A Multiscale Method for Interacting Particle Systems

Motivated by biological ion channels, we develop a new multiscale method for interacting particle systems coupling a particle and a continuum model. The method aims at the computation of particle interactions on the molecular scale and therefore incorporates particle correlations induced by short and long range interactions. To construct the multiscale method we use a stochastic particle model and derive a macroscopic equation hierarchy using the Fokker-Planck equation. Instead of closing the hierarchy by the molecular chaos assumption, we use the particle model to compute a closure to the equation hierarchy. We perform numerical experiments comparing the multiscale method to the stochastic particle model and a mean-field equation which can be interpreted as the hierarchy closed by the molecular chaos assumption. We find that under some restrictions the method is capable to handle long range and also additional short range interactions.