In this work, we present a reduced-order model for nonlinear cross-diffusion problem from population dynamics, the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volterra kinetics. The finite-difference discretization of SKT in space results system linear--quadratic ordinary differential equations (ODEs). reduced order (ROM) has same linear-quadratic structure as full (FOM). Using ROM, s...

In this study, we demonstrate how the diffusion of probe particles in aqueous poly(vinyl alcohol) (PVA) solutions and gels is affected by: (i) the presence of cross-links, (ii) the cross-link density, (iii) the polymer concentration. We apply fluorescence correlation spectroscopy (FCS) to measure the diffusion time of a rhodamine-based fluorescent particle (TAMRA) and TAMRA-labeled dextran in P...

We explore the effects of cross-diffusion dynamics in epidemiological models. Using reaction–diffusion models infectious disease, we explicitly consider situations where an individual a category will move according to concentration individuals other categories. Namely, model susceptible moving away from infected and individuals. Here, show that including these results delay onset epidemic incre...