The investigator is developing a calculus of stochastic partial differential equations (SPDEs) for the distribution of particles and vortices. These SPDEs are partial differential equations (PDEs) of parabolic type which are corrected by an additional fluctuation term. The fluctuation term has to be derived from the particle distribution. One of the advantages of this approach is that all quantities in the SPDE can be interpreted in physical terms, and conservation laws will hold for the SPDE if they hold for the underlying physical model. The investigator is developing a method of studying stochastic systems which arise in theoretical physics, fluid dynamics, chemistry and various fields of mathematics. The quantities in the models can be interpreted in physical terms, which should help in the analysis.
