Universality in effective-conductivity of regular 2D and 3D composites

We have found that for variety of composite materials there is a domain of universal behaviour of the effective conductivity sigma (eff). This domain can be qualitatively characterized as a range of 'low contrast' of the comp onents (0.2 less than or equal to sigma (1)/sigma (2) less than or equal to 5). In the domain of the universality the equation sigma (eff) approximate to exp (Sigma n(i) ln sigma (1)) gives a good approximation for sigma (eff ) of all the investigated regular structures (2D and 3D composites, two and three component composites, isotropic and anisotropic composites, composit es with equal and different concentrations of components) as well for rando m random media (ZBLAN20 glass-forming melt). Equally these results are vali d for the thermal conductivity and diffusivity of the composite media.