Hard discs in circular cavities: density functional theory versus simulation

Three different density functional approaches, namely the Rickayzen, Takamiya-Nakanishi and Rosenfeld approximations, have been employed to study the equilibrium particle density distributions of hard-disc fluids in hard circular cavities. Also, Monte Carlo simulations have been performed to test the theoretical results. The comparison with the simulation data shows that the Rosenfeld approximation, which is based on the fundamental geometrical measures of the particles, is better than the Takamiya-Nakanishi and Rickayzen approximations and yields good agreement with the computer simulation data even for higher densities.