Dynamics of chemical reacting systems in low dimensional lattices via the Equation Free Method

In this report we show how it is possible to reconstruct the dynamics of a chemical reacting systems on lattice via an appropriate choice of macroscopic variable set. When chemical reactions fire on a low dimensional setting the usual mean field approximation (MF) may fail to accurately describe the proper dynamics of the system. Consequently it is not possible to use the concentrations of different species as sole quantities to describe macroscopically such systems and more involved approximations are needed. Traditional approaches introduces higher order correlation functions as extra macroscopic variables, however such expansions usually require closure procedures and tend to quickly demand high number of terms even for simple systems. It is also possible to describe the system in a microscopic way via a Kinetic Monte Carlo (KMC) algorithm, but this approach requires much longer computation time. In this report we study such a problem from a different perspective using the Equation Free Method (EFM) framework; with such approach it is possible to "bridge" between the macroscopic dynamics (mean field) and the microscopic one (KMC). We analyze different techniques to move between these two descriptions of the system trying to understand what information needs to be preserved at the macroscopic level in order to recover correctly all the features of the microscopic dynamics.