APPLICATION OF ALMOST-EVERYWHERE SINGULAR DISTRIBUTIONS IN CHEMICAL-ENGINEERING

Almost-everywhere singular (AES) distributions, usually referred to as multifractal measures, provide an intermediate link between atomic di stributions (distributions represented by a countable superposition of Dirac's delta terms) and smooth regular distributions. This article s houts how AES distributions can be rigorously treated in connection wi th distributed-parameter models and presents closed-form expressions a nd/or recursive, uniformly converging approximation methods for integr al transforms (Laplace and Stieltjes). In particular, exact results ar e obtained and discussed for linear and uniform nonlinear kinetics and for transport schemes in the presence of continuous mixtures. The phy sical origin of AES distributions in real systems is also detailed.