Hostname: page-component-7b7567c8c-lpg2g Total loading time: 0 Render date: 2026-11-15T22:08:27.441Z Has data issue: false hasContentIssue false
  • English
  • Français

New Wave Dynamics in Granular State

Published online by Cambridge University Press:  01 February 2011

Vitali F. Nesterenko
Vitali F. Nesterenko*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, U.S.A.
Get access

Abstract

The unusual feature of granular state is the negligible linear range of the interaction force between neighboring particles resulting in zero sound speed in uncompressed material. This makes linear and weakly nonlinear continuum approach based on Korteveg - de Vries equation invalid. This paper describes a results based on more general approach.

Information

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 627: Symposium BB – The Granular State , 2000, BB3.1
Copyright
Copyright © Materials Research Society 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

1. Nesterenko, V.F., Journal of Applied Mechanics and Technical Physics, 5, 733 (1983).Google Scholar
2. Landau, L. D., Lifshitz, E.M. Theory of Elasticity, (Pergamon Press, 1986), pp. 26–31.Google Scholar
3. Kunin, I. A., Theory of Elastic Media with Microstructure, (Nauka, 1975).Google Scholar
4. Korteweg, D.J. and Vries, de G., London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, 39, 422, (1895).Google Scholar
5. Remoissenet, M., Waves Called Solitons (Concepts and Experiments), 3-rd revised and enlarged edition, (Springer-Verlag, 1999).Google Scholar
6. Benjamin, T.B., Bona, J.L., and Mahony, J.J., Philosophical Transactions of the Royal Society of London A. Mathematical and Physical Sciences, 272, 47 (1972).Google Scholar
7. Kruskal, M., in: Lecture Notes in Physics, 38 (Dynamical Systems, Theory and Applications), (Springer-Verlag, 1975) pp. 310–354.Google Scholar
8. Whitham, G.B., Linear and Nonlinear Waves, (John Wiley & Sons Inc., 1974).Google Scholar
9. Nesterenko, V.F., Journal De Physique IV, Colloque C8, 4, C8–729 (1994).Google Scholar
10. Nesterenko, V.F., High-Rate Deformation of Heterogeneous Materials. (Nauka, 1992), Chapter. 2, pp. 51–80 (in Russian).Google Scholar
11. Gavrilyuk, S.L, and Nesterenko, V.F., J. of Appl. Mechanics and Tech. Physics 6, 784 (1993).Google Scholar
12. A.N., , Lazaridi, , and Nesterenko, V.F., J. of Appl. Mechanics and Tech. Physics, 3, 405 (1985).Google Scholar
13. Sinkovits, R.S., and Sen, S., Phys. Rev., E, 54, 6857 (1996).Google Scholar
14. Coste, C., Falcon, E., and Fauve, S., Physical Review E, 56, 6104 (1997).Google Scholar
15. Chatterjee, A., Phys. Rev. B, 59, 5912 (1999).Google Scholar
16. Wright, T.W., Studies in Applied Mechanics, 72, 149 (1985).Google Scholar
17. Wright, T.W., Int. J. Solids Structures, 20, 911 (1984).Google Scholar
18. Scott, D.R., and Stevenson, D.J., Geophysical Research Letters, 11, 1161 (1984).Google Scholar
19. Takahashi, D., and Satsuma, J., J. Phys. Soc. Japan, 57, 417 (1988).Google Scholar
20. Takahashi, D., Sachs, J.R., and Satsuma, J., in Research Reports in Physics, Nonlinear Physics, Eds. Chaohao, Gu, Yishen, Li, and Guizhang, Tu (Springer-Verlag, 1990), pp. 214–220.Google Scholar
21. Hinch, E.J. and Saint-Jean, S., Proc. R. Soc. Lond. A, 455, 3201 (1999).Google Scholar
22. Friesecke, G., and Wattis, J.A.D., Communications in Mathematical Physics, 161, 391 (1994).Google Scholar
23. MacKay, R.S., Physics Letters A, 251, 191 (1999).Google Scholar
24. Sen, S., Manciu, M., Physica A, 268, 644 (1999).Google Scholar
25. Falcon, E., Laroche, C., Fauve, S., and Coste, C., The EuropPhys. Journal B, 5, 111 (1998).Google Scholar
26. Nesterenko, V.F., Lazaridi, A.N., and Sibiryakov, E.B, Journal of Applied Mechanics and Technical Physics, 4, 166 (1995).Google Scholar
27. Sen, S., Manciu, M., and Wright, J.D., Phys. Rev., E, 57, 2386 (1998).Google Scholar
28. Dash, P. C., and Patnaik, K., Progress in Theoretical Physics, 65, 526 (1981).Google Scholar
29. Coste, C., Gilles, B. The European Physical Journal B, 7, 155 (1999).Google Scholar
30. Goddard, J.D., Proc. R. Soc. London A, 430, 105 (1990).Google Scholar
31. Nesterenko, V.F., Combustion, Explosion and Shock Waves, July, 116 (1995).Google Scholar
32. Nesterenko, V.F., Solitons, Shock Waves in Strongly Nonlinear Particulate Media, in Shock Compression of Condensed Matter-1999, edited by Furnish, M.D., Chabildas, L.C., and Hixson, R.S., AIP, 2000, pp. 177–180.Google Scholar