Energy Propagation in Classical Harmonic Lattices with Diluted Disorder

We consider the problem of a harmonic lattice in which masses' distribution is a superposition of a random and a periodic distribution. Classical equations for the mass displacement and velocities are solved using a second-order Euler formalism. Energy flow was investigated on two distinct experiments: (i) We injected an initial wave-packet with energy E (0) and analyzed the dynamics of the resulting energy pulse; (ii) we pumped one of the sides of the lattice with a external signal and then we observed the propagation of the pulse until the other side of chain. Our calculations suggest that the diluted disordered mass distribution promotes energy dynamics at high frequency limit.