The book contains the only available complete presentation of the
mode-coupling theory (MCT) of complex dynamics of glass-forming
liquids, dense polymer melts, and colloidal suspensions. It
describes in a self-contained manner the derivation of the MCT
equations of motion and explains that the latter define a model for
a statistical description of non-linear dynamics.
It is shown that the equations of motion exhibit bifurcation
singularities, which imply the evolution of dynamical scenarios
different from those studied in other non-linear dynamics theories.
The essence of the scenarios is explained by the asymptotic
solution theory of the equations of motion. The leading-order
results deal with scaling laws and the range of validity of these
general laws is obtained by the derivation of the
leading-correction results.
Comparisons of numerical solutions of the MCT equations of motion
with the results of the analytic results of the asymptotic analysis
demonstrate various facets of the MCT dynamics. Some comparisons of
MCT results with data are used to show the relevance of MCT for the
discussion of amorphous matter dynamics.
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