We investigate the statistical properties and ordering-disordering states colloidal particle interacting through a long range repulsive Yukawa potential, confined by a 2D periodic substrate potential.

The study of ordering of colloidal particles and the variation of the statistical quantities of them resemble that of a KBT-like defect topological in low temperature phase. We found a strong dependence of the substrate strength on arrangement of the particles and the diffusive behavior of them. We study the equilibrium properties such as order parameter, potential per energy and heat capacity through a Monte Carlo simulation. The evolution of the correlation function with increasing temperature is also discussed.

In addition, we perform the dynamic properties of particles structure through a MD simulation, which cannot provide by equilibrium sampling method. Specifically, we study the fluctuation of velocity and instantaneous temperature of particles versus the time-step. By studying of these quantities, we finally reach to an equilibrium steady state system, which is completely dependent to the substrate strength and density of particles.