'Coarse' integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods

We present a time-stepper based approach to the 'coarse' integration and stability/bifurcation analysis of distributed reacting system models. The methods we discuss are applicable to systems for which the traditional modeling approach through macroscopic evolution equations (usually partial differential equations, PDEs) is not possible because the PDEs are not available in closed form. If an alternative, microscopic (e.g. Monte Carlo or Lattice Boltzmann) description of the physics is available, we illustrate how this microscopic simulator can be enabled (through a computational superstructure) to perform certain integration and numerical bifurcation analysis tasks directly at the coarse, systems level. This approach, when successful, can circumvent the derivation of accurate, closed form, macroscopic PDE descriptions of the system. The direct 'systems level' analysis of microscopic process models, facilitated through such numerical 'enabling technologies', may, if practical, advance our understanding and use of nonequilibrium systems.