Correlated disorder suppresses solitary-wave attenuation in Hertzian chains

Mass disorder attenuates solitary waves traveling through Hertzian chains in a way that resembles viscous damping, even though the microscopic dynamics remains Hamiltonian and conserves energy. We show that this attenuation depends not only on the strength of the disorder, but also on its spatial organization. While the leading pulse remains identifiable, simulations reveal an approximately exponential decay, with an attenuation rate proportional to the mass variance in the weak-disorder regime. At fixed variance, spatial correlations are found to considerably reduce the attenuation rate. We describe this suppression using a spectral-overlap framework, in which attenuation depends on how the disorder spectrum couples to the response of the solitary wave. This response is measured directly using sinusoidally graded chains: long-wavelength variations interact weakly with the pulse, whereas variations at shorter spatial scales scatter it more strongly. The apparent damping therefore reflects a redistribution of energy from the coherent pulse into secondary excitations and an irregular wake, rather than true dissipation.