  We investigate the propagation and scattering of highly nonlinear waves in
disordered granular chains composed of diatomic (two-mass) units of spheres
that interact via Hertzian contact. Using ideas from statistical mechanics, we
consider each diatomic unit to be a "spin", so that a granular chain can be
viewed as a spin chain composed of units that are each oriented in one of two
possible ways. Experiments and numerical simulations both reveal the existence
of two different mechanisms of wave propagation: In low-disorder chains, we
observe the propagation of a solitary pulse with exponentially decaying
amplitude. Beyond a critical level of disorder, the wave amplitude instead
decays as a power law, and the wave transmission becomes insensitive to the
level of disorder. We characterize the spatio-temporal structure of the wave in
both propagation regimes and propose a simple theoretical interpretation for
such a transition. Our investigation suggests that an elastic spin chain can be
used as a model system to investigate the role of heterogeneities in the
propagation of highly nonlinear waves.
