With three-dimensional(3D) filtering in Monte Carlo rough dose distributions with less particle history and short simulation time convergence is accelerated.We improve 3D Gaussian and Savitzky-Golay filters considering features of Monte Carlo dose distribution. Parallel and cascade mixture methods with 3D Gaussian and Savitzky-Golay filters are compared.A method simplifying mixture filter structure using equivalent convolution kernel is put forward.It shows that the improved Gaussian and Savitzky-Golay filters enhance denoising.The mixture filter reduces local errors of filtering results.Two types of mixture filters reduce noise in Monte Carlo dose distributions.Filtering of cascade mixture filter is slightly better than that of parallel mixture filter.

The percolation threshold and critical parameters are obtained for the site-percolation problem on the square lattice with next-nearest-neighbour interactions by using Monte Carlo position space renormalization group procedure.It is shown that the site percolaton problems on the square lattice with next-nearest-neighbour interactions belongs to the same universality class as that with nearest-neighbour interactions.