In the first part of this talk I will give a very brief overview on what questions on glasses can be addressed by means of computer simulations. As a result I will argue why the response to the above question is "No". In the second part of the talk I will discuss a method, called "parallel tempering", that allows to overcome one of the big issues encountered in the simulation of glasses, the equilibration at low fictive temperatures.

We use large scale computer simulations of a glass-forming liquid in which a fraction c of the particles has been permanently pinned. We find that the relaxation dynamics shows an exponential dependence on c. This result can be rationalized by assuming that the configurational entropy of the pinned liquid decreases linearly upon increasing of c. This behavior is discussed in the context of thermodynamic theories for the glass transition, notably the Adam-Gibbs picture and the random first order transition theory. For intermediate and low temperatures we find that the slowing down of the dynamics due to the pinning saturates and that the cooperativity decreases with increasing c, results which indicate that in glass-forming liquids there is a dynamic crossover at which the shape of the relaxing entities changes.

We study the relaxation dynamics of a binary Lennard-Jones liquid in the presence of an amorphous wall generated from equilibrium particle configurations. In qualitative agreement with the results presented in Nature Phys. {\bf 8}, 164 (2012) for a liquid of harmonic spheres, we find that our binary mixture shows a saturation of the dynamical length scale close to the mode-coupling temperature $T_c$. Furthermore we show that, due to the broken symmetry imposed by the wall, signatures of an additional change in dynamics become apparent at a temperature well above $T_c$. We provide evidence that this modification in the relaxation dynamics occurs at a recently proposed dynamical crossover temperature $T_s > T_c$, which is related to the breakdown of the Stokes-Einstein relation. We find that this dynamical crossover at $T_s$ is also observed for a system of harmonic spheres as well as a WCA liquid, showing that it may be a general feature of glass-forming systems.

We use large-scale molecular dynamics simulations of a simple glass-forming system to investigate how its liquid-gas phase separation kinetics depends on temperature. A shallow quench leads to a fully demixed liquid-gas system whereas a deep quench makes the dense phase undergo a glass transition and become an amorphous solid. This glass has a gel-like bicontinuous structure that evolves very slowly with time and becomes fully arrested in the limit where thermal fluctuations become negligible. We show that the phase separation kinetics changes qualitatively with temperature, the microscopic dynamics evolving from a surface tension-driven diffusive motion at high temperature to a strongly intermittent, heterogeneous and thermally activated dynamics at low temperature, with a logarithmically slow growth of the typical domain size. These results shed light on recent experimental observations of various porous materials produced by arrested spinodal decomposition, such as nonequilibrium colloidal gels and bicontinuous polymeric structures, and they elucidate the microscopic mechanisms underlying a specific class of viscoelastic phase separation.