Asymptotic laws and preasymptotic correction formulas for the relaxation near glass-transition singularities

Within the mode-coupling theory (MCT) for the dynamics of simple liquids, the leading corrections to the asymptotic solutions for the relaxation in the vicinity of an ideal glass transition are derived. The formulas are used to determine the range of validity of the scaling-law description of the MCT results for the alpha and beta processes in glass-forming systems. Solutions of the MCT equations of motion are calculated for a hard-sphere colloidal suspension model and compared with the derived analytical results. The leading-order formulas are shown to describe the major qualitative features of the bifurcation scenario near the transition and the leading-plus-next-to-leading-order formulas are demonstrated to give a quantitative description of the evolution of structural relaxation for the model.