Abstract
We here study the behaviour of highly non-linear solitary waves when interact with boundaries. We compare a model developed by the author with the Kubawara-Kono model. We show that this last model does not give the best results when compared with our model, proposed in Vergara (Phys. Rev. Lett. 104:118001, 2010 [1]).
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References
L. Vergara, Phys. Rev. Lett. 104, 118001 (2010)
H.M. Jaeger, S.R. Nagel, Science 255, 1523 (1992); H.J. Herrmann, J.-P. Hovi, S. Luding (eds.), Physics of Dry Granular Media, NATO ASI Series (Kluwer, Dordrecht, 1998); H. Hinrichsen, D. Wolf (eds.), The Physics of Granular Media (Wiley, Berlin, 2004); R. GarcĂa-Rojo, H.J. Herrmann, S. McNamara (eds.), Powders and Grains 2005 (Taylor and Francis, 2005)
V.F. Nesterenko, Dynamics of Heterogeneous Materials (Springer, New York, 2001)
H. Hertz, Journal fĂĽr die reine und angewandte Mathematik 92, 156 (1882)
C. Coste, E. Falcon, S. Fauve, Phys. Rev. E. 56, 6104 (1997)
S. Sen, M. Manciu, J.D. Wright, Phys. Rev. E 57, 2386 (1998); E.J. Hinch, S. Saint-Jean, Proc. R. Soc. A 455, 3210 (1999); Hascoet, H.J. Herrmann, Eur. Phys. J. B 14, 183 (2000); M. Manciu, S. Sen, A.J. Hurd, Physica D 157, 2386 (2001); S. Sen et al. Phys. Rep. 46, 21 (2008), and references therein
W. Goldsmith, Impact (Edward Arnold Publications, London, 1960); R. Sondergaard, K. Chaney, C.E. Brennen. J. Appl. Mech. 57, 694 (1990)
K.L. Johnson, Contact Mechanics (Cambridge University Press, London, 1992)
G. Kuwabara, K. Kono, Jpn. J. Appl. Phys. 26, 1230 (1987)
W.A.M. Morgado, I. Oppenheim, Phys. Rev. E. 55, 1940 (1997)
N.V. Brilliantov, F. Spahn, J.-M. Hertzsch, T. Pöschel, Phys. Rev. E. 53, 5382 (1996)
R. Ramirez, T. Pöschel, N.V. Brilliantov, T. Schwager, Phys. Rev. E. 60, 4465 (1999)
S. Job, F. Melo, A. Sokolow, S. Sen, Phys. Rev. Lett. 94, 178002 (2005)
C. Daraio, V.F. Nesterenko, E.B. Herbold, S. Jin, Phys. Rev. E 73, 026610 (2006)
R. Carretero-González, D. Khatri, M.A. Porter, P.G. Kevrekidis, C. Daraio, Phys. Rev. Lett. 102, 024102 (2009)
A. Rosas, A.H. Romero, V.F. Nesterenko, K. Lindenberg, Phys. Rev. E 78, 051303 (2008)
T. Pöschl, Zeit. f. Phys. 46, 142 (1927)
Acknowledgments
The author thanks Prof. Daraio for allowing me to use data that I have used to test my model. This work was partially supported by Fondecyt, Grant No. 1130492.
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Vergara, L. (2016). How Dissipative Highly Non-linear Solitary Waves Interact with Boundaries in a 1D Granular Medium. In: Tlidi, M., Clerc, M. (eds) Nonlinear Dynamics: Materials, Theory and Experiments. Springer Proceedings in Physics, vol 173. Springer, Cham. https://doi.org/10.1007/978-3-319-24871-4_14
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DOI: https://doi.org/10.1007/978-3-319-24871-4_14
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