The collapse phenomenon in one-dimensional inelastic point particle systems

Physica D: Nonlinear Phenomena

Volumn 132, Issue 4, 1999, Pages 457-475

  Benedetto, Dario ^a   Caglioti, Emanuele ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Collapse; Granular media; Inelastic collision; Kinetic equations; Particle system

Indexed keywords

EID: 0037764158     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00056-1     Document Type: Article

References (22)

1. Campbell C.S. Rapid granular flows. Annu. Rev. Fluid. Mech. 22:1990;57-92.
2. Benedetto D., Caglioti E., Carrillo J.A., Pulvirenti M. A non Maxwellian equilibrium distribution for one-dimensional granular media. J. Stat. Phys. 91(5/6):1998;979-990.
3. Benedetto D., E.Caglioti, Pulvirenti M. A kinetic equation for granular media. Math. Mod. Num. An. 31(5):1997;615-641.
4. D. Benedetto, E. Caglioti, M. Pulvirenti, A one dimensional Boltzmann equation with inelastic collisions, 1998, Rend. Sem. Mat. Fis. Milano, in press.
5. Bernu B., Mazighi R. One-dimensional bounce of inelastically colliding marbles on a wall. J. Phys. 23:1990;5745-5754.
6. Constantin P., Grossman E., Mungan M. Inelastic collisions of three particles on a line as a two-dimensional billiard. Physica D. 83:1995;409-420.
7. Du Y., Li H., Kadanoff L.P. Breakdown of hydrodynamics in one-dimensional system of inelastic particles. Phys. Rev. Lett. 74(8):1995;1268-1271.
8. Goldhirsch I., Zanetti G. Clustering instability in dissipative gases. Phys. Rev. Lett. 70:1993;1619-1622.
9. S. McNamara, Inelastic collapse, contribution to NATO-ASI Dynamics: Models and Kinetic methods for non-equilibrium many body systems, 1998.
10. McNamara S., Young W.R. Inelastic collapse and clumping in a one-dimensional granular medium. Phys. Fluids A. 4(3):1992;496-504.
11. McNamara S., Young W.R. Kinetics of a one-dimensional granular medium in the quasi-elastic limit. Phys. Fluids A. 5(1):1993;34-45.
12. A. Puglisi, V. Loreto, U.M.B. Marconi, A Petri, A. Vulpiani, Clustering and non-Gaussian behavior in granular matter, 1997, preprint.
13. Sela N., Goldhirsch I. Hydrodynamics of a one-dimensional granular medium. Phys. Fluids. 7(3):1995;34-45.
14. E W., Rykov Yu.G., Sinai Ya.G. Generalized variational principles, global weak solutions and behavior with random initial data for system of conservation laws arising in adhesion particle dynamics. Comm. Math. Phys. 177(2):1996;349-380.
15. Grenier E. Existence globale pour le système des gaz sans pression. C. R. Acad. Sci. Paris Sr. I Math. 321(2):1995;171-174.
16. McNamara S., Young W.R. Inelastic collapse in two dimension. Phys. Rev. E. 50:1994;R28.
17. Zhou T., Kadanoff L.P. Inelastic collapse of three particles. Phys. Rev. E. 54:1996;623.
18. Goldshtein A., Shapiro M. Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations. J. Fluid Mech. 282:1995;75-114.
19. Sela N., Goldhirsch I. Hydrodynamics equations for rapid flows of smooth inelastic spheres to Burnett order. J. Fluid Mech. 361:1998;41-74.
20. Esipov S.E., Pöschel T. Boltzmann equation and granular hydrodynamics. J. Stat. Phys. 86:1997;1385.
21. Cornell S.J., Swift M.R., Bray A.J. Inelastic collapse of a randomly forced particle. Phys. Rev. Lett. 81:1998;1142.
22. I.I. Gihman, A.V. Skorohod, Stochastic Differential Equations, Springer, Berlin, 1972.