Pattern formation in reacting systems: Continuum modeling, experiments and stochastic simulations

Our work focuses on the computational study of spatiotemporal pattern formation in catalytic CO oxidation on microcomposite and microaddressable Pt(110) surfaces. We also demonstrate the implementation of new numerical methodologies for the analysis of two special types of dynamical systems.; The first part of the work explores heterogeneous catalytic reactions in complex geometries; in particular, we study the effect of two-dimensional composite catalyst geometry and spatiotemporal laser heating on the dynamics of CO oxidation on a Pt (110) surface. The project involves a combination of modeling, computation and experimentation, with the supporting experiments performed by our collaborators Dr. C. Punckt, Dr. H. H. Rotermund and Prof. G. Ertl at the Fritz-Haber-Institut in Berlin. We study reacting pulse propagation in curved catalytic channels (two-dimensional rings). The effects of operating parameters (such as reactant gas-phase pressures) as well as geometry design parameters (such as channel width and curvature) are quantified. We show, using custom-designed Y-shaped catalyst junctions, how to direct the propagation of reacting pulses by varying the details of the geometry. We demonstrate through both simulation and specially designed experiments that local laser heating actuation appropriately designed in space and time can be critical in directing the reactive pulse propagation. We also explore the effect of spatiotemporally varying substrate temperature profiles on the dynamics of CO oxidation on Pt(110). Experiments and modelling are used to rationalize the existence of a characteristic maximum in the averaged surface reaction rate when the catalytic surface is scanned by a focused laser beam at different speed.; We implement "equation-assisted" computation, a modification of the so-called "equation-free" algorithms, to investigate computationally pattern formation in reactiondiffusion models of morphogenesis (in collaboration with Dr. R. Erban at Oxford University). The reasoning behind this work is that, when accurate macroscopic closures for an atomistic simulation model (generally in the form of partial differential equations) are not available, we can exploit a "not-so-accurate" macroscopic description of the system to construct a preconditioner that accelerates computations based on microscopic/stochastic simulators.; We also develop a statistical parametric analysis framework to study the dynamics of cellular signalling pathways characterized by high levels of uncertainty in the parameters (in collaboration with Prof. Shvartsman at Princeton). We argue that, for such systems, model analysis should emphasize the statistics of systems-level properties (e.g. various types of dynamics), rather than the detailed structure of solutions or boundaries separating different dynamic regimes.