EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 6 / No 4 (2011) Math. Model. Nat. Phenom., 6 4 (2011) 37-76 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 4, 2011
Granular hydrodynamics
Page(s) 37 - 76
DOI https://doi.org/10.1051/mmnp/20116403
Published online 18 July 2011
  1. M. Abramowitz, I. A. Stegun, eds. Handbook of Mathematical Functions. Dover, New York, 1972, ch. 15. [Google Scholar]
  2. A. Astillero, A. Santos. Aging to non-Newtonian hydrodynamics in a granular gas. Europhys. Lett., 78 (2007), No. 2, 24002. [CrossRef] [Google Scholar]
  3. A. Baldasarri, U. M. B. Marconi, A. Puglisi. Influence of correlations on the velocity statistics of scalar granular gases. Europhys. Lett., 58 (2002), No. 1, 14–20. [CrossRef] [Google Scholar]
  4. A. Barrat, E. Trizac, M.H. Ernst. Quasi-elastic solutions to the nonlinear Boltzmann equation for dissipative gases. J. Phys. A: Math. Theor., 40 (2007), No. 15, 4057–4076. [CrossRef] [Google Scholar]
  5. E. Ben-Naim, P. L.Krapivsky. Multiscaling in inelastic collisions. Phys. Rev. E, 61 (2000), No. 1, R5–R8. [CrossRef] [Google Scholar]
  6. E. Ben-Naim, P. L. Krapivsky. Scaling, multiscaling, and nontrivial exponents in inelastic collision processes. Phys. Rev. E, 66 (2002), No. 1, 011309. [CrossRef] [Google Scholar]
  7. E. Ben-Naim, P. L. Krapivsky. Impurity in a granular fluid. Eur. Phys. J. E, 8 (2002), No. 5, 507–515. [EDP Sciences] [Google Scholar]
  8. E. Ben-Naim, P. L. Krapivsky. The inelastic Maxwell model. Granular Gas Dynamics. T. Pöschel, S. Luding, eds. Lecture Notes in Physics 624, Springer, Berlin, Germany, 2003, 65–94. [Google Scholar]
  9. G. A. Bird. Molecular Gas Dynamics and the Direct Simulation Monte Carlo of Gas Flows. Clarendon Press, Oxford, UK, 1994. [Google Scholar]
  10. A. V. Bobylev, J. A. Carrillo, I. M. Gamba. On some properties of kinetic and hydrodynamic equations for inelastic interactions. J. Stat. Phys., 98 (2000), Nos. 3–4, 743–773. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. V. Bobylev, C. Cercignani. Moment equations for a granular material in a thermal bath. J. Stat. Phys., 106 (2002), Nos. 3–4, 547–567. [CrossRef] [Google Scholar]
  12. A. V. Bobylev, C. Cercignani. Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions. J. Stat. Phys., 110 (2003), Nos. 1–2, 333–375. [CrossRef] [Google Scholar]
  13. A. V. Bobylev, C. Cercignani, G. Toscani. Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials. J. Stat. Phys., 111 (2003), Nos. 1–2, 403–416. [CrossRef] [Google Scholar]
  14. A. V. Bobylev, I. M. Gamba. Boltzmann equations for mixtures of Maxwell gases: Exact solutions and power like tails. J. Stat. Phys. 124 (2006), Nos. 2–4, 497–516. [CrossRef] [MathSciNet] [Google Scholar]
  15. F. Bolley, J. A. Carrillo. Tanaka theorem for inelastic Maxwell models. Comm. Math. Phys., 276 (2007), No. 2, 287–314. [CrossRef] [MathSciNet] [Google Scholar]
  16. J. J. Brey, D. Cubero. Hydrodynamic transport coefficients of granular gases. Granular Gases. T. Pöschel, T., S. Luding, eds. Lecture Notes in Physics 564, Springer, Berlin, Germany, 2001, 59–78. [Google Scholar]
  17. J. J. Brey, J. W. Dufty, C. S. Kim, A. Santos. Hydrodynamics for granular flow at low density. Phys. Rev. E, 58 (1998), No. 4, 4638–4653. [CrossRef] [Google Scholar]
  18. J. J. Brey, J. W. Dufty, A. Santos. Dissipative dynamics for hard spheres. J. Stat. Phys., 87 (1997), Nos. 5–6, 1051–1066. [CrossRef] [Google Scholar]
  19. J. J. Brey, M. I. García de Soria, P. Maynar. Breakdown of hydrodynamics in the inelastic Maxwell model of granular gases. Phys. Rev. E, 82 (2010), No. 2, 021303. [CrossRef] [Google Scholar]
  20. J. J. Brey, M. J. Ruiz-Montero, D. Cubero. Homogeneous cooling state of a low-density granular gas. Phys. Rev. E, 54 (1996), No. 4, 3664–3671. [NASA ADS] [CrossRef] [Google Scholar]
  21. N. Brilliantov, T. Pöschel. Kinetic Theory of Granular Gases. Clarendon Press, Oxford, UK, 2004. [Google Scholar]
  22. N. Brilliantov, T. Pöschel. Breakdown of the Sonine expansion for the velocity distribution of granular gases. Europhys. Lett., 74 (2006), No. 3, 424–430; 75 (2006), 1, 188. [CrossRef] [Google Scholar]
  23. R. Brito, M. H. Ernst. Anomalous velocity distributions in inelastic Maxwell gases. Advances in Condensed Matter and Statistical Mechanics. E. Korutcheva, R. Cuerno, eds. Nova Science Publishers, New York, USA, 2004, 177–202. [Google Scholar]
  24. C. S. Campbell. Rapid granular flows. Annu. Rev. Fluid Mech., 22 (1990), 57–92. [Google Scholar]
  25. J. A. Carrillo, C. Cercignani, I. M. Gamba. Steady states of a Boltzmann equation for driven granular media. Phys. Rev. E, 62 (2000), No. 6, 7700–7707. [CrossRef] [MathSciNet] [Google Scholar]
  26. C. Cercignani. Shear flow of a granular material. J. Stat. Phys., 102 (2001), Nos. 5–6, 1407–1415. [CrossRef] [Google Scholar]
  27. S. Chapman, T. G. Cowling. The Mathematical Theory of Nonuniform Gases. Cambridge University Press, Cambridge, UK, 1970. [Google Scholar]
  28. F. Coppex, M. Droz, E. Trizac. Maxwell and very hard particle models for probabilistic ballistic annihilation: Hydrodynamic description. Phys. Rev. E, 72 (2005), No. 2, 021105. [CrossRef] [Google Scholar]
  29. J. W. Dufty. Kinetic theory and hydrodynamics for a low density granular gas. Adv. Compl. Syst., 4 (2001), No. 4, 397–406. [Google Scholar]
  30. J. W. Dufty, J. J. Brey. Origins of Hydrodynamics for a Granular Gas. Modellings and Numerics of Kinetic Dissipative Systems. L. Pareschi, G. Russo, G., G. Toscani, eds. Nova Science Publishers, New York, USA, 2006, 17–30. [Google Scholar]
  31. M. H. Ernst. Exact solutions of the nonlinear Boltzmann equation. Phys. Rep., 78 (1981), No. 1, 1–171. [Google Scholar]
  32. M. H. Ernst, R. Brito. High-energy tails for inelastic Maxwell models. Europhys. Lett., 58 (2002), No. 2, 182–187. [CrossRef] [Google Scholar]
  33. M. H. Ernst, R. Brito. Scaling solutions of inelastic Boltzmann equations with over-populated high-energy tails. J. Stat. Phys., 109 (2002), Nos. 3–4, 407–432. [CrossRef] [Google Scholar]
  34. M. H. Ernst, R. Brito. Driven inelastic Maxwell models with high energy tails. Phys. Rev. E, 65 (2002), No. 4, 040301. [CrossRef] [Google Scholar]
  35. M. H. Ernst, E. Trizac, A. Barrat. The rich behaviour of the Boltzmann equation for dissipative gases. Europhys. Lett., 76 (2006), No. 1, 56–62. [CrossRef] [MathSciNet] [Google Scholar]
  36. M. H. Ernst, E. Trizac, A. Barrat. The Boltzmann equation for driven systems of inelastic soft spheres. J. Stat. Phys., 124 (2006), Nos. 2–4, 549–586. [CrossRef] [MathSciNet] [Google Scholar]
  37. S. E. Esipov, T. Pöschel. The granular phase diagram. J. Stat. Phys., 86 (1997), Nos. 5–6, 1385–1395. [CrossRef] [Google Scholar]
  38. V. Garzó. Nonlinear transport in inelastic Maxwell mixtures under simple shear flow. J. Stat. Phys., 112 (2003), Nos. 3–4, 657–683. [CrossRef] [Google Scholar]
  39. V. Garzó. Transport coefficients for an inelastic gas around uniform shear flow: Linear stability analysis. Phys. Rev. E, 73 (2006), No. 2, 021304. [CrossRef] [MathSciNet] [Google Scholar]
  40. V. Garzó. Shear-rate dependent transport coefficients for inelastic Maxwell models. J. Phys. A: Math. Theor., 40 (2007), No. 35, 10729–10757. [CrossRef] [Google Scholar]
  41. V. Garzó. Mass transport of an impurity in a strongly sheared granular gas. J. Stat. Mech., (2007), P02012. [Google Scholar]
  42. V. Garzó, A. Astillero. Transport coefficients for inelastic Maxwell mixtures. J. Stat. Phys., 118 (2005), Nos. 5–6, 935–971. [CrossRef] [MathSciNet] [Google Scholar]
  43. V. Garzó, J. W. Dufty. Dense fluid transport for inelastic hard spheres. Phys. Rev. E, 59 (1999), No. 5, 5895–5911. [CrossRef] [Google Scholar]
  44. V. Garzó, J. W. Dufty. Homogeneous cooling state for a granular mixture. Phys. Rev. E, 60 (1999), No. 5, 5706–5713. [CrossRef] [Google Scholar]
  45. V. Garzó, J. W. Dufty. Hydrodynamics for a granular mixture at low density. Phys. Fluids, 14 (2002), No. 4, 1476–1490. [CrossRef] [Google Scholar]
  46. V. Garzó, J. W. Dufty, C. M. Hrenya. Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport. Phys. Rev. E, 76 (2007), No. 3, 031303. [CrossRef] [MathSciNet] [Google Scholar]
  47. V. Garzó, C. M. Hrenya, J. W. Dufty Enskog theory for polydisperse granular mixtures. II. Sonine polynomial approximation. Phys. Rev. E, 76 (2007), No. 3, 031304. [Google Scholar]
  48. V. Garzó, J. M. Montanero. Transport coefficients of a heated granular gas. Physica A, 313 (2002), Nos. 3–4, 336–356. [Google Scholar]
  49. V. Garzó, A. Santos. Kinetic Theory of Gases in Shear Flows. Nonlinear Transport. Kluwer, Dordrecht, The Netherlands, 2003. [Google Scholar]
  50. V. Garzó, V., and A. Santos. Third and fourth degree collisional moments for inelastic Maxwell models. J. Phys. A: Math. Theor., 40 (2007), No. 50, 14927–14943. [CrossRef] [Google Scholar]
  51. V. Garzó, A. Santos, J. M. Montanero. Modifed Sonine approximation for the Navier-Stokes transport coefficients of a granular gas. Physica A, 376 (2007), 94–107. [CrossRef] [Google Scholar]
  52. V. Garzó, F. Vega Reyes, J. M. Montanero Modified Sonine approximation for granular binary mixtures. J. Fluid Mech. (2009), 623, 387–411. [CrossRef] [MathSciNet] [Google Scholar]
  53. I. Goldhirsch. Rapid granular flows. Annu. Rev. Fluid Mech., 35 (2003), 267–293. [Google Scholar]
  54. A. Goldshtein, M. Shapiro. Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations. J. Fluid Mech., 282 (1995), 75–114. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  55. P. K. Haff. Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech., 134 (1983), 401–430. [NASA ADS] [CrossRef] [Google Scholar]
  56. K. Kohlstedt, A. Snezhko, M. V. Sapozhnikov, I. S. Aranson, E. Ben-Naim Velocity distributions of granular gases with drag and with long-range interactions. Phys. Rev. Lett., 95 (2005), No. 6, 068001. [CrossRef] [PubMed] [Google Scholar]
  57. P. L. Krapivsky, E. Ben-Naim. Nontrivial velocity distributions in inelastic gases. J. Phys. A: Math. Gen., 35 (2002), No. 11, L147–L152. [CrossRef] [Google Scholar]
  58. M. Lee, J. W. Dufty. Transport far from equilibrium: Uniform shear flow. Phys. Rev. E, 56 (1997), No. 2, 1733–1745. [CrossRef] [Google Scholar]
  59. A. W. Lees, S. F. Edwards. The computer study of transport processes under extreme conditions. J. Phys. C, 5 (1972), No. 5, 1921–1928. [Google Scholar]
  60. J. F. Lutsko. Transport properties of dense dissipative hard-sphere fluids for arbitrary energy loss models. Phys. Rev. E, 72 (2005), No. 2, 021306. [CrossRef] [Google Scholar]
  61. J. F. Lutsko Chapman–Enskog expansion about nonequilibrium states with application to the sheared granular fluid. Phys. Rev. E, 73 (2006), No. 2, 021302. [CrossRef] [MathSciNet] [Google Scholar]
  62. U. M. B. Marconi, A. Puglisi. Mean-field model of freely cooling inelastic mixtures. Phys. Rev. E, 65 (2002), No. 5, 051305. [CrossRef] [Google Scholar]
  63. U. M. B. Marconi, A. Puglisi. Steady state properties of a mean field model of driven inelastic mixtures. Phys. Rev. E, 66 (2002), No. 1, 011301. [NASA ADS] [CrossRef] [Google Scholar]
  64. J. C. Maxwell. On the Dynamical Theory of Gases. Phil. Trans. Roy. Soc. (London), 157 (1867), 49–88; reprinted in S. G. Brush. The Kinetic Theory of Gases. An Anthology of Classic Papers with Historical Commentary. Imperial College Press, London, UK, 2003, 197–261. [Google Scholar]
  65. J. M. Montanero, A. Santos. Computer simulation of uniformly heated granular fluids. Gran. Matt., 2 (2000), No. 2, 53–64. [CrossRef] [Google Scholar]
  66. J. M. Montanero, A. Santos, V. Garzó. First-order Chapman-Enskog velocity distribution function in a granular gas. Physica A, 376 (2007), 75–93. [CrossRef] [Google Scholar]
  67. O. Narayan, S. Ramaswamy. Anomalous heat conduction in one-dimensional momentum-conserving systems. Phys. Rev. Lett., 89 (2002), No. 20, 200601. [CrossRef] [PubMed] [Google Scholar]
  68. A. Santos. Transport coefficients of d-dimensional inelastic Maxwell models. Physica A, 321 (2003), Nos. 3–4, 442–466. [CrossRef] [MathSciNet] [Google Scholar]
  69. A. Santos. A simple model kinetic equation for inelastic Maxwell particles. Rarefied Gas Dynamics: 25th International Symposium on Rarefied Gas Dynamics. A. K. Rebrov, M. S. Ivanov, eds. Publishing House of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia, 2007, pp 143-148. [Google Scholar]
  70. A. Santos. Solutions of the moment hierarchy in the kinetic theory of Maxwell models. Cont. Mech. Therm., 21 (2009), No. 5, 361–387. [CrossRef] [Google Scholar]
  71. A. Santos, M. H. Ernst. Exact steady-state solution of the Boltzmann equation: A driven one-dimensional inelastic Maxwell gas. Phys. Rev. E, 68 (2003), No. 1, 011305. [CrossRef] [Google Scholar]
  72. A. Santos, V. Garzó. Exact non-linear transport from the Boltzmann equation. Rarefied Gas Dynamics. J. Harvey, G. Lord, eds. Oxford University Press, Oxford, UK, 1995, 13–22. [Google Scholar]
  73. A. Santos, V. Garzó. Simple shear flow in inelastic Maxwell models. J. Stat. Mech., (2007), P08021. [Google Scholar]
  74. A. Santos, V. Garzó, J. W. Dufty. Inherent rheology of a granular fluid in uniform shear flow. Phys. Rev. E, 69 (2004), No. 6, 061303. [CrossRef] [Google Scholar]
  75. A. Santos, V. Garzó, F Vega Reyes. An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux. Eur. Phys. J.-Spec. Top., 179 (2009), No. 1, 141–156. [CrossRef] [EDP Sciences] [Google Scholar]
  76. A. Santos, J. M. Montanero. The second and third Sonine coefficients of a freely cooling granular gas revisited. Gran. Matt., 11 (2009), No. 3, 157-168. [CrossRef] [Google Scholar]
  77. M. Tij, E. E. Tahiri, J. M. Montanero, V. Garzó, A. Santos, J. W. Dufty. Nonlinear Couette flow in a low density granular gas. J. Stat. Phys., 103 (2001), Nos. 5–6, 1035–1068. [CrossRef] [Google Scholar]
  78. E. Trizac, E., P. L. Krapivsky. Correlations in ballistic processes. Phys. Rev. Lett., 91 (2003), No. 21, 218302. [CrossRef] [PubMed] [Google Scholar]
  79. C. Truesdell, R. G. Muncaster. Fundamentals of Maxwell’s Kinetic Theory of a Simple Monatomic Gas. Academic Press, New York, USA, 1980. [Google Scholar]
  80. T. P. C. van Noije, M. H. Ernst. Velocity distributions in homogeneous granular fluids: the free and the heated case. Gran. Matt., 1 (1998), No. 2, 57–64. [Google Scholar]
  81. F. Vega Reyes, V. Garzó, A. Santos. Class of dilute granular Couette flows with uniform heat flux. Phys. Rev. E, 83 (2011), No. 2, 021302. [CrossRef] [Google Scholar]
  82. F. Vega Reyes, A. Santos, V. Garzó. Non-Newtonian granular hydrodynamics. What do the inelastic simple shear flow and the elastic Fourier flow have in common? Phys. Rev. Lett., 104 (2010), No. 2, 028001. [CrossRef] [PubMed] [Google Scholar]
  83. F. Vega Reyes, J. S. Urbach. Steady base states for Navier–Stokes granular hydrodynamics with boundary heating and shear. J. Fluid Mech., 636 (2009), 279–293. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.