  We investigate the energy transport in one-dimensional disordered granular
solids by extensive numerical simulations. In particular, we consider the case
of a polydisperse granular chain composed of spherical beads of the same
material and with radii taken from a random distribution. We start by examining
the linear case, in which it is known that the energy transport strongly
depends on the type of initial conditions. Thus, we consider two sets of
initial conditions: i) an initial displacement and ii) an initial momentum
excitation of a single bead. After establishing the regime of sufficiently
strong disorder, we focus our studies on the role of nonlinearity for both sets
of initial conditions. By increasing the initial excitation amplitudes we are
able to identify three distinct dynamical regimes with different energy
transport properties: a near linear, a weakly nonlinear and a highly nonlinear
regime. Although energy spreading is found to be increasing for higher
nonlinearities, in the weakly nonlinear regime no clear asymptotic behavior of
the spreading is found. In this regime, we additionally find that energy,
initially trapped in a localized region, can be eventually detrapped and this
has a direct influence on the fluctuations of the energy spreading. We also
demonstrate that in the highly nonlinear regime, the differences in energy
transport between the two sets of initial conditions vanish. Actually, in this
regime the energy is almost ballistically transported through shock-like
excitations.
