Localized vibrations in slider-block models

We consider linear and two-dimensional arrays of slider blocks connected by springs. The blocks interact with a surface through a static coefficient of friction; the dynamic friction is taken to be zero so that energy is conserved. The initial energy of the system is prescribed and the only control parameter μ is proportional to the ratio of the mean initial energy to the static frictional force squared. “Molecular-dynamics” simulations of the temporal evolution of these systems have been carried out. For arbitrary initial conditions the arrays self-organize into patches of oscillating blocks with a dominant normal mode vibration. The fraction of blocks within the oscillating patches is almost independent of the prescribed energy, but the size of the patches systematically increases with increasing energy. The larger patches accommodate the larger available energies. The behavior of these systems is strikingly different from the behavior seen in regular slider-block models.