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We use computer simulations to study the glass transition of dense fluidsmade of polydisperse, repulsive spheres. For hard particles, we vary the volumefraction, phi, and use compressible particles to explore finite temperatures,T>0. In the hard sphere limit, our dynamic data show evidence of an avoidedmode-coupling singularity near phi_{MCT} ~ 0.592, they are consistent with adivergence of equilibrium relaxation times occurring at phi_0 ~ 0.635, but theyleave open the existence of a finite temperature singularity for compressiblespheres at volume fraction phi > phi_0. Using direct measurements and a newscaling procedure, we estimate the equilibrium equation of state for the hardsphere metastable fluid up to phi_0, where pressure remains finite, suggestingthat phi_0 corresponds to an ideal glass transition. We use non-equilibriumprotocols to explore glassy states above phi_0 and establish the existence ofmultiple equations of state for the unequilibrated glass of hard spheres, alldiverging at different densities in the range phi \in [0.642, 0.664].Glassiness thus results in the existence of a continuum of densities wherejamming transitions can occur.

The glass transition of dense fluids of hard and compressible spheres