Local characterization of phase diagrams

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Abstract
A classification of the local topological type of phase diagrams for fluid mixtures is obtained. The classification derives from ideas of Thom and results of Arnol'd in the theory of singularities of smooth real-valued functions, together with the assumption that the state of the system corresponds to a minimum of a smooth function on a space of internal variables which can have arbitrarily high dimension. Griffith's notions of elementary and compound entities emerge in a natural manner. The methods used are phenomenological. Some attention is given to the question of why these seem to work so well and how they might be rigorously established.

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