances in establishing statistical ensembles for athermal materials. The broad class of granular and particulate materials is immune to the effects of thermal fluctuations because the constituents are macroscopic. In addition, interactions between grains are frictional and dissipative, which invalidates the fundamental postulates of equilibrium statistical mechanics. However, granular materials exhibit distributions of microscopic quantities that are reproducible and often depend on only a few macroscopic parameters. We explore the history of statistical ensemble ideas in the context of granular materials, clarify the nature of such ensembles and their foundational principles, highlight advances in testing key ideas, and discuss applications of ensembles to analyze the collective behavior of granular materials.

Keyword(s): athermal, granular materials, statistical physics
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2015-03-10
2024-04-23
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Literature Cited

  1. Bouchaud J-P. 2002. Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter: Les Houches Session LXXVII, ed. J Kurchan, J-L Barrat, M Feigelman, J Dalibard, pp. 131–97. Berlin/Heidelberg: Springer
  2. Falk ML, Langer JS. 2011. Annu. Rev. Condens. Matter Phys 2:353–73
  3. Cates ME, Wittmer JP, Bouchaud JP, Claudin P. 1998. Phys. Rev. Lett. 81:1841–44
  4. Cates ME, Wittmer JP, Bouchaud JP, Claudin P. 1999. Phys. A 263:354–61
  5. Edwards SF, Oakeshott RBS. 1989. Phys. A 157:1080–90
  6. Chakraborty B, Behringer RP. 2009. In Encyclopedia of Complexity and Systems Science, ed. RA Meyers, pp. 4997–5021. Berlin/Heidelberg: Springer
  7. Liu C-H, Nagel SR, Schecter DA, Coppersmith SN, Majumdar S et al. 1995. Science 269:513–15
  8. Majmudar TS, Behringer RP. 2005. Nature 435:1079–82
  9. Howell DW, Behringer RP, Vege CT. 1999. Phys. Rev. Lett. 82:265241–44
  10. Chandler D. 1987. Introduction to Modern Statistical Mechanics New York: Oxford Univ. Press
  11. Edwards SF, Grinev DV. 2002. Adv. Phys. 51:81669–84
  12. Donev A, Torquato S, Stillinger FH, Connelly R. 2004. J. Appl. Phys. 95:989–99
  13. Liu AJ, Nagel SR. 2010. Annu. Rev. Condens. Matter Phys. 1:347–69
  14. Bernal JD, Mason J. 1960. Nature 188:4754910–11
  15. Ciamarra MP, Richard P, Schröter M, Tighe BP. 2012. Soft Matter 8:389731–37
  16. Song C, Wang P, Makse HA. 2008. Nature 453:7195629–32
  17. Jerkins M, Schröter M, Harry L, Senden TJ, Saadatfar M, Aste T. 2008. Phys. Rev. Lett. 101:118301–4
  18. Onoda GY, Liniger EG. 1990. Phys. Rev. Lett. 64:222727–30
  19. Dantu P. 1957. Proc. Int. Conf. Soil Mech. Found. Eng., 4th, London, pp. 144–48. London: Butterworths Sci. Publ
  20. Drescher A, de Josselin de Jong G. 1972. J. Mech. Phys. Solids 20:337–40
  21. Blumenfeld R, Edwards SF. 2009. J. Phys. Chem. B 113:123981–87
  22. Edwards SF. 2005. Phys. A 353:114–18
  23. Henkes S, Chakraborty B. 2005. Phys. Rev. Lett. 95:198002
  24. Henkes S, O’Hern CS, Chakraborty B. 2007. Phys. Rev. Lett. 99:3038002
  25. Henkes S, Chakraborty B. 2009. Phys. Rev. E 79:061301
  26. Metzger PT. 2008. Phys. Rev. E 77:011307
  27. Tighe BP, van Eerd ART, Vlugt TJH. 2008. Phys. Rev. Lett. 100:23238001
  28. Chakraborty B. 2010. Soft Matter 6:2884–93
  29. Cugliandolo L, Kurchan J. 1999. Phys. A 263:242–51
  30. Langer JS, Manning ML. 2007. Phys. Rev. E 76:056107
  31. Barrat A, Kurchan J, Loreto V, Sellitto M. 2000. Phys. Rev. Lett. 85:5034–37
  32. Barrat A, Kurchan J. , Loreto V, Sellitto M. 2001. Phys. Rev. E 63:051301
  33. Coniglio A, Fierro A, Nicodemi M. . 2001. Phys. A 302:1–4193–201
  34. Coniglio A, Fierro A, Nicodemi M. 2002. Eur. Phys. J. E 9:3219–26
  35. Kurchan J. 2001. C. R. Acad. Sci. Ser. IV Phys. Astrophys. 2:239–47
  36. Makse HA, Kurchan J. 2002. Nature 415:6872614–17
  37. Gao G-J, Blawzdziewicz J, O’Hern CS, Shattuck M. 2009. Phys. Rev. E 80:061301
  38. McNamara S, Richard P, de Richter S, Le Caër G, Delannay R. 2009. Phys. Rev. E 80:3031301
  39. Asenjo D, Paillusson F, Frenkel D. 2014. Phys. Rev. Lett. 112:9098002
  40. Bertin E, Dauchot O, Droz M. 2004. Phys. Rev. Lett. 93:230601
  41. Bertin E, Dauchot O, Droz M. 2005. Phys. Rev. E 71:046140
  42. Bertin E, Dauchot O, Droz M. 2006. Phys. Rev. Lett. 96:120601
  43. Ball R, Blumenfeld R. 2002. Phys. Rev. Lett. 88:115505
  44. Blumenfeld R. 2008. Lecture Notes in Complex Systems, ed. T Aste, pp. 43–53. Singapore:World Sci.
  45. Goddard JD. 1986. Recent Developments in Structered Continua. Pitman Research Notes in Mathematics No. 143, ed. D DeKee, PN Kaloni, p. 179. New York: J. Wiley
  46. DeGiuli E, McElwaine J. 2011. Phys. Rev. E 84:041310
  47. Liu I-S. 2002. Continuum Mechanics Berlin/Heidelberg: Springer
  48. Dhar A, Chaudhuri P, Dasgupta C. 2000. Phys. Rev. B 61:6227–37
  49. Mezard M, Parisi G. 1999. Phys. Rev. Lett. 82:747–50
  50. Sastry S. 2001. Nature 409:164–67
  51. Stillinger FH. 1995. Science 267:1935–39
  52. Nowak ER, Knight JB, Ben-Naim E, Jaeger HM, Nagel SR. 1998. Phys. Rev. E 57:21971–82
  53. Schröter M, Goldman DI, Swinney HL. 2005. Phys. Rev. E 71:330301
  54. Métayer J-F, Suntrup DJ 3rd, Radin C, Swinney HL, Schröter M. 2011. Europhys. Lett. 93:664003
  55. Schröter M, Nägle S, Radin C, Harry L. 2007. Europhys. Lett. 78:444004
  56. Aste T, Matteo T. 2008. Eur. Phys. J. B 64:3–4511–17
  57. Brisco C, Song C, Wang P, Makse HA. 2008. Phys. Rev. Lett. 101:18188001
  58. Ciamarra MP, Coniglio A, Nicodemi M. 2006. Phys. Rev. Lett. 97:158001
  59. Pugnaloni LA, Maza D, Sanchez I, Gago PA, Damas J, Zuriguel I. 2010. Phys. Rev. E 82:050301
  60. Schröder-Turk GE, Mickel W, Schröter M, Delaney GW, Saadatfar M et al. 2010. Europhys. Lett. 90:334001
  61. Daniels KE, Behringer RP. 2006. J. Stat. Mech. Theory Exp. 7:P07018
  62. Puckett JG, Lechenault F, Daniels KE. 2011. Phys. Rev. E 83:4041301
  63. Dean D, Lefèvre A. 2003. Phys. Rev. Lett. 90:198301
  64. Zhao S-C, Sidle S, Swinney HL, Schröter M. 2012. Europhys. Lett. 97:334004
  65. Aste T, Di Matteo T. 2008. Phys. Rev. E 77:221309
  66. Blumenfeld R, Edwards SF. 2003. Phys. Rev. Lett. 90:11114303
  67. Blumenfeld R, Jordan JF. 2012. Phys. Rev. Lett. 109:23238001
  68. Schröter M, Zhao S-C. 2014. Soft Matter 10:4208–16
  69. Puckett JG, Daniels KE. 2013. Phys. Rev. Lett. 110:5058001
  70. Bi D, Zhang J, Behringer RP, Chakraborty B. 2013. Europhys. Lett 102:34002
  71. Lois G, Zhang J, Majmudar TS, Henkes S, Chakraborty B et al. 2009. Phys. Rev. E 80:060303
  72. Wang K, Song C, Wang P, Makse HA. 2010. Europhys. Lett. 91:668001
  73. DeGiuli E. . 2013. Continuum limits of granular systems. PhD Thesis. Univ. B. C., Vancouver
  74. Metzger PT, Donahue CM. 2005. Phys. Rev. Lett. 94:148001
  75. Metzger PT. 2004. Phys. Rev. E 70:5051303
  76. Snoeijer JH, van Hecke M, Somfai E, van Saarloos W. 2004. Phys. Rev. E 67:030302
  77. Snoeijer JH, Vlugt TJH, Ellenbroek WG, van Hecke M, van Leeuwen JMJ. 2004. Phys. Rev. E 70:061306
  78. Tighe BP, Socolar JES, Schaeffer DG, Garrett Mitchener W, Huber ML. 2005. Phys. Rev. E 72:031306
  79. van Eerd ART, Ellenbroek WG, van Hecke M, Snoeijer JH, Vlugt TJH. 2007. Phys. Rev. E 75:6060302
  80. Unger T, Kertész J, Wolf DE. 2005. Phys. Rev. Lett. 94:17178001
  81. Tighe, B P. 2010. Soft Matter 6:132908–17
  82. van Eerd ART, Tighe BP, Vlugt TJH. 2009. Mol. Simul. 35:141168–84
  83. Tighe BP, Vlugt TJH. 2011. J. Stat. Mech. Theory Exp. 4:P04002
  84. Tighe BP, Vlugt TJH. 2010. J. Stat. Mech. Theory Exp. 1:P01015
  85. Sarkar S, Bi D, Zhang J. 2013. Phys. Rev. Lett. 111:6068301
  86. Bi D, Zhang J, Chakraborty B, Behringer RP. 2011. Nature 480:7377355–58
  87. Ren J. 2013. Nonlinear dynamics and network properties in granular materials under shear. PhD Thesis, Duke Univ., Durham, NC
  88. Monthus C, Bouchaud J-P. 1996. J. Phys. Math. Gen. 29:3847–69
  89. Sollich P. 1998. Phys. Rev. E 58:738–59
  90. Langer JS. 2008. Phys. Rev. E 77:021502
  91. Kamrin K, Koval G. . 2012. Phys. Rev. Lett. 108:178301
  92. Reddy KA, Forterre Y, Pouliquen O. 2011. Phys. Rev. Lett. 106:10108301
  93. Behringer RP, Bi D, Chakraborty B, Henkes S, Hartley RR. 2008. Phys. Rev. Lett. 101:268301
  94. Bi D, Chakraborty B. 2009. Philos. Trans. R. Soc. A 367:5073–90
  95. Hartley RR, Behringer RP. 2003. Nature 421:928–31
/content/journals/10.1146/annurev-conmatphys-031214-014336
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The Statistical Physics of Athermal Materials
Annual Review of Condensed Matter Physics 6, 63 (2015); https://doi.org/10.1146/annurev-conmatphys-031214-014336
/content/journals/10.1146/annurev-conmatphys-031214-014336
/content/journals/10.1146/annurev-conmatphys-031214-014336
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