Free Access
Volume 37, Number 1, January/February 2003
Page(s) 73 - 90
Published online 15 March 2003
  1. D. Benedetto, E. Caglioti and M. Pulvirenti, A kinetic equation for granular media. Math. Mod. Numer. Anal. 31 (1997) 615-641. [Google Scholar]
  2. D. Benedetto, E. Caglioti, J.A. Carrillo and M. Pulvirenti, A non maxwellian steady distribution for one-dimensional granular media. J. Statist. Phys. 91 (1998) 979-990. [CrossRef] [MathSciNet] [Google Scholar]
  3. G.A. Bird, Molecular gas dynamics and direct simulation of gas flows. Clarendon Press, Oxford, UK (1994). [Google Scholar]
  4. C. Bizon, M.D. Shattuck, J.B. Swift and H.L. Swinney, Transport coefficients from granular media from molecular dynamics simulations. Phys. Rev. E 60 (1999) 4340-4351. [CrossRef] [Google Scholar]
  5. A.V. Bobylev, J.A. Carrillo and I. Gamba, On some properties of kinetic and hydrodynamics equations for inelastic interactions. J. Statist. Phys. 98 (2000) 743-773. [Google Scholar]
  6. A.V. Bobylev and K. Nanbu, Theory of collision algorithms for gases and plasmas based on the Boltzmann equation and the Landau-Fokker-Planck equation. Phys. Rev. E 61 (2000) 4576-4586. [CrossRef] [Google Scholar]
  7. N.V. Brilliantov and T. Pöschel, Granular gases the early stage, in Coherent Structures in Classical Systems, Miguel Rubi Ed., Springer (in press). [Google Scholar]
  8. C. Buet, A discrete-velocity scheme for the Boltzmann operator of rarefied gas dynamics. Transport Theory Statist. Phys. 25 (1996) 33-60. [Google Scholar]
  9. J.A. Carrillo, C. Cercignani and I.M. Gamba, Steady states of a Boltzmann equation for driven granular media. Phys. Rev. E 62 (2000) 7700-7707. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.A. Carrillo, R.J. McCann and C. Villani, Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates. Rev. Mat. Iberoamericana (to appear). [Google Scholar]
  11. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral methods in fluid dynamics. Springer Verlag, New York (1988). [Google Scholar]
  12. P. Degond and B. Lucquin-Desreux, The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case. Math. Models Methods Appl. Sci. 2 (1992) 167-182. [Google Scholar]
  13. L. Desvillettes, On asymptotics of the Boltzmann equation when the collisions become grazing. Transport Theory Statist. Phys. 21 (1992) 259-276. [Google Scholar]
  14. L. Desvillettes, C. Graham and S. Melehard, Probabilistic interpretation and numerical approximation of a Kac equation without cutoff. Stochastic Process. Appl. 84 (1999) 115-135. [CrossRef] [MathSciNet] [Google Scholar]
  15. Y. Du, H. Li and L.P. Kadanoff, Breakdown of hydrodynamics in a one-dimensional system of inelastic particles. Phys. Rev. Lett. 74 (1995) 1268-1271. [CrossRef] [PubMed] [Google Scholar]
  16. F. Filbet and L. Pareschi, A numerical method for the accurate solution of the Fokker-Planck-landau equation in the nonhomogeneous case. J. Comput. Phys 179 (2002) 1-26. [CrossRef] [MathSciNet] [Google Scholar]
  17. I. Goldhirsch, Scales and kinetics of granular flows. Chaos 9 (1999) 659-672. [CrossRef] [PubMed] [Google Scholar]
  18. H. Guérin and S. Méléard, Convergence from Boltzmann to Landau process with soft potential and particle approximations. Preprint PMA 698, Paris VI (2001). [Google Scholar]
  19. L. Kantorovich, On translation of mass (in Russian). Dokl. AN SSSR 37 (1942) 227-229. [Google Scholar]
  20. H. Li and G. Toscani, Long-time asymptotics of kinetic models of granular flows. Preprint (2002). [Google Scholar]
  21. B. Lucquin-Desreux and S. Mancini, A finite element approximation of grazing collisions. Preprint N. 1034, Laboratoire d'Analyse Numérique, Paris VI (2001). [Google Scholar]
  22. S. McNamara and W.R. Young, Kinetics of a one-dimensional granular medium in the quasi-elastic limit. Phys. Fluids A 5 (1993) 34-45. [CrossRef] [MathSciNet] [Google Scholar]
  23. K. Nanbu, Direct simulation scheme derived from the Boltzmann equation. J. Phys. Soc. Japan 49 (1980) 2042-2049. [Google Scholar]
  24. L. Pareschi, On the fast evaluation of kinetic equations for driven granular flows. Proceedings ENUMATH 2001 (to appear). [Google Scholar]
  25. L. Pareschi and B. Perthame, A Fourier spectral method for homogeneous Boltzmann equations. Transport Theory Statist. Phys. 25 (1996) 369-383. [CrossRef] [MathSciNet] [Google Scholar]
  26. L. Pareschi and G. Russo, Numerical solution of the Boltzmann equation. I. Spectrally accurate approximation of the collision operator. SIAM J. Numer. Anal. 37 (2000) 1217-1245. [CrossRef] [MathSciNet] [Google Scholar]
  27. L. Pareschi, G. Toscani and C. Villani, Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit. Numer. Math. 93 (2003) 527-548. Electronic DOI 10.1007/s002110100384. [CrossRef] [MathSciNet] [Google Scholar]
  28. R. Ramírez, T. Pöschel, N.V. Brilliantov and T. Schwager, Coefficient of restitution of colliding viscoelastic spheres. Phys. Rev. E 60 (1999) 4465-4472. [Google Scholar]
  29. F. Rogier and J. Schneider, A direct method for solving the Boltzmann equation. Transport Theory Statist. Phys. 23 (1994) 313-338. [Google Scholar]
  30. G. Toscani, One-dimensional kinetic models of granular flows. ESAIM: M2AN 34 (2000) 1277-1291. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  31. G. Toscani and C. Villani, Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. J. Statist. Phys. 94 (1999) 619-637. [CrossRef] [MathSciNet] [Google Scholar]
  32. L.N. Vasershtein, Markov processes on countable product space describing large systems of automata (in Russian). Problemy Peredachi Informatsii 5 (1969) 64-73. [Google Scholar]
  33. C. Villani, On a new class of weak solutions for the spatially homogeneous Boltzmann and Landau equations. Arch. Ration. Mech. Anal. 143 (1998) 273-307. [Google Scholar]
  34. C. Villani, On the spatially homogeneous Landau equation for Maxwellian molecules. Math. Models Methods Appl. Sci. 8 (1998) 957-983. [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.

Recommended for you