where D i j is a diffusion matrix specifying hydrodynamic interactions, Oseen tensor for example, in non-diagonal entries interacting between the target particle i and the surrounding particle j , F is the force exerted on the particle j , and R ( t ) is a Gaussian noise vector with zero mean and a standard deviation of 2 D Δ Δ t in each vector entry. The subscripts i and j indicate the ID of the particles and N refers to the total number of particles. This equation works for the dilute system where the near-field effect is ignored.