FRACTAL DIMENSIONALITIES OF BROWNIAN TRAJECTORIES AND BROWN ISOSETS IN SUPERIONIC AND MOLTEN Ag//2S.

From the fractal point of view Brownian motion has two interesting aspects. One of them is concerned with the fractal behavior of Brownian trajectories and the other with isosets of Brown functions. Their fractal dimensionalities D and OVER BAR D are related through the relation D OVER BAR equals 1-1/D. For ordinary fluids D and D OVER BAR are expected to be 2 and one-half , respectively. Superionic conductors are a class of systems in which phenomena observed in fluids and solids come together in a most interesting manner. Silver sulfide in the superionic phase can be thought of as a strongly interacting Coulomb liquid in which the silver ions move under the effective one-body potential of cubic symmetry due to the bcc sulfur lattice. Unlike the superionic phase, sulfurs have a finite diffusion and silver and sulfur ions form an isotropic liquid. These results confirm Mandelbrot's prediction for the values D and D OVER BAR and the relation between them.