Levy defects in fluctuating pattern of liquids. A quasi thermodynamic   approach to the dynamic glass transition in classical molecular liquids
  This theoretical paper is to advance a phenomenological, quasi thermodynamic approach to the dynamics of classical liquids which uses the Levy distribution of probability theory. Doubts from the chemical physics community about the application of its unusual properties to this field are tried to be removed. In particular, to understand the preponderant component of the Levy sum for Glarum Levy defects and Fischer speckles, the classical mathematical proof [D. A. Darling, Trans. Amer. Math. Soc. 73, 95 (1952)] for the existence and the influence of this component is accompanied by addition of physical arguments related to these defects. It is tried to explain an underlying fluctuating spatial pattern of free volume with weak contrast and a pattern of mobility with strong contrast, and to explain the characteristic lengths for the main transition and the Fischer modes. The structure of the relaxation chart (dynamic glass transition) and several properties of, and relations between, the slower dispersion zones therein, are reviewed for classical glassforming liquids of moderate complexity. For the main transition, the preponderant component is pushed in the midst of the defect and induces the molecule to its diffusion step across the cage door of the next neighbors. An Experimentum Crucis for an indirect proof of the existence of defects - via characteristic lengths - is also described. 
E. Donth