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Patterns and collective behavior in granular media: Theoretical concepts

Igor S. Aranson* and Lev S. Tsimring†

Igor S. Aranson*

  • Materials Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439, USA

Lev S. Tsimring†

  • Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA

  • *Electronic address: aronson@msd.anl.gov
  • †Electronic address: ltsimring@ucsd.edu
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Rev. Mod. Phys. 78, 641 – Published 1 June, 2006

DOI: https://doi.org/10.1103/RevModPhys.78.641

Abstract

Granular materials are ubiquitous in our daily lives. While they have been the subject of intensive engineering research for centuries, in the last two decades granular matter has attracted significant attention from physicists. Yet despite major efforts by many groups, the theoretical description of granular systems remains largely a plethora of different, often contradictory concepts and approaches. Various theoretical models have emerged for describing the onset of collective behavior and pattern formation in granular matter. This review surveys a number of situations in which nontrivial patterns emerge in granular systems, elucidates important distinctions between these phenomena and similar ones occurring in continuum fluids, and describes general principles and models of pattern formation in complex systems that have been successfully applied to granular systems.

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References (368)

  1. Aegerter, C. M., R. Günter, and R. J. Wijngaarden, 2003, Phys. Rev. E 67, 051306.
  2. Aegerter, C. M., K. A. Lorincz, M. S. Welling, and R. J. Wijngaarden, 2004, Phys. Rev. Lett. 92, 058702.
  3. Alexander, A., F. J. Muzzio, and T. Shinbrot, 2004, Granular Matter 5, 171.
  4. Ambroso, M. A., R. D. Kamien, and D. J. Durian, 2005, Phys. Rev. E 72, 041305.
  5. Andereck, D., S. S. Liu, and H. L. Swinney, 1986, J. Fluid Mech. 164, 155.
  6. Andersen, K. H., M. L. Chabanol, and M. van Hecke, 2001, Phys. Rev. E 63, 066308.
  7. Andreotti, B., P. Claudin, and S. Douady, 2002, Eur. Phys. J. B 28, 341.
  8. Aoki, K. M., T. Akiyama, Y. Maki, and T. Watanabe, 1996, Phys. Rev. E 54, 874.
  9. Aradian, A., E. Raphaël, and P.-G. de Gennes, 2002, C. R. Acad. Sci., Ser IV: Phys., Astrophys. 3, 187.
  10. Aranson, I. S., D. Blair, V. A. Kalatsky, G. W. Crabtree, W.-K. Kwok, V. M. Vinokur, and U. Welp, 2000, Phys. Rev. Lett. 84, 3306.
  11. Aranson, I. S., D. Blair, W.-K. Kwok, G. Karapetrov, U. Welp, G. W. Crabtree, V. M. Vinokur, and L. S. Tsimring, 1999, Phys. Rev. Lett. 82, 731.
  12. Aranson, I. S., and L. Kramer, 2002, Rev. Mod. Phys. 74, 99.
  13. Aranson, I. S., B. Meerson, P. V. Sasorov, and V. M. Vinokur, 2002, Phys. Rev. Lett. 88, 204301.
  14. Aranson, I. S., and J. S. Olafsen, 2002, Phys. Rev. E 66, 061302.
  15. Aranson, I. S., and M. V. Sapozhnikov, 2004, Phys. Rev. Lett. 92, 234301.
  16. Aranson, I. S., and L. S. Tsimring, 1998, Physica A 249, 103.
  17. Aranson, I. S., and L. S. Tsimring, 1999, Phys. Rev. Lett. 82, 4643.
  18. Aranson, I. S., and L. S. Tsimring, 2001, Phys. Rev. E 64, 020301(R).
  19. Aranson, I. S., and L. S. Tsimring, 2002, Phys. Rev. E 65, 061303.
  20. Aranson, I. S., and L. S. Tsimring, 2003, Phys. Rev. E 67, 021305.
  21. Aranson, I. S., and L. S. Tsimring, 2005, Phys. Rev. E 71, 050901(R).
  22. Aranson, I. S., L. S. Tsimring, and V. M. Vinokur, 1999, Phys. Rev. E 59, R1327.
  23. Aranson, I. S., L. S. Tsimiring, and V. M. Vinokur, 1999b, Phys. Rev. E 60, 1975.
  24. Aranson, I. S., L. S. Tsimring, and V. M. Vinokur, 2002, Phys. Rev. B 65, 125402.
  25. Argentina, M., M. G. Clerc, and R. Soto, 2002, Phys. Rev. Lett. 89, 044301.
  26. Arndt, T., T. Siegmann-Hegerfeld, S. J. Fiedor, J. M. Ottino, and R. M. Lueptow, 2005, Phys. Rev. E 71, 011306.
  27. Asakura, S., and F. Oosawa, 1958, J. Polym. Sci. 33, 183.
  28. Aumaître, S., C. A. Kruelle, and I. Rehberg, 2001, Phys. Rev. E 64, 041305.
  29. Ayrton, H., 1910, Proc. R. Soc. London, Ser. A 84, 285.
  30. Babić, M., 1993, J. Fluid Mech. 254, 127.
  31. Bagnold, R. A., 1954, The Physics of Blown Sand and Desert Dunes (Methuen, London), p. 265.
  32. Bagnold, R. A., 1956, Proc. R. Soc. London, Ser. A 187, 1.
  33. Bak, P., C. Tang, and K. Wiesenfeld, 1987, Phys. Rev. Lett. 59, 381.
  34. Barashenkov, I. V., N. V. Alexeeva, and E. V. Zemlyanaya, 2002, Phys. Rev. Lett. 89, 104101.
  35. Ben-Naim, E., and P. L. Krapivsky, 2003, Phys. Rev. E 68, 031104.
  36. Betat, A., V. Frette, and I. Rehberg, 1999, Phys. Rev. Lett. 83, 88.
  37. Bizon, C., M. D. Shattuck, J. R. de Bruyn, J. B. Swift, W. D. McCormick, and H. L. Swinney, 1998, J. Stat. Phys. 93, 449.
  38. Bizon, C., M. D. Shattuck, J. T. Newman, P. B. Umbanhowar, J. B. Swift, W. D. McCormick, and H. L. Swinney, 1997, Phys. Rev. Lett. 79, 4713.
  39. Bizon, C., M. D. Shattuck, J. B. Swift, W. D. McCormick, and H. L. Swinney, 1998, Phys. Rev. Lett. 80, 57.
  40. Blair, D., I. S. Aranson, G. W. Crabtree, V. Vinokur, L. S. Tsimring, and C. Josserand, 2000, Phys. Rev. E 61, 5600.
  41. Blair, D. L., and A. Kudrolli, 2003, Phys. Rev. E 67, 021302.
  42. Blair, D. L., T. Neicu, and A. Kudrolli, 2003, Phys. Rev. E 67, 031303.
  43. Börzsönyi, T., T. C. Halsey, and R. E. Ecke, 2005, Phys. Rev. Lett. 94, 208001.
  44. Bouchaud, J.-P., M. E. Cates, J. Ravi Prakash, and S. F. Edwards, 1994, J. Phys. I 4, 1393.
  45. Bouchaud, J.-P., M. E. Cates, J. R. Prakash, and S. F. Edwards, 1995, Phys. Rev. Lett. 74, 1982.
  46. Bougie, J., J. Kreft, J. B. Swift, and H. L. Swinney, 2005, Phys. Rev. E 71, 021301.
  47. Bougie, J., Sung Joon Moon, J. B. Swift, and H. L. Swinney, 2002, Phys. Rev. E 66, 051301.
  48. Boutreux, T., and P. G. de Gennes, 1996, J. Phys. I 6, 1295.
  49. Boutreux, T., E. Raphael, and P.-G. de Gennes, 1998, Phys. Rev. E 58, 4692.
  50. Bray, A. J., 1994, Adv. Phys. 43, 357.
  51. Brendel, L., T. Unger, and D. E. Wolf, 2004, in The Physics of Granular Media, edited by H. Hinrichsen and D. E. Wolf (Wiley-VCH, Weinheim), p. 325.
  52. Brey, J. J., J. W. Dufty, C. S. Kim, and A. Santos, 1998, Phys. Rev. E 58, 4638.
  53. Brilliantov, N. V., and Th. Pöschel, 2004, Kinetic Theory of Granular Gases (Oxford University Press, Oxford), p. 329.
  54. Brito, R., and M. H. Ernst, 1998, Int. J. Mod. Phys. C 8, 1339.
  55. Brown, R. L., 1939, J. Inst. Fuel 13, 15.
  56. Buehler, R. J., J. R. H. Wentorf, J. O. Hirschfelder, and C. F. Curtiss, 1951, J. Chem. Phys. 19, 61.
  57. Burtally, N., P. J. King, and M. R. Swift, 2002, Science 295, 1877.
  58. Cafiero, R., S. Luding, and H. J. Herrmann, 2000, Phys. Rev. Lett. 84, 6014.
  59. Caps, H., and N. Vandewalle, 2001, Phys. Rev. E 64, 041302.
  60. Carlson, J. M., and A. A. Batista, 1996, Phys. Rev. E 53, 4153.
  61. Carnahan, N. F., and K. E. Starling, 1969, J. Chem. Phys. 51, 635.
  62. Cattuto, C., and U. M. Marconi, 2004, Phys. Rev. Lett. 92, 174502.
  63. Cerda, E., F. Melo, and S. Rica, 1997, Phys. Rev. Lett. 79, 4570.
  64. Charles, C. R. J., Z. S. Khan, and S. W. Morris, 2005, Granular Matter 11, 46.
  65. Chicarro, R., R. Peralta-Fabi, and R. M. Velasco, 1997, in Powders & Grains 97, edited by R. P. Behringer and J. T. Jenkins (Balkema, Rotterdam), p. 479.
  66. Chladni, E. F. F., 1787, Entdeckungen ber die Theorie des Klanges (Bey Weidmanns erben und Reich, Leipzig), p. 77.
  67. Choo, K., M. W. Baker, T. C. A. Molteno, and S. W. Morris, 1998, Phys. Rev. E 58, 6115.
  68. Choo, K., T. C. A. Molteno, and S. W. Morris, 1997, Phys. Rev. Lett. 79, 2975.
  69. Ciamarra, M. P., A. Coniglio, and M. Nicodemi, 2005, Phys. Rev. Lett. 94, 188001.
  70. Clément, E., L. Vanel, J. Rajchenbach, and J. Duran, 1996, Phys. Rev. E 53, 2972.
  71. Conti, M., B. Meerson, A. Peleg, and P. V. Sasorov, 2002, Phys. Rev. E 65, 046117.
  72. Conway, S. L., D. J. Goldfarb, T. Shinbrot, and B. J. Glasser, 2003, Phys. Rev. Lett. 90, 074301.
  73. Conway, S. L., T. Shinbrot, and B. J. Glasser, 2004, Nature (London) 431, 433.
  74. Cooke, M. H., D. J. Stephens, and J. Bridgewater, 1976, Powder Technol. 15, 1.
  75. Corvin, E. I., H. M. Jaeger, and S. R. Nagel, 2005, Nature (London) 435, 1075.
  76. Costello, R. M., K. L. Cruz, C. Egnatuk, D. T. Jacobs, M. C. Krivos, T. Sir Louis, R. J. Urban, and H. Wagner, 2003, Phys. Rev. E 67, 041304.
  77. Coullet, P., J. Lega, B. Houchmanzadeh, and J. Lajzerowicz, 1990, Phys. Rev. Lett. 65, 1352.
  78. Coussot, P., Q. D. Nguyen, H. T. Huynh, and D. Bonn, 2002, Phys. Rev. Lett. 88, 175501.
  79. Coussot, P., J. S. Raynaud, F. Bertrand, P. Moucheront, J. P. Guilbaud, H. T. Huynh, S. Jarny, and D. Lesueur, 2002, Phys. Rev. Lett. 88, 218301.
  80. Crawford, C., and H. Riecke, 1999, Physica D 129, 83.
  81. Cross, M. C., and P. C. Hohenberg, 1993, Rev. Mod. Phys. 65, 851.
  82. Cundall, P. A., and O. D. L. Strack, 1979, Geotechnique 29, 47.
  83. DaCruz, F., F. Chevoir, D. Bonn, and P. Coussot, 2002, Phys. Rev. E 66, 051305.
  84. Daerr, A., 2001a, Phys. Fluids 13, 2115.
  85. Daerr, A., 2001b, Ph.D. thesis, Univ. Paris VII, Paris, p. 181.
  86. Daerr, A., and S. Douady, 1999, Nature (London) 399, 241.
  87. Daerr, A., P. Lee, J. Lanuza, and E. Clément, 2003, Phys. Rev. E 67, 065201(R).
  88. Dammer, S. M., and D. E. Wolf, 2004, Phys. Rev. Lett. 93, 150602.
  89. Das, S. K., and S. Puri, 2003, Europhys. Lett. 61, 749.
  90. Davies, R. H., 1990, J. Hydrol. 29, 18.
  91. de Bruyn, J. R., C. Bizon, M. D. Shattuck, D. Goldman, J. B. Swift, and H. L. Swinney, 1998, Phys. Rev. Lett. 81, 1421.
  92. de Gennes, P.-G., 1999, Rev. Mod. Phys. 71, S374.
  93. de Gennes, P.-G., and P. Pincus, 1970, Phys. Kondens. Mater. 11, 189.
  94. Dennin, M., and C. M. Knobler, 1997, Phys. Rev. Lett. 78, 2485.
  95. Dinkelacker, F., A. Hübler, and E. Lüscher, 1987, Biol. Cybern. 56, 51.
  96. Dolgunin, V. N., A. N. Kudy, and A. A. Ukolov, 1998, Powder Technol. 96, 211.
  97. Douady, S., B. Andreotti, and A. Daerr, 1999, Eur. Phys. J. B 11, 131.
  98. Douady, S., B., Andreotti, A. Daerr, and P. Clade, 2002, C. R. Acad. Sci., Ser IV: Phys., Astrophys. 3, 177.
  99. Douady, S., S. Fauve, and C. Laroche, 1989, Europhys. Lett. 8, 621.
  100. Dufty, J. W., J. J. Brey, and J. Lutsko, 2002, Phys. Rev. E 65, 051303.
  101. Duong, Nhat-Hang P., A. E. Hosoi, and T. Shinbrot, 2004, Phys. Rev. Lett. 92, 224502.
  102. Duran, J., 1999, Sands, Powders and Grains: Introduction to the Physics of Granular Materials (Springer-Verlag, New York), p. 214.
  103. Duran, J., 2000, Phys. Rev. Lett. 84, 5126.
  104. Duran, J., 2001, Phys. Rev. Lett. 87, 254301.
  105. Duru, P., M. Nicolas, E. J. Hinch, and C. Guazelli, 2002, J. Fluid Mech. 452, 371.
  106. Edwards, S. F., and D. V. Grinev, 1998, Phys. Rev. E 58, 4758.
  107. Efrati, E., E. Livne, and B. Meerson, 2005, Phys. Rev. Lett. 94, 088001.
  108. Eggers, J., and H. Riecke, 1999, Phys. Rev. E 59, 4476.
  109. Ehrhardt, G. C. M. A., A. Stephenson, and P. M. Reis, 2005, Phys. Rev. E 71, 041301.
  110. Elperin, T., and A. Vikhansky, 1998, Europhys. Lett. 42, 619.
  111. Eshuis, P., K. van deer Weele, D. van deer Meer, and D. Lohse, 2005, Phys. Rev. Lett. 95, 258001.
  112. Evesque, P., 1990, J. Phys. II 311, 393.
  113. Evesque, P., and J. Rajchenbach, 1989, Phys. Rev. Lett. 62, 44.
  114. Falcon, E., K. Kumar, K. M. S. Bajaj, and J. K. Bhattacharjee, 1999, Phys. Rev. E 59, 5716.
  115. Falcon, É., R. Wunenburger, P. Évesque, S. Fauve, C. Chabot, Y. Garrabos, and D. Beysens, 1999, Phys. Rev. Lett. 83, 440.
  116. Falk, M. L., and J. S. Langer, 1998, Phys. Rev. E 57, 7192.
  117. Faraday, M., 1831, Philos. Trans. R. Soc. London 52, 299.
  118. Fauve, S., S. Douady, and C. Laroche, 1989, J. Phys.: Condens. Matter 50, 187.
  119. Ferguson, A., B. Fisher, and B. Chakraborty, 2004, Europhys. Lett. 66, 277.
  120. Fiedor, S. J., and J. M. Ottino, 2003, Phys. Rev. Lett. 91, 244301.
  121. Forterre, Y., and O. Pouliquen, 2001, Phys. Rev. Lett. 86, 5886.
  122. Forterre, Y., and O. Pouliquen, 2002, J. Fluid Mech. 467, 361.
  123. Forterre, Y., and O. Pouliquen, 2003, J. Fluid Mech. 486, 21.
  124. Fraerman, A. A., A. S. Melnikov, I. M. Nefedov, I. A. Shereshevskii, and A. V. Shpiro, 1997, Phys. Rev. B 55, 6316.
  125. Frette, V., and J. Stavans, 1997, Phys. Rev. E 56, 6981.
  126. Fried, E., A. Q. Shen, and S. T. Thoroddsen, 1998, Phys. Fluids 10, 10.
  127. Fuchs, M., and M. E. Cates, 2002, Phys. Rev. Lett. 89, 248304.
  128. Gallas, J. A. C., H. J. Herrmann, and S. Sokołowski, 1992a, Phys. Rev. Lett. 69, 1371.
  129. Gallas, J. A. C., H. J. Herrmann, and S. Sokołowski, 1992b, J. Phys. II 2, 1389.
  130. Gallas, J. A. C., H. J. Herrmann, and S. Sokołowski, 1992c, Physica A 189, 437.
  131. Gallas, J. A. C., and S. Sokołowski, 1992, Int. J. Mod. Phys. B 7, 2037.
  132. Gao, D., S. Subramaniam, R. O. Fox, and D. K. Hoffman, 2005, Phys. Rev. E 71, 021302.
  133. Garcimartín, A., D. Maza, J. L. Ilquimiche, and I. Zuriguel, 2002, Phys. Rev. E 65, 031303.
  134. Garzó, V., and J. W. Dufty, 1999, Phys. Rev. E 59, 5895.
  135. G. D. R. MiDi (collective work), 2004, Eur. Phys. J. E 14, 341.
  136. Gidaspow, D., 1994, Multiphase Flows and Fluidization (Academic, Boston), p. 467.
  137. Goldenberg, C., and I. Goldhirsch, 2002, Phys. Rev. Lett. 89, 084302.
  138. Goldenberg, C., and I. Goldhirsch, 2005, Nature (London) 435, 188.
  139. Goldfarbs, D., B. Glasser, and T. Shinbrot, 2002, Nature (London) 415, 302.
  140. Goldhirsch, I., 2003, Annu. Rev. Fluid Mech. 35, 267.
  141. Goldhirsch, I., and G. Zanetti, 1993, Phys. Rev. Lett. 70, 1619.
  142. Goldman, D. I., J. B. Swift, and H. L. Swinney, 2004, Phys. Rev. Lett. 92, 174302.
  143. Goldsmith, W., 1964, Impact: The Theory and Physical Behaviour of Colliding Solids (Edward Arnold, London), p. 379.
  144. Goldstein, A., and M. Shapiro, 1995, J. Fluid Mech. 282, 75.
  145. Gollub, J. P., and J. S. Langer, 1999, Rev. Mod. Phys. 71, S396.
  146. Gray, J. M. N. T., and K. Hutter, 1997, Continuum Mech. Thermodyn. 9(1), 341.
  147. Gray, J. N. M. T., and A. R. Thornton, 2005, Proc. R. Soc. London, Ser. A 461, 1447.
  148. Grégoire, G., and H. Chaté, 2004, Phys. Rev. Lett. 92, 025702.
  149. Grossman, E. L., T. Zhou, and E. Ben-Naim, 1997, Phys. Rev. E 55, 4200.
  150. Gurbatov, S. N., A. I. Saichev, and S. F. Shandarin, 1985, Sov. Phys. Dokl. 30, 921.
  151. Haff, P. K., 1983, J. Fluid Mech. 134, 401.
  152. He, H., B. Meerson, and G. Doolen, 2002, Phys. Rev. E 65, 030301(R).
  153. Helbing, D., 2001, Rev. Mod. Phys. 73, 1067.
  154. Helbing, D., I. J. Farkas, and T. Vicsek, 2000, Phys. Rev. Lett. 84, 1240.
  155. Hersen, P., K. H. Andersen, H. Elbelrhiti, B. Andreotti, P. Claudin, and S. Douady, 2004, Phys. Rev. E 69, 011304.
  156. Hill, J. M., 1997, in IUTAM Symposium on Mechanics of Granular and Porous Materials, edited by N. A. Fleck and A. C. E. Cocks (Kluwer, Dordrecht), pp. 251–262.
  157. Hill, K. M., and J. Kakalios, 1994, Phys. Rev. E 49, R3610.
  158. Hill, K. M., and J. Kakalios, 1995, Phys. Rev. E 52, 4393.
  159. Hill, S. A., and G. F. Mazenko, 2003, Phys. Rev. E 67, 061302.
  160. Israelachvili, J. N., P. M. McGuiggan, and A. M. Homola, 1988, Science 240, 189.
  161. Ivanova, A., V. Kozlov, and P. Evasque, 1996, Europhys. Lett. 35, 159.
  162. Iverson, R. M., 1997, Rev. Geophys. 35, 245.
  163. Jackson, R., 2000, The Dynamics of Fluidized Particles (Cambridge University Press, Cambridge, England), p. 368.
  164. Jaeger, H. M., C. H. Liu, and S. R. Nagel, 1989, Phys. Rev. Lett. 62, 40.
  165. Jaeger, H. M., S. R. Nagel, and R. P. Behringer, 1996, Rev. Mod. Phys. 68, 1259.
  166. Jenkins, J. T., and M. W. Richman, 1985, Phys. Fluids 28, 3485.
  167. Jenkins, J. T., and D. K. Yoon, 2002, Phys. Rev. Lett. 88, 194301.
  168. Jenkins, J. T., and C. Zhang, 2002, Phys. Fluids 14, 1228.
  169. Jenny, H., 1964, Wave Phenomena, Vibrational Effects, Harmonic Oscillations, with their Structure, Kinetics, and Dynamics, Cymatics Vol. 2 (Basilius, Basel), p. 368.
  170. Jia, L. C., P.-Y. Lai, and C. K. Chan, 1999, Phys. Rev. Lett. 83, 3832.
  171. Kadanoff, L. P., 1999, Rev. Mod. Phys. 71, 435.
  172. Kevrekidis, I., C. W. Gear, and G. Hummer, 2004, AIChE J. 50, 1346.
  173. Khain, E., and B. Meerson, 2002a, Phys. Rev. E 66, 021306.
  174. Khain, E., and B. Meerson, 2002b, Phys. Rev. E 67, 021306.
  175. Khain, E., and B. Meerson, 2004, Europhys. Lett. 65, 193.
  176. Khain, E., B. Meerson, and P. V. Sasorov, 2004, Phys. Rev. E 70, 051310.
  177. Khakhar, D. V., J. J. McCarthy, and J. M. Ottino, 1997, Phys. Fluids 9, 3600.
  178. Khakhar, D. V., J. J. McCarthy, and J. M. Ottino, 1999, Chaos 9, 594.
  179. Khakhar, D. V., A. V. Opre, P. Andersén, and J. M. Ottino, 2001, J. Fluid Mech. 441, 255.
  180. Khan, Z. S., and S. W. Morris, 2005, Phys. Rev. Lett. 94, 048002.
  181. Khan, Z. S., W. A. Tokaruk, and S. W. Morris, 2004, Europhys. Lett. 66, 212.
  182. Kiyashko, S. V., L. N. Korzinov, M. I. Rabinovich, and L. S. Tsimring, 1996, Phys. Rev. E 54, 5037.
  183. Knight, J. B., H. M. Jaeger, and S. R. Nagel, 1993, Phys. Rev. Lett. 70, 3728.
  184. Koeppe, J. P., M. Enz, and J. Kakalios, 1998, Phys. Rev. E 58, R4104.
  185. Kohlstedt, K., A. Snezhko, M. V. Sapozhnikov, I. S. Aranson, J. S. Olafsen, and E. Ben-Naim, 2005, Phys. Rev. Lett. 95, 068001.
  186. Kroy, K., G. Sauermann, and H. J. Herrmann, 2002a, Phys. Rev. Lett. 88, 054301.
  187. Kroy, K., G. Sauermann, and H. J. Herrmann, 2002b, Phys. Rev. E 66, 031302.
  188. Kudrolli, A., 2004, Rep. Prog. Phys. 67, 209.
  189. Kudrolli, A., M. Wolpert, and J. P. Gollub, 1997, Phys. Rev. Lett. 78, 1383.
  190. Kunii, D., and O. Levenspiel, 1991, Fluidization Engineering (Butterworth, Boston), p. 491.
  191. Lajeunesse, E., A. Mangeney-Castelnau, and J.-P. Vilotte, 2004, Phys. Fluids 14, 7.
  192. Landau, L. D., and E. M. Lifshitz, 1959, Fluid Mechanics (Pergamon, London), p. 536.
  193. Landry, J. W., G. S. Grest, L. E. Silbert, and S. J. Plimpton, 2003, Phys. Rev. E 67, 041303.
  194. Langlois, V., and A. Valance, 2005, Phys. Rev. Lett. 94, 248001.
  195. Laroche, C., S. Douady, and S. Fauve, 1989, J. Phys. (France) 50, 699.
  196. Lauridsen, J., G. Chanan, and M. Dennin, 2004, Phys. Rev. Lett. 93, 018303.
  197. Lauridsen, J., M. Twardos, and M. Dennin, 2002, Phys. Rev. Lett. 89, 098303.
  198. Lemaître, A., 2002, Phys. Rev. Lett. 89, 195503.
  199. Lemaître, A., and J. Carlson, 2004, Phys. Rev. E 69, 061611.
  200. Lemieux, P.-A., and D. J. Durian, 2000, Phys. Rev. Lett. 85, 4273.
  201. Levin, Y., 1999, Phys. Rev. Lett. 83, 1159.
  202. Levine, D., 1999, Chaos 9, 573.
  203. Levitan, B., 1998, Phys. Rev. E 58, 2061.
  204. Li, H., and J. J. McCarthy, 2005, Phys. Rev. E 71, 021305.
  205. Li, J., I. S. Aranson, W.-K. Kwok, and L. S. Tsimring, 2003, Phys. Rev. Lett. 90, 134301.
  206. Liffman, K., G. Metcalfe, and P. Cleary, 1997 Phys. Rev. Lett. 79, 4574.
  207. Lifshitz, I. M., and V. V. Slyozov, 1958, Zh. Eksp. Teor. Fiz. 35, 479 [Sov. Phys. JETP 8, 331 (1959)].
  208. Lifshitz, I. M., and V. V. Slyozov, 1961, J. Phys. Chem. Solids 19, 35.
  209. Linz, S. J., and P. Hänggi, 1995, Phys. Rev. E 51, 2538.
  210. Lioubashevski, O., Y. Hamiel, A. Agnon, Z. Reches, and J. Fineberg, 1999, Phys. Rev. Lett. 83, 3190.
  211. Liu, A., and S. R. Nagel, 1998, Nature (London) 396, 21.
  212. Livne, E., B. Meerson, and P. V. Sasorov, 2002a, Phys. Rev. E 65, 021302.
  213. Livne, E., B. Meerson, and P. V. Sasorov, 2002b, Phys. Rev. E 66, 050301(R).
  214. Lohse, D., R. Bergmann, R. M. Rauhe, and D. van der Meer, 2004, Nature (London) 432, 689.
  215. Lois, G., A. Lemaître, and J. M. Carlson, 2005, Phys. Rev. E 72, 051303.
  216. Losert, W., L. Bocquet, T. C. Lubensky, and J. P. Gollub, 2000, Phys. Rev. Lett. 85, 1428.
  217. Losert, W., D. G. W. Cooper, and J. P. Gollub, 1999, Phys. Rev. E 59, 5855.
  218. Luding, S., 2001, Phys. Rev. E 63, 042201.
  219. Luding, S., 2004, in The Physics of Granular Media, edited by H. Hinrichsen and D. E. Wolf (Wiley-VCH, Weinheim), p. 299.
  220. Luding, S., E. Clément, A. Blumen, J. Rajchenbach, and J. Duran, 1994, Phys. Rev. E 50, R1762.
  221. Luding, S., E. Clément, J. Rajchenbach, and J. Duran, 1996, Europhys. Lett. 36, 247.
  222. Majmudar, T. S., and R. P. Behringer, 2005, Nature (London) 435, 1079.
  223. Makse, H. A., 1999, Phys. Rev. Lett. 83, 3186.
  224. Makse, H. A., P. Cizeau, and H. E. Stanley, 1997, Phys. Rev. Lett. 78, 3298.
  225. Makse, H. A., S. Havlin, P. R. King, and H. E. Stanley, 1997, Nature (London) 386, 379.
  226. Makse, H. A., and J. Kurchan, 2002, Nature (London) 415, 614.
  227. Malloggi, F., J. Lanuza, B. Andreotti, and E. Clement, 2005, in Powders and Grains 2005, edited by R. Garcia-Rojo, H. J. Herrmann, and S. McNamara (Rotterdam, Balkema), p. 997.
  228. McNamara, S., R. García-Rojo, and H. Herrmann, 2005, Phys. Rev. E 72, 021304.
  229. McNamara, S., and W. R. Young, 1996, Phys. Rev. E 53, 5089.
  230. Meerson, B., 1996, Rev. Mod. Phys. 68, 215.
  231. Meerson, B., Th. Pöschel, and Y. Bromberg, 2003, Phys. Rev. Lett. 91, 024301.
  232. Meerson, B., Th. Pöschel, P. V. Sasorov, and T. Schwager, 2004, Phys. Rev. E 69, 021302.
  233. Meerson, B., and A. Puglisi, 2005, Europhys. Lett. 70, 478.
  234. Mehta, A., 1994, in Granular Matter. An Interdisciplinary Approach, edited by A. Mehta (Springer-Verlag, New York), p. 306.
  235. Mehta, A., and J. M. Luck, 1990, Phys. Rev. Lett. 65, 393.
  236. Melo, F., P. Umbanhowar, and H. L. Swinney, 1994, Phys. Rev. Lett. 72, 172.
  237. Melo, F., P. B. Umbanhowar, and H. L. Swinney, 1995, Phys. Rev. Lett. 75, 3838.
  238. Metcalfe, G., and M. Shattuck, 1998, Physica A 233, 709.
  239. Metcalfe, G., T. Shinbrot, J. J. McCarthy, and J. M. Ottino, 1995, Nature (London) 374, 39.
  240. Möbius, M., B. E. Lauderdale, S. R. Nagel, and H. M. Jaeger, 2001, Nature (London) 414, 270.
  241. Moon, S. J., D. I. Goldman, J. B. Swift, and H. L. Swinney, 2003, Phys. Rev. Lett. 91, 134301.
  242. Moon, S. J., M. D. Shattuck, C. Bizon, D. I. Goldman, J. B. Swift, and H. L. Swinney, 2002, Phys. Rev. E 65, 011301.
  243. Moreau, J. J., 1994, Eur. J. Mech. A/Solids 13, 93.
  244. Mujica, N., and F. Melo, 1998, Phys. Rev. Lett. 80, 5121.
  245. Mullin, T., 2000, Phys. Rev. Lett. 84, 4741.
  246. Mullin, T., 2002, Science 2002, 1851.
  247. Nasuno, S., A. Kudrolli, and J. P. Gollub, 1997, Phys. Rev. Lett. 79, 949.
  248. Nedderman, R. M., 1992, Statics and Kinematics of Granular Materials (Cambridge University Press, Cambridge, England), p. 368.
  249. Newey, M., J. Ozik, S. M. van der Meer, E. Ott, and W. Losert, 2004, Europhys. Lett. 66, 205.
  250. Nie, X., E. Ben-Naim, and S. Y. Chen, 2000, Europhys. Lett. 51, 679.
  251. Nie, X., E. Ben-Naim, and S. Y. Chen, 2002, Phys. Rev. Lett. 89, 204301.
  252. Nishimori, H., and N. Ouchi, 1993, Phys. Rev. Lett. 71, 197.
  253. Oh, J., and G. Ahlers, 2003, Phys. Rev. Lett. 91, 094501.
  254. O’Hern, C. S., A. J. Liu, and S. R. Nagel, 2004, Phys. Rev. Lett. 93, 165702.
  255. Olafsen, J. S., and J. S. Urbach, 1998, Phys. Rev. Lett. 81, 4369.
  256. Ono, I. K., C. S. O’Hern, D. J. Durian, S. A. Langer, A. J. Liu, and S. R. Nagel, 2002, Phys. Rev. Lett. 89, 095703.
  257. Onsager, L., 1949, Ann. N.Y. Acad. Sci. 51, 627.
  258. Orpe, A., and D. Khakhar, 2006, unpublished.
  259. Orpe, A. V., and D. V. Khakhar, 2001, Phys. Rev. E 64, 031302.
  260. Ottino, J. M., and D. V. Khakhar, 2000, Annu. Rev. Fluid Mech. 32, 55.
  261. Ottino, J. M., and D. V. Khakhar, 2002, Chaos 12, 400.
  262. Oyama, Y., 1939, Chaos 5, 600.
  263. Paczuski, M., and S. Boettcher, 1996, Phys. Rev. Lett. 77, 111.
  264. Pak, H. K., and R. P. Behringer, 1993, Phys. Rev. Lett. 71, 1832.
  265. Pak, H. K., E. Van Doorn, and R. P. Behringer, 1995, Phys. Rev. Lett. 74, 4643.
  266. Paolotti, D., A. Barrat, Umberto Marini Bettolo Marconi, and A. Puglisi, 2004, Phys. Rev. E 69, 061304.
  267. Park, H.-K., and H.-T. Moon, 2002, Phys. Rev. E 65, 051310.
  268. Pooley, C. M., and J. M. Yeomans, 2004, Phys. Rev. Lett. 93, 118001.
  269. Pöschel, Th., and Th. Schwager, 2005, Computational Granular Dynamics (Springer, Berlin), p. 322.
  270. Pouliquen, O., 1999, J. Fluid Mech. 11, 542.
  271. Pouliquen, O., C. Cassar, Y. Forterre, P. Jop, and M. Nicolas, 2005, in Powders & Grains 2005, edited by R. García-Rojo, H. J. Herrmann, and S. McNamara (Balkema, Rotterdam), pp. 859–865.
  272. Pouliquen, O., J. Delour, and S. B. Savage, 1997, Nature (London) 386, 816.
  273. Prevost, A., P. Melby, D. A. Egolf, and J. S. Urbach, 2004, Phys. Rev. E 70, 050301(R).
  274. Prigozhin, L., 1999, Phys. Rev. E 60, 729.
  275. Pye, K., and H. Tsoar, 1991, Aeolian Sand and Sand Dunes (Unwin Hyman, London), p. 396.
  276. Radjai, F., D. E. Wolf, M. Jean, and J. J. Moreau, 1998, Phys. Rev. Lett. 80, 61.
  277. Rajchenbach, J., 1990, Phys. Rev. Lett. 65, 2221.
  278. Rajchenbach, J., 2000, Adv. Phys. 49, 229.
  279. Rajchenbach, J., 2002a, Phys. Rev. Lett. 88, 014301.
  280. Rajchenbach, J., 2002b, Phys. Rev. Lett. 89, 074301.
  281. Rajchenbach, J., 2003, Phys. Rev. Lett. 90, 144302.
  282. Ramirez, R., T. Pöschel, N. V. Brilliantov, and T. Schwager, 1999, Phys. Rev. E 60, 4465.
  283. Rapaport, D. C., 2002, Phys. Rev. E 65, 061306.
  284. Rapaport, D. C., 2004, The Art of Molecular Dynamics Simulations, 2nd ed. (Cambridge University Press, Cambridge, England), p. 549.
  285. Reis, P. M., and T. Mullin, 2002, Phys. Rev. Lett. 89, 244301.
  286. Rericha, E. C., C. Bizon, M. D. Shattuck, and H. L. Swinney, 2002, Phys. Rev. Lett. 88, 014302.
  287. Richardson, J. F., and W. N. Zaki, 1954, Trans. Inst. Chem. Eng. 32, 35.
  288. Risso, D., R. Soto, S. Godoy, and P. Cordero, 2005, Phys. Rev. E 72, 011305.
  289. Ristow, G. H., 2000, Pattern Formation in Granular Materials (Springer, New York), p. 161.
  290. Ristow, G. H., G. Strassburger, and I. Rehberg, 1997, Phys. Rev. Lett. 79, 833.
  291. Rosato, A., K. J. Strandburg, F. Prinz, and R. H. Swendsen, 1987, Phys. Rev. Lett. 58, 1038.
  292. Samadani, A., and A. Kudrolli, 2000, Phys. Rev. Lett. 85, 5102.
  293. Samadani, A., and A. Kudrolli, 2001, Phys. Rev. E 64, 051301.
  294. Samadani, A., A. Pradhan, and A. Kudrolli, 1999, Phys. Rev. E 60, 7203.
  295. Sapozhnikov, M. V., I. S. Aranson, W. K. Kwok, and Y. V. Tolmachev, 2004, Phys. Rev. Lett. 93, 084502.
  296. Sapozhnikov, M. V., I. S. Aranson, and J. S. Olafsen, 2003, Phys. Rev. E 67, 010302(R).
  297. Sapozhnikov, M. V., A. Peleg, B. Meerson, I. S. Aranson, and K. L. Kohlstedt, 2005, Phys. Rev. E 71, 011307.
  298. Sapozhnikov, M. V., Y. V. Tolmachev, I. S. Aranson, and W. K. Kwok, 2003, Phys. Rev. Lett. 90, 114301.
  299. Savage, S., 1979, J. Fluid Mech. 92, 53.
  300. Savage, S., and K. Hutter, 1989, J. Fluid Mech. 199, 177.
  301. Savage, S. B., 1988, J. Fluid Mech. 194, 457.
  302. Savage, S. B., 1993, in Disorder and Granular Media, edited by D. Bideau (North-Holland, Amsterdam), p. 264.
  303. Schäffer, J., S. Dippel, and D. E. Wolf, 1996, J. Phys. I 6, 5.
  304. Scherer, M. A., F. Melo, and M. Marder, 1999, Phys. Fluids 11, 58.
  305. Schofield, J., and I. Oppenheim, 1994, Physica A 204, 555.
  306. Schröter, M., D. I. Goldman, and H. L. Swinney, 2005, Phys. Rev. E 71, 030301(R).
  307. Schwämmle, V., and H. J. Herrmann, 2003, Nature (London) 426, 619.
  308. Sela, N., and I. Goldhirsch, 1998, J. Fluid Mech. 361, 44.
  309. Shandarin, S. F., and Ya. B. Zeldovich, 1989, Rev. Mod. Phys. 61, 185.
  310. Sheffler, T., and D. E. Wolf, 2002, Granular Matter 4, 103.
  311. Shen, A. Q., 2002, Phys. Fluids 14, 462.
  312. Shinbrot, T., 1997, Nature (London) 389, 574.
  313. Shinbrot, T., 2004, Nature (London) 429, 352.
  314. Shoichi, S., 1998, Mod. Phys. Lett. B 12, 115.
  315. Silbert, L. E., 2005, Phys. Rev. Lett. 94, 098002.
  316. Silbert, L. E., D. Ertas, G. S. Grest, T. C. Halsey, and D. Levine, 2002a, Phys. Rev. E 65, 031304.
  317. Silbert, L. E., D. Ertas, G. S. Grest, T. C. Halsey, and D. Levine, 2002b, Phys. Rev. E 65, 051307.
  318. Silbert, L. E., G. S. Grest, and J. W. Landry, 2002, Phys. Rev. E 66, 061303.
  319. Silbert, L. E., J. W. Landry, and G. S. Grest, 2003, Phys. Fluids 15, 1.
  320. Snezhko, A., I. S. Aranson, and W. K. Kwok, 2005, Phys. Rev. Lett. 94, 108002.
  321. Song, Y., E. A. Mason, and R. M. Stratt, 1989, J. Phys. Chem. 93, 6916.
  322. Stambaugh, J., D. P. Lanthrop, E. Ott, and W. Losert, 2004, Phys. Rev. E 68, 026207.
  323. Stambaugh, J., Z. Smith, E. Ott, and W. Losert, 2004, Phys. Rev. E 70, 031304.
  324. Staron, L., J.-P. Vilotte, and F. Radjai, 2002, Phys. Rev. Lett. 89, 204302.
  325. Stegner, A., and J. E. Wesfreid, 1999, Phys. Rev. E 60, R3487.
  326. Sunthar, P., and V. Kumaran, 2001, Phys. Rev. E 64, 041303.
  327. Swift, J. B., and P. C. Hohenberg, 1977, Phys. Rev. A 15, 319.
  328. Taberlet, N., W. Losert, and P. Richard, 2004, Europhys. Lett. 68, 522.
  329. Taguchi, Y.-H., 1992, J. Phys. II 69, 1367.
  330. Talbot, J., and P. Viot, 2002, Phys. Rev. Lett. 89, 064301.
  331. Tan, M.-L., and I. Goldhirsch, 1998, Phys. Rev. Lett. 81, 3022.
  332. Tegzes, P., T. Vicsek, and P. Schiffer, 2002, Phys. Rev. Lett. 89, 094301.
  333. Tegzes, P., T. Vicsek, and P. Schiffer, 2003, Phys. Rev. E 67, 051303.
  334. Tennakoon, S. G. K., L. Kondic, and R. P. Behringer, 1998, Europhys. Lett. 99, 1.
  335. Thomas, C. C., and J. P. Gollub, 2004, Phys. Rev. E 70, 061305.
  336. Toner, J., and Y. Tu, 1995, Phys. Rev. Lett. 75, 4326.
  337. Troian, S. M., E. Herbolzheimer, S. A. Safran, and J. F. Joanny, 1989, Europhys. Lett. 10, 25.
  338. Tsai, J.-C., F. Ye, J. Rodriguez, J. P. Gollub, and T. C. Lubensky, 2005, Phys. Rev. Lett. 94, 214301.
  339. Tsimring, L. S., and I. S. Aranson, 1997, Phys. Rev. Lett. 79, 213.
  340. Tsimring, L. S., and D. Volfson, 2005, in Powders & Grains 2005, edited by H. H. R. Garcia-Rojo, and S. McNamara (Balkema, Rotterdam), Vol. 2, p. 1215.
  341. Tu, Y., J. Toner, and S. Ramaswamy, 2005, Ann. Phys. (N.Y.) 318, 170.
  342. Uehara, J., M. Ambroso, R. Ojha, and D. Durian, 2003, Phys. Rev. Lett. 90, 194301.
  343. Umbanhowar, P. B., F. Melo, and H. L. Swinney, 1996, Nature (London) 382, 793.
  344. Umbanhowar, P. B., and H. L. Swinney, 2000, Physica A 288, 344.
  345. Unger, T., J. Kertész, and D. E. Wolf, 2005, Phys. Rev. Lett. 94, 178001.
  346. Urbach, M., J. Klafter, D. Gourdon, and J. Israelachvili, 2004, Nature (London) 699, 255.
  347. van Noije, T. P. C., and M. H. Ernst, 2000, Phys. Rev. E 61, 1765.
  348. Venkataramani, S. C., and E. Ott, 1998, Phys. Rev. Lett. 80, 3495.
  349. Venkataramani, S. C., and E. Ott, 2001, Phys. Rev. E 63, 046202.
  350. Villarruel, F. X., B. E. Lauderdale, D. M. Mueth, and H. M. Jaeger, 2000, Phys. Rev. E 61, 6914.
  351. Volfson, D., A. Kudrolli, and L. S. Tsimring, 2004, Phys. Rev. E 70, 051312.
  352. Volfson, D., L. S. Tsimring, and I. S. Aranson, 2003a, Phys. Rev. Lett. 90, 254301.
  353. Volfson, D., L. S. Tsimring, and I. S. Aranson, 2003b, Phys. Rev. E 68, 021301.
  354. Volfson, D., L. S. Tsimring, and I. S. Aranson, 2004, Phys. Rev. E 69, 031302.
  355. Voth, G. A., B. Bigger, M. R. Buckley, W. Losert, M. P. Brenner, H. A. Stone, and J. P. Gollub, 2002, Phys. Rev. Lett. 88, 234301.
  356. Wagner, C., 1961, Z. Elektrochem. 65, 681.
  357. Walker, J., 1982, Sci. Am. 247 (2), 166.
  358. Walsh, A., K. Holloway, P. Habdas, and J. de Bruyn, 2003, Phys. Rev. Lett. 91, 104301.
  359. Walton, O. R., 1993, Mech. Mater. 16, 259.
  360. Wildman, R. D., J. M. Huntley, and D. J. Parker, 2001, Phys. Rev. Lett. 86, 3304.
  361. Wildman, R. D., T. W. Martin, P. Krouskop, J. Talbot, J. M. Huntley, and D. J. Parker, 2005, Phys. Rev. E 71, 061301.
  362. Williams, J. C., 1976, Powder Technol. 15, 245.
  363. Xu, N., and C. S. O’Hern, 2005, Phys. Rev. Lett. 94, 055701.
  364. Yanagita, T., 1999, Phys. Rev. Lett. 82, 3488.
  365. Yeh, S.-R., M. Seul, and B. I. Shraiman, 1997, Nature (London) 386, 57.
  366. Zhang, W., and J. Viñals, 1997, J. Fluid Mech. 336, 301.
  367. Zhou, J., B. Dupuy, A. L. Bertozzi, and A. E. Hosoi, 2005, Phys. Rev. Lett. 94, 117803.
  368. Zik, O., D. Levine, S. G. Lipson, S. Shtrikman, and J. Stavans, 1994, Phys. Rev. Lett. 73, 644.

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