One-dimensional kinetic models of granular flows

Giuseppe Toscani

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 6, page 1277-1291
  • ISSN: 0764-583X

How to cite

top

Toscani, Giuseppe. "One-dimensional kinetic models of granular flows." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.6 (2000): 1277-1291. <http://eudml.org/doc/194037>.

@article{Toscani2000,
author = {Toscani, Giuseppe},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {granular flows; one-dimensional kinetic model; Boltzmann equation; dissipative collisions; variable coefficient of restitution; quasi-elastic limit; nonlinear friction},
language = {eng},
number = {6},
pages = {1277-1291},
publisher = {Dunod},
title = {One-dimensional kinetic models of granular flows},
url = {http://eudml.org/doc/194037},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Toscani, Giuseppe
TI - One-dimensional kinetic models of granular flows
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 6
SP - 1277
EP - 1291
LA - eng
KW - granular flows; one-dimensional kinetic model; Boltzmann equation; dissipative collisions; variable coefficient of restitution; quasi-elastic limit; nonlinear friction
UR - http://eudml.org/doc/194037
ER -

References

top
  1. [1] R. Alexandre and C. Villani, On the Boltzmann equation for long range interactions and the Landau approximation in plasma physics. Preprint DMA, École Normale Supérieure (1999). 
  2. [2] L. Arkeryd, Intermolecular forces of infinite range and the Boltzmann equation. Arch. Rational Mech. Anal. 77 (1981) 11-21. Zbl0547.76085MR630119
  3. [3] G. I. Barenblatt, Scaling, Self-similarity, and Intermediate Asymptotics. Cambridge Univ. Press, New York (1996). Zbl0907.76002MR1426127
  4. [4] D. Benedetto, E. Caglioti and M. Pulvirenti, A kinetic equation for granular media. RAIRO Modél. Math. Anal. Numér. 31 (1997) 615-641. Zbl0888.73006MR1471181
  5. [5] D. Benedetto, E. Caglioti and M. Pulvirenti, Erratum : A kinetic equation for granular media [RAIRO Modél. Math. Anal. Numér. 31 (1997) 615-641]. ESAIM : M2AN 33 (1999) 439-441. Zbl0888.73006MR1471181
  6. [6] C. Bizon, J. B. Shattuck, M. D. Swift, W. D. Mc Cormick and H. L. Swinney, Pattern in 2D vertically oscillated granular layers : simulation and experiments. Phys. Rev. Lett. 80 (1998) 57-60. 
  7. [7] A. V. Bobylev, J. A. Carillo and I. Gamba, On some properties of kinetic and hydrodynamics equations for inelastic interactions. J. Statist. Phys. 98 (2000) 743-773. Zbl1056.76071MR1749231
  8. [8] C. Cercignani, R. Illner and M. Pulvirenti, The mathematical theory of dilute gases. Springer Ser. Appl. Math. Sci. 106, Springer-Verlag, New York (1994). Zbl0813.76001MR1307620
  9. [9] L. Desvillettes, About the regularizing properties of the non-cut-off Kac equation. Comm. Math. Phys. 168 (1995) 417-440. Zbl0827.76081MR1324404
  10. [10] 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. 
  11. [11] D. Goldman, M. D. Shattuck, C. Bizon, W. D. McCormick, J. B. Swift and H. L. Swinney, Absence of inelastic collapse in a realistic three ball model. Phys. Rev. E 57 (1998) 4831-4833. 
  12. [12] I. Goldhirsch, Scales and kinetics of granular flows. Chaos 9 (1999) 659-672. Zbl1055.76569
  13. [13] M. Kac, Probability and related topics in the physical sciences. New York (1959). Zbl0087.33003MR102849
  14. [14] L. Kantorovich, On translation of mass (in Russian). Dokl. AN SSSR 37 (1942) 227-229. 
  15. [15] L. Landau, Die kinetische Gleichung für den Fall Coulombscher Wechselwirkung. Phys. Z. Sowjet. 10 (1936) 154. Trad.: The transport equation in the case of Coulomb interactions, in Collected papers of L.D. Landau, D. ter Haar Ed., Pergamon Press, Oxford (1981) 163-170. Zbl0015.38202
  16. [16] S. McNamara and W. R. Young, Inelastic collapse and clumping in a one-dimensional granular medium. Phys. Fluids A 4 (1992) 496-504. 
  17. [17] 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. MR1196416
  18. [18] G. Naldi, L. Pareschi and G. Toscani, Spectral methods for a singular Boltzmann equation for granular flows and numerical quasi elastic limit. Preprint (2000). Zbl1046.76034
  19. [19] G. Toscani, The grazing collision asymptotic of the non cut-off Kac equation. RAIRO Modél. Math. Anal. Numér. 32 (1998) 763-772. Zbl0912.76081MR1652617
  20. [20] I. Vaida, Theory of statistical Inference and Information. Kluwer Academic Publishers, Dordrecht (1989). Zbl0711.62002
  21. [21] L. N. Vasershtein, Markov processes on countable product space describing large systems of automata (in Russian). Problemy Peredachi Informatsii 5 (1969) 64-73. Zbl0273.60054MR314115
  22. [22] C. Villani, Contribution à l'étude mathématique des équations de Boltzmann et de Landau en théorie cinétique des gaz et des plasmas. Ph. D. thesis, Univ. Paris-Dauphine (1998). 
  23. [23] C. Villani, On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Arch. Rational Mech. Anal. 143 (1998) 273-307. Zbl0912.45011MR1650006
  24. [24] C. Villani, Contribution à l'étude mathématique des collisions en théorie cinétique. Ceremade, Paris IX-Dauphine, January 24 (2000). 
  25. [25] V. M. Zolotarev, Probability Metrics. Theory Probab. Appl. 28 (1983) 278-302. Zbl0533.60025

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.