PRESS probability dynamics
This framework applies well to situations where the presence of a few molecules (e.g. as catalysts) dramatically affects the local processing fate of the system. This is usually the case in evolving chemical or biological systems. PRESS is an acronym for Probability Reduced Evolution of Spatially Discrete Species. The PRESS platform extends stochastic chemical system dynamics to the spatial domain, making use of a self-consistent probabilty field theoretical framework. The master equations for the time evolution of the probabilities of local occupation of a site with discrete numbers of chemicals are coupled self-consistently to the probability dynamics on other sites. The formulation admits an analytic treatment of stationary solutions and efficient integration of dynamics via coupled ODEs in the general case. It has been tested against Monte Carlo simulations of the full spatial systems in 2D and 3D for various catalytic chemical processes.