Three simple analytic expressions satisfying the limitation condition at low densities for the radial distribution function of hard spheres are developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan–Starling equation of state. The simplicity and precision for these expressions are superior to the well-known Percus–Yevick expression. The coefficients contained in these expressions have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of Percus-Yevick expression for the second coordination shell. One of the expressions has been applied to develop an analytic equation of state for the square-well fluid, and the numerical results are in good agreement with the computer simulation data.

With a two-step approach，a pressure，P，and temperature，T，dependent constitutive model of shear modulus，G，applicable to metals was developed in this work. The goal of the first step is to find the relation of G with P along 0 K isotherm，i.e. the functional form of G1=G1（P，0 K），and the second one is to find the relation of G，starting from a given state of （P，0 K） with a value that was already determined in the first step，with T along the isobar of P，i.e. the functional form of G=G（P，T） or the constitutive model proposed by us. In both steps，results of supersonic measurement and first principles calculation were used. Aluminum，as a model material，was utilized to validate the rationality of this model. It is demonstrated that the predicted results of this model are in satisfactory agreement with the measured and numerically simulated G despite whether it evolves along shock compressed，isentropic，isothermal，or isobaric loci，thereby displaying the rationality and the universal nature of this constitutive model.

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Flyers with wave impedance gradient can be regarded as a new kind of functionally graded material, which has come to show great potential for the application in dynamic high-pressure technology. In the present paper, a theoretical model of generating quasi-isentropic compression via the W-Mo-Ti system flyer was established, and the numerical simulation has been carried out. The results show that the design for flyers with graded wave impedance should conform to the parabolic or cubic function relationship of the change in the thickness. The thickness of target and the impact velocity should also be well controlled for creating a be tter quasi-isentropic compressive wave profile.

By means of molecular dynamics simulation and the effective optimized two_body Tosi-Fumi potential, the isothermal compression curve and thermophysical parameters of sodium chloride solids in the temperature range 298—1073?K are calculat ed.The result demonstrates that the Gruneisen parameter of sodium chloride γ= γ0(V/V0)q is approximately correct in the te mperature range 298—1073? K and the pressure range 0—80?GPa,and the exponent q in the formula is abo ut 1078.