关于硬球流体的Carnahan-Starling状态方程的改进

使用Weierstrass和Chebyshev定理， 并参考标度粒子理论和Percus-Yevick积分方程理论的状态方程，证明硬球流体存在一个多项式序列，致使其状态方程由该序列的极限给出. 获得了从三阶到八阶的最佳多项式，这样Carnahan-Starling方程可以逐级改进. 得到的状态方程和在稳定和亚稳定流体分支上的模拟结果符合得很好.

Improvement on the Carnahan-Starling Equation of State for Hard-sphere Fluids

Making use ofWeierstrass's theorem and Chebyshev's theorem and referring to the equations of state of the scaled-particle theory and the Percus-Yevick integration equation, we demon-strate that there exists a sequence of polynomials such that the equation of state is given by the limit of the sequence of polynomials. The polynomials of the best approximation from the third order up to the eighth order are obtained so that the Carnahan-Starling equation can be improved successively. The resulting equations of state are in good agreement with the simulation results on the stable fluid branch and on the metastable fluid branch.