Mapping from a fragile glass-forming system to a simpler one near their glass transitions

Extensive molecular-dynamics simulations on two different glass-forming systems are performed to test the prediction proposed recently by the mean-field theory (MFT) of glass transition that a fragile system can be mimicked by a simpler one near their glass transitions. One is a simulation for a hard-sphere fluid with size polydispersity where the volume fraction φ is a control parameter and the other is for a Lennard-Jones binary mixture where the inverse temperature 1/T is a control parameter. Then, their mean-square displacements are fully analyzed by MFT. Thus, we show that both results are collapsed on a master curve given by MFT when DSL(φ)=DSL(T), where DSL is a long-time self-diffusion coefficient. We also investigate the non-singular behavior of DSL consistently from a unified standpoint based on MFT. Thus, we show that macroscopic physical quantities in a fragile system can be transformed into those in a simpler one through a universal parameter DSL.