Shocks near Jamming
  Non-linear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are dynamically compressed, and demonstrate that the elementary excitations are strongly non-linear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity by a surprisingly simple analytical model. 
Leopoldo R. Gomez, Ari M. Turner, Martin van Hecke, and Vincenzo   Vitelli
cond-mat.soft cond-mat.mtrl-sci cond-mat.stat-mech