Dissipative Solitary Waves in Granular Crystals

Details Dissipative Solitary Waves in Granular Crystals Dissipative Solitary Waves in Granular Crystals

2008-12-03

arxiv.org/abs/0812.0662v1

Phys. Rev. Lett. 102 (2009) 024102

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 4 figures, accepted in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.102.024102

We provide a quantitative characterization of dissipative effects in one-dimensional granular crystals. We use the propagation of highly nonlinear solitary waves as a diagnostic tool and develop optimization schemes that allow one to compute the relevant exponents and prefactors of the dissipative terms in the equations of motion. We thereby propose a quantitatively-accurate extension of the Hertzian model that encompasses dissipative effects via a discrete Laplacian of the velocities. Experiments and computations with steel, brass, and polytetrafluoroethylene reveal a {\em common} dissipation exponent with a material-dependent prefactor.

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