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The breakdown of the Stokes-Einstein (SE) law in fragile glassformers is examined by Molecular-Dynamics simulations of atomic liquids and polymers and consideration of the experimental data concerning the archetypical ortho-terphenyl glassformer. All the four systems comply with the universal scaling between the viscosity (or the structural relaxation) and the Debye-Waller factor ⟨u2⟩, the mean square amplitude of the particle rattling in the cage formed by the surrounding neighbors. It is found that the SE breakdown is scaled in a master curve by a reduced ⟨u2⟩. Two approximated expressions of the latter, with no and one adjustable parameter, respectively, are derived.
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