  We demonstrate the existence of high--order jamming crossovers in systems of
particles with repulsive contact interactions, which originate from the
collapse of successive coordination shells. At zero temperature, these
crossovers induce an anomalous behavior of the bulk modulus, which varies
non--monotonically with the density, while at finite temperature they induce
density anomalies consisting in an increased diffusivity upon isothermal
compression and in a negative thermal expansion coefficient. We rationalize the
dependence of these crossovers on the softness of the interaction potential,
and relate the jamming crossovers and the anomalous diffusivity through the
investigation of the vibrational spectrum.
