3.9 Modeling collisions in PIC simulations

(check**However, the grid-less approach in particle method makes it difficult to handle general Landau collision operators that involve the velocity gradients of the distribution function and evaluating these gradients usually needs velocity grids. For some simple collision operators, a corresponding Langevin equation can be constructed, which makes the collisional effect be able to be modeled by stochastic change in marker trajectories. However, this correspondence can not be found for all collisional operators.)