"Coarse" integration/bifurcation analysis via microscopic simulators: micro-galerkin methods
I will present a time-stepper based approach to the ``coarse" integration and stability/bifurcation analysis of distributed reacting system models. The methods I will 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, I will illustrate how the microscopic simulator can be enabled (through a computational superstructure) to perform certain
integration and numerical bifurcation analysis tasks at the coarse, systems-level directly. This approach, when successful, can circumvent the derivation of accurate, closed form, macroscopic PDE descriptions of the system.
Facilitating, through such numerical "enabling technologies" the direct, systems level analysis of microscopic process models may advance our understanding and use of nonequilibrium systems.