Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-09-08
Soft Matter 6, 3007 (2010)
Physics
Condensed Matter
Disordered Systems and Neural Networks
6 pages, 1 figure
Scientific paper
We study the attenuation of long-wavelength shear sound waves propagating through model jammed packings of frictionless soft spheres interacting with repulsive springs. The elastic attenuation coefficient, $\alpha(\omega)$, of transverse phonons of low frequency, $\omega$, exhibits power law scaling as the packing fraction $\phi$ is lowered towards $\phi_c$, the critical packing fraction below which rigidity is lost. The elastic attenuation coefficient is inversely proportional to the scattering mean free path and follows Rayleigh law with $\alpha(\omega)\sim \omega^4 (\phi - \phi_c)^{-5/2}$ for $\omega$ much less than $\omega^* \sim (\phi - \phi_c)^{1/2}$, the characteristic frequency scale above which the energy diffusivity and density of states plateau. This scaling of the attenuation coefficient, consistent with numerics, is obtained by assuming that a jammed packing can be viewed as a mosaic composed of domains whose characteristic size $\ell^ * \sim (\phi-\phi_c) ^{-1/2}$ diverges at the transition.
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