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References
R.P. Behringer, E. Clément, J. Geng, D. Howell, L. Kondic, G. Metcalfe, C. O'Hern, G. Reydellet, S. Tennakoon, L. Vanel, and C. Veje, Science in the sandbox: fluctuations, friction and instabilities, in Coherent Structures in Complex Systems, (Ed. by D. Reguera, L.L. Bonilla, J.M. Rubí, Lecture Notes in Physics, Springer, New York), vol. 567, 351-391,(2001).
P. Martinet, Flow and clogging mechanisms in porous media with application to dams, doctoral thesis, The Royal Institute of Technology, Stockholm, Sweden, TRITA-AMI PHD 1017, 1998.
M.A.Koenders and A.F. Williams, Flow equations of particle fluid mixtures, Acta Mech., 92, 91-116,1992.
M.A.Koenders, Invited review article, A first order constitutive model for a particulate suspension of spherical particles, Acta Mech., 122, 1-19, 1997.
M.A.Koenders, J.R.F Arthur, and T. Dunstan, The behavior of granular materials at peak stress, yielding, damage and failure of anisotropic solids, EGF5, 805-818, 1990.
M.A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid, J. Acoust. Soc. Am. 28, 168-191 (1956).
N.R. Paterson, Seismic wave propagation in porous granular media, Geophysics VXXI(3), 691-714 (1955).
N.P. Chotiros, An inversion for Biot parameters in water-saturated sand, J. Acoust. Soc. Am. 112(5), 1853-1868 (2002).
N.A. Vilchinska and Y.L Dzilna, Resonance frequencies in sands, In: Field Measurements in Geo-mechanics. Edited by Geraldine Sørum (Balkema, Rotterdam, 1991), pp. 927-935.
T.J. Plona, Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies, Appl. Phys. Lett. 36(4), 259-261 (1980).
P.B. Nagy, L. Adler, and B.P. Bonner, Slow wave propagation in air- filled porous materials and natural rocks, Appl. Phys. Lett. 56, 2504-2506 (1990).
R.G. Stearns, Measurement of a multicomponent granular system using acoustic slow waves, J. Appl. Phys. 71(2), 606-611 (1992).
A. Moussatov, B. Castagnède, and V. Gusev, Observation of nonlinear interaction of acoustic waves in granular materials: Demoulation process, Phys. Lett. A 283, 216-223 (2001).
V.N. Nikolaevskii, Soviet Science Academic Doklady 283(3), 1321-1324 (1985) (in Russian).
V.N. Nikolaevskiy, Nonlinear models of waves in granulated partially wet media. In: Nonlinear Acoustics at the Beginning of the 21st Century. Edited by O.V.Rudenko and O.A.Sapozhnikov, Faculty of Physics, MSU, Moscow, 2002, Vol.1, 245-250.
V.E. Nazarov, A.V. Radostin, and Y.A. Stepanyants, Influence of water content in river sand on the self-brightening of acoustic waves, Appl. Acoust. 62, 1347-1358, (2001).
V.Yu. Zaitsev, A.B. Kolpakov, and V.E. Nazarov, Detection of acoustic pulses in river sand: experiment, Acoust. Phys. 45, 235-241, (1999).
F.D. Shields, and J.M. Sabatier, The effect of moisture on compressional and shear wave speeds in unconsolidated granular material, J. Acoust. Soc. Am. 108(5), 1998-2004 (2000).
J.E. White, Underground Sound. Application of Seismic Waves, Elsevier, Amstrdam, 1983.
V.G. Bykov Nonlinear Wave Processes in Geological Media, Vladivostok, Dalnauka, 2000 (in Russian).
T. Metcalf, J.B. Knight, and H.M. Jaeger, Surface patterns in shallow beds of vibrated granular material, Physica A, 236, 202 (1997).
Density waves in narrow pipe by Thorsten P öschel [http://www.edpsciences.org/articles/jp1/abs/1994/04/jp1v4p499/jp1v4p499.html].
Pattern formation in granular avalanches[http://www.ma.man.ac.uk/sngray/Papers/CMT 9 1997.pdf]}.
S.N. Coppersmith, C.-H. Liu, S. Majumdar, O. Narayan, and T.A. Witten, Model of force fluctuations in bead packs, Phys. Rev. E, 53, 4673 (1996).
D.M. Mueth, H.M. Jaeger, and S.R. Nagel, Force distribution in a granular medium, Phys. Rev. E 57,3164(1998).
O.V. Rudenko, Nonlinear methods in acoustic diagnostics, Russian J. Nondestructive Testing, 29(8), 583-588 (1993).
C.M.Hedberg, Nonlinear dynamics of grains in a liquid-saturated soil, In: Nonlinear Acoustics at the Beginning of the 21st Century. Edited by O.V.Rudenko and O.A.Sapozhnikov, Faculty of Physics,MSU, Moscow, 2002, Vol.2, 735-738.
O.V. Rudenko and C.M. Hedberg Nonlinear dynamics of grains in a liquid-saturated soil, Nonlinear Dynamics, 35, 2004, 187-200.
M.B. Vinogradova, O.V.Rudenko, A.P.Sukhorukov, Theory of Waves, Moscow, Nauka, 1990 (2nd edition, in Russian).
N.N. Kochina, P.Ya. Kochina, V.N. Nikolaevskii, The World of Underground Liquids, Earth Physics Institute, Moscow, 1994 (in Russian).
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Hedberg, C., Martinet, P. (2006). Nonlinear Dynamics in Granular Materials. In: Delsanto, P.P. (eds) Universality of Nonclassical Nonlinearity. Springer, New York, NY. https://doi.org/10.1007/978-0-387-35851-2_20
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