Homogenization of a reaction-diffusion system modeling sulfate corrosion in locally-periodic perforated domains

We discuss a reaction–diffusion system modeling concrete corrosion in sewer pipes. The system is coupled, semi-linear, and partially dissipative. It is defined on a locally-periodic perforated domain with nonlinear Robin-type boundary conditions at water-air and solid-water interfaces. We apply asymptotic homogenization techniques to obtain upscaled reaction–diffusion models together with explicit formulae for the effective transport and reaction coefficients. We show that the averaged system contains additional terms appearing due to the deviation of the assumed geometry from a purely periodic distribution of perforations for two relevant parameter regimes: (1) all diffusion coefficients are of order of O(1) and (2) all diffusion coefficients are of order of O("2) except the one for H2S(g) which is of order of O(1). In case (1), we obtain a set of macroscopic equations, while in case (2) we are led to a two-scale model that captures the interplay between microstructural reaction effects and the macroscopic transport

Oscillatory pulses in FitzHugh-Nagumo type systems with cross-diffusion

We study FitzHugh–Nagumo type reaction–diffusion systems with linear cross-diffusion terms. Based on an analytical description using piecewise linear approximations of the reaction functions, we completely describe the occurrence and properties of wavy pulses, patterns of relevance in several biological contexts, in two prototypical systems. The pulse wave profiles arising in this treatment contain oscillatory tails similar to those in travelling fronts. We find a fundamental, intrinsic feature of pulse dynamics in cross-diffusive systems—the appearance of pulses in the bistable regime when two fixed points exist

Homogenization of a reaction-diffusion system modeling sulfate corrosion in locally-periodic perforated domains

We discuss a reaction–diffusion system modeling concrete corrosion in sewer pipes. The system is coupled, semi-linear, and partially dissipative. It is defined on a locally-periodic perforated domain with nonlinear Robin-type boundary conditions at water-air and solid-water interfaces. We apply asymptotic homogenization techniques to obtain upscaled reaction–diffusion models together with explicit formulae for the effective transport and reaction coefficients. We show that the averaged system contains additional terms appearing due to the deviation of the assumed geometry from a purely periodic distribution of perforations for two relevant parameter regimes: (1) all diffusion coefficients are of order of O(1) and (2) all diffusion coefficients are of order of O("2) except the one for H2S(g) which is of order of O(1). In case (1), we obtain a set of macroscopic equations, while in case (2) we are led to a two-scale model that captures the interplay between microstructural reaction effects and the macroscopic transport