A generic phenomenological theory of the glass transition is developed in the framework of a quasilinear formulation of the thermodynamics of irreversible processes. Starting from one of the basic principles of this science in its approximate form given by de Donder’s equation, after a change of variables the temperature dependence of the structural parameter ξ(T), the thermodynamic potentials ΔG̃(T), the thermodynamic functions and the time of molecular relaxation τ of vitrifying systems is constructed. In doing so, a new effect in the ΔG̃(T) course is observed. The analysis of the higher derivatives of the thermodynamic potential, and especially the nullification of the second derivative of the configurational specific heats ΔC̃p(T) of the vitrifying liquid defines glass transition temperature T̃g and leads directly to the basic dependence of glass transition kinetics: the Frenkel–Kobeko–Reiner equation. The conditions guaranteeing the fulfillment of this equation specify the temperature dependence of the activation energy U(T,ξ̃) for viscous flow and give a natural differentiation of glass formers into fragile and strong liquids. The effect of thermal prehistory on the temperature dependence of both thermodynamic functions and kinetic coefficients is established by an appropriate separation of de Donder’s equation.
Two basic approaches to the cluster counting task in the percolation and related models are discussed. The Hoshen-Kopelman multiple labeling technique for cluster statistics is redescribed. Modifications for random and aperiodic lattices are sketched as well as some parallelised versions of the algorithm are mentioned. The graph-theoretical basis for the spanning tree approaches is given by describing the breadth-first search and depth-first search procedures. Examples are given for extracting the elastic and geometric "backbone" of a percolation cluster. An implementation of the "pebble game" algorithm using a depth-first search method is also described.
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