OÕHern simulation: isotropic hard particle pack
Place soft frictionless spheres in a box at random at high density
 
 
compressed
Slowly shrink spheres until pressure¨0
Find closest configuration of minimum energy
marginally jammed
Maintain equilibrium
Scaling properties near jamming threshold Þ well characterized.
f ¼ fc
log(pressure)
log(f - fc)
Hertzian interaction
Harmonic interaction
volume fraction
Anomalous excitations of jammed-together particles.The arrangement of grains in a static sandpile is dictated by kinetics.  The particles are mutually trapped in the first stable configuration they encounter.  Glassy materials share this quenched or jammed character.  Both systems share another property: a great excess of slow vibrational modes.  The recent simulation of marginal jamming by the Nagel group shows a constant density of modes extending to zero frequency, in qualitative contrast to the density of acoustic modes of an elastic solid.  This behavior forces us to ask: "What is the counterpart of acoustic modes in a marginally jammed solid?"  This talk describes a theory of these anomalous modes by Matthieu Wyart, Sidney Nagel and T. Witten.  A variational argument shows that any minimally-connected (isostatic) solid must have a nonzero density of extended, lowest-frequency modes.  We account for the observed crossover to ordinary solid behavior with increasing compression and connectivity.  We comment on the implications of these modes for molecular glasses.