Modelling of Spatially Extended Open Chemical Systems

The development of open well-mixed chemical reactors led to tremendous advances in the understanding of the temporal behavior of nonlinear chemical systems. For instance, many transitions between different asymptotic states of the system are now well understood in terms of bifurcation theory. However, for spatially extended (unmixed) reactions, only closed systems were experimentally available, and theoretical investigation of such systems naturally focused on matters other than bifurcations between the asymptotic states of the system. The recent introduction of open, unmixed chemical systems has now thrown open the door to theoretical investigation of these systems in terms of the different asymptotic states available to the system, as well as how and when the system can undergo transitions from one state to another. We have formulated models for several such open chemical systems, and have used both analytic and numerical methods to study various aspects of their dynamical behavior. We examine the bifurcations that occur between the different kinds of spatio-temporal structures that can appear in these systems. We will consider the effects that spatial inhomogeneities, both intended and not, can have on the dynamical behavior of these structures. We will also examine in several contexts the connection between the complex spatio-temporal structures in the extended system and the underlying local behavior of the chemistry. This will lead to a qualitative understanding of why the system is doing what it is. We will also examine the process of convection-enhanced diffusion, which is used in some open spatially-extended chemical systems to increase the size of the spatial patterns occurring in the system.