It has been established that the low frequency quasi-localized modes of amorphous solids at zero temperature exhibit universal density of states, depending on the frequencies as D(ω) ∼ ω 4. It remains an open question whether this universal law extends to finite temperatures. In this Letter we show that well quenched model glasses at temperatures as high as Tg/3 possess the same universal density of states. The only condition required is that average particle positions stabilize before thermal diffusion destroys the cage structure of the material. The universal density of quasilocalized low frequency modes refers then to vibrations around the thermally averaged configuration of the material.

We present large-scale molecular dynamics simulations to study the free evolution of granular gases. Initially, the density of particles is homogeneous and the velocity follows a Maxwell-Boltzmann (MB) distribution. The system cools down due to solid friction between the granular particles. The density remains homogeneous, and the velocity distribution remains MB at early times, while the kinetic energy of the system decays with time. However, fluctuations in the density and velocity fields grow, and the system evolves via formation of clusters in the density field and the local ordering of velocity field, consistent with the onset of plug flow. This is accompanied by a transition of the velocity distribution function from MB to non-MB behavior. We used equal-time correlation functions and structure factors of the density and velocity fields to study the morphology of clustering. From the correlation functions, we obtain the cluster size, L, as a function of time, t. We show that it exhibits power law growth with L(t)∼t^{1/3}.

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