Singular perturbation theory of traveling waves in excitable media (a review)

JJ Tyson, JP Keener - Physica D: Nonlinear Phenomena, 1988 - Elsevier
Waves of chemical or electrical activity, traveling through space, have been observed in
several contexts: chemical reaction mixtures in non-convecting liquid phase, cell …

Micro-and nanotechnology via reaction–diffusion

BA Grzybowski, KJM Bishop, CJ Campbell… - Soft Matter, 2005 - pubs.rsc.org
Reaction–diffusion (RD) processes are common throughout nature, which uses them
routinely to build and control structures on length scales from molecular to macroscopic. At …

Nonlinear chemical dynamics: oscillations, patterns, and chaos

IR Epstein, K Showalter - The Journal of Physical Chemistry, 1996 - ACS Publications
Chemical reactions with nonlinear kinetic behavior can give rise to a remarkable set of
spatiotemporal phenomena. These include periodic and chaotic changes in concentration …

Front propagation into unstable states. II. Linear versus nonlinear marginal stability and rate of convergence

W Van Saarloos - Physical Review A, 1989 - APS
In an earlier paper, we developed a general physical picture for the linear-marginal-stability
mechanism governing the dynamics of front propagation into linearly unstable states. The …

Traveling fronts of methacrylic acid polymerization

JA Pojman - Journal of the American Chemical Society, 1991 - ACS Publications
Figure 1 shows the front position versus time for one experiment. The initial burst of heat
causes rapid propagation, but the front reaches a steady velocityafter a few minutes. Visual …

Reaction‐diffusion systems in intracellular molecular transport and control

S Soh, M Byrska… - Angewandte Chemie …, 2010 - Wiley Online Library
Chemical reactions make cells work only if the participating chemicals are delivered to
desired locations in a timely and precise fashion. Most research to date has focused on …

Nonlinear chemical dynamics

F Sagués, IR Epstein - Dalton transactions, 2003 - pubs.rsc.org
The interdisciplinary field of nonlinear chemical dynamics has grown significantly in breadth
and depth over the past three decades. Its subject matter and applications encompass all …

Discrete models for chemically reacting systems

R Kapral - Journal of Mathematical Chemistry, 1991 - Springer
Nonequilibrium spatially distributed chemically reacting systems are usually described in
terms of reaction-diffusion equations. In this article, a hierarchy of discrete models is studied …

Convective effects on chemical waves. 1. Mechanisms and stability criteria

JA Pojman, IR Epstein - Journal of Physical Chemistry, 1990 - ACS Publications
We consider the effects of convection on chemical waves in which density gradients result
from the exothermicity as well as from the isothermal volumechange of the reaction. If the …

Convective instabilities in traveling fronts of addition polymerization

JA Pojman, R Craven, A Khan… - The Journal of Physical …, 1992 - ACS Publications
Traveling fronts of polymerization have been observed in unstirred solutions of methacrylic
acid and benzoyl peroxide. Three types of convective instabilities have been observed.(1) …