Homogeneous cooling states are not always good approximations to granular flows

Archive for Rational Mechanics and Analysis

Volumn 163, Issue 4, 2002, Pages 329-343

  Caglioti, E ^a   Villani, C ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036021909     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050200204     Document Type: Article

References (21)

1. BENEDETTO, D., CAGLIOTI, E., CARRILLO, J. A. & PULVIRENTI, M. A non-Maxwellian steady distribution for one-dimensional granular media. J. Statist. Phys. 91 (1998), 979-990.
2. BENEDETTO, D., CAGLIOTI, E. & PULVIRENTI, M. A kinetic equation for granular media. RAIRO Modél. Math. Anal. Numér. 31 (1997), 615-641.
3. BENEDETTO, D., CAGLIOTI, E. & PULVIRENTI, M. A one-dimensional Boltzmann equation with inelastic collisions. Rend. Sem. Mat. Fis. Milano 67 (1997), 169-179.
4. BENEDETTO, D., CAGLIOTI, E. & PULVIRENTI, M. Collective behavior of one-dimensional granular media. Modelling in Applied Sciences, A Kinetic Theory Approach (N. BELLOMO & M. PULVIRENTI, editors), Modelling and Simulation in Science, Engineering and Technology Series, Birkhäuser, 2000.
5. BERNU, B. & MAZIGHI, R. One-dimensional bounce of inelastically colliding marbles on a wall. Jour. of Phys. A: Math. Gen. 23 (1990), 5745-5754.
6. CAMPBELL, S. Rapid granular flows. Ann. Rev. of Fluid Mech. 22 (1990), 57-92.
7. CARRILLO, J.A., MCCANN, R. & VILLANI, C. Kinetic equilibration rates for granular media and related equations via entropy dissipation and mass transportation estimates. To appear in Rev. Mat. Iberoamericana.
8. DU, Y., LI, H. & KADANOFF, L.P. Breakdown of hydrodynamics in one-dimensional system of inelastic particles. Phys. Rev. Lett. 74 (1995), 1268-1271.
9. ESIPOV, S.E. & PÖSCHEL, T. Boltzmann equation and granular hydrodynamics. J. Statist. Phys. 86 (1997), 1385.
10. GAMBA, I., PANFEROV, V. & VILLANI, C. On the Boltzmann equation for diffusively excited granular media. Work in progress.
11. GOLDHIRSCH, I. & ZANETTI, G. Clustering instability in dissipative gases. Phys. Rev. Lett. 70 (1993), 1619-1622.
12. GOLDSHTEIN, A. & SHAPIRO, M. Mechanics of collisional motion of granular materials. Part 1: General hydrodynamic equations. J. Fluid Mech. 282 (1995), 75-114.
13. MCNAMARA, S. & YOUNG, W.R. Inelastic collapse and clumping in a one-dimensional granular medium. Phys. Fluids A 4 (1992), 496-504.
14. MCNAMARA, S. & YOUNG, W.R. Kinetics of a one-dimensional granular medium in the quasi-elastic limit. Phys. Fluids A 5(1993), 34-45.
15. RAVHEV, S., AND RÜSCHENDORF, L. Mass Transportation Problems. Probability and its applications, Springer-Verlag, 1998.
16. SELA, N. & GOLDHIRSCH, I. Hydrodynamics of a one-dimensional granular medium. Phys. of Fluids 7 (1995), 34-45.
17. SELA, N. & GOLDHIRSCH, I. Hydrodynamic equations for rapid flows of smooth inelastic spheres to Burnett order. J. Fluid Mech. 361 (1998), 41-74.
18. TOSCANI, G. One-dimensional kinetic models with dissipative collisions. M2AN Math. Model. Numer. Anal. 34 (2000), 1277-1292.
19. TOSCANI, G. & VILLANI, C. Unpublished work.
20. VILLANI, C. Topics in mass transportation. Lecture notes.
21. PUGLISI, A., LORETO, V., MARINI BETTOLO MARCONI, U., PETRI, A. & VULPIANI, A. Clustering and non-Gaussian behavior in granular matter. Phys. Rev. Lett. 81 (1998), 3848-3851.