From Stochastic Interacting Particle Systems (IPS) Models to Lattice Differential Equations for Reaction-diffusion Processes
Monday, April 1, 2013 - 10:30am - 12:00pm
A realistic molecular-level description of reaction-diffusion processes is often provided by spatially-discrete stochastic interacting particle systems (IPS). Spatially discreteness may be innate to the system (e.g., for reactions on 2D crystalline catalyst surfaces), or may just be a convenient modeling tool (e.g., for reactions in 1D nanoporous materials). Spatially homogeneous and heterogeneous state in these IPS can be described exactly by hierarchical master equations. These reduce to lattice differential equations, i.e., to discrete reaction-diffusion equations (RDE), after making a hierarchical truncation approximation, and the discrete RDE become continuum RDE in the hydrodynamic limit of rapid diffusion. However, the correct description of diffusion is invariably non-trivial (with concentration-dependent and tensorial diffusion coefficients), and not captured by simple approximations. Examples are provided for simple models for reaction fronts in bistable reactions such as CO-oxidation on 2D surfaces, and for catalytic conversion inside 1D linear nanopores.