Dissipative solitary waves in granular crystals (original) (raw)

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 common dissipation exponent with a material-dependent prefactor. PACS numbers: 05.45.Yv, 43.25.+y, 45.70.-n, 46.40.Cd Introduction. Since the advent of the famous Fermi-Pasta-Ulam model over fifty years ago, nonlinear oscillator chains have received a remarkable amount of attention in a wide range of physical settings [1]. Areas of intense theoretical and experimental interest over the last decade include (but are not limited to) DNA doublestrand dynamics in biophysics [2], coupled waveguide arrays in nonlinear optics [3], breathing oscillations in micromechanical cantilever arrays [4], and Bose-Einstein condensation in optical lattices in atomic physics [5].

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