In the conventional Avrami–Kolmogorov–Johnson–Mehl model, the reaction or phase transition occurring in the 2D or 3D infinite medium is considered to start and proceed around randomly distributed and/or appearing nucleation centers. The radius of the regions transformed is assumed to...

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...

We study the transient dynamics of single species reaction diffusion systems whose reaction terms f(u) vary nonlinearly near u ≈ 0, specifically as f(u) ≈ u<Superscript>2</Superscript> and f(u) ≈ u<Superscript>3</Superscript>. We consider three cases, calculate their traveling wave fronts and speeds analytically and solve the equations...</superscript></superscript>

We have investigated the influence of a weak radial temperature gradient in a wide gap and large aspect ratio Couette-Taylor system. The inner cylinder is rotating and can be heated or cooled, the outer cylinder is at rest and immersed in a large thermal bath. We found that a radial temperature...

We study the propagation of periodic pulse trains in excitable media exposed to external spatio-temporal noise using the light-sensitive Belousov-Zhabotinsky reaction with the underlying Oregonator model as representative example. In the weak noise approximation we find noise-induced transitions...