Flow and diffusion distributed structures (FDS) are stationary spatially periodic patterns that can be observed in reaction-diffusion-advection systems. These structures arise when the flow rate exceeds a certain bifurcation point provided that concentrations of interacting species at the inlet...

Stem-cell niches represent microscopic compartments formed of environmental cells that nurture stem cells and enable them to maintain tissue homeostasis. The spatio–temporal kinetics of proliferation and differentiation of cells in such niches depend on the specifics of the niche structure and...

We establish rigorous upper and lower bounds for the speed of pulled fronts with a cut-off. For all reaction terms of KPP type a simple analytic upper bound is given. The lower bounds however depend on details of the reaction term. For a small cut-off parameter the two leading order terms in the...

By comparing microscopic traffic flow models with a different number of phases in the context of a simple scenario, the similarities as well as the differences of the various traffic flow models can be discussed. It turns out that there is a certain range of traffic flow conditions, where it is...