Monte Carlo simulations are adopted to study the distribution of the nonlinear electric field in the reaction field of diamond film growth at low temperature via EACVD. The results indicate that the distribution of the electric field near the anode in the reaction field changes by exponential rules. Under certain bias voltages with the changing of pressure, there will be a reverse electric field near the anode. This reverse electric field is very important to some positive ions in diamond film growth at low temperature.

A BGK model on the 2D adaptive unstructured mesh is developed within a finite volume framework, which consists of two steps:the solution reconstruction step and the gas evolution step. The computation domain is tessellated with triangular elements. In the reconstruction step, a high-order ENO scheme based on the least-square principle is employed to obtain the derivatives. In the gas evolution step, with the axis rotation, the flux through each side of the triangular element is obtained. Some test cases validate the capability of the current numerical approach to provide a highly accurate solution in complex geometries. It is observed that the BGK model provides a reasonable alternative to Riemann solvers.

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.