To be or not to be jammed

When are packings of soft athermal spheres jammed? Any experimentally relevant definition must at least require a jammed packing to resist compression and shear. Numerical algorithms usually rely on a global compression monitored by a parameter (like pressure) that signals whether the packing is jammed or not. Here we show that compression is not sufficient to ensure properly jammed packings : some of those packings have positive pressures and bulk moduli, but negative shear moduli, and even for large systems, the number of these ``bad apples'' diverges as the jamming point is approached. We will discuss how to understand this situation and propose as a remedy the boundary relaxation, that is including the boundary shape parameters as variables in the equilibration process; finally we will compare the distribution of shear moduli obtained for both methods.