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The dynamics of random walkers under the influence of an external potential can be described by a stochastic partial differential equation (SPDE) known as the Dean-Kawasaki equation. However, the SPDE description breaks down when the local number density is sufficiently small. In this talk, we describe a hybrid algorithm that models the system using the SPDE when the number density is large but dynamically switches to a particle description when the number density is small. The coupling between the different models is based on a generalization of the basic adaptive mesh refinement (AMR) methodology. We discuss how to use the core AMR tools in AMReX to implement this type of algorithm and present some numerical examples illustrating the behavior of the algorithm.
