The method allows the development of perturbation theories for high-density fluids without necessitating a density-dependent hard-sphere diameter. We refer to the approach as double-hard-sphere (DHS) perturbation theory. When applied using a Weeks-Chandler-Andersen (WCA) division of the intermolecular...
The hard sphere model for liquids attempts to capture the physical behavior of a real liquid in a simple conceptual model: a fluid of fixed size spheres that only interact repulsively when they come into contact. Is the model good enough to use for modeling internal planetary structure? To an...
In addition, in the extended system, interactions are defined in terms of the scattering length, positive or negative, identified with the hard-sphere diameter only when it is positive. We are then able to obtain, directly in the thermodynamic limit, the ground-state energy of the strongly ...
We present an analytic expression containing no imaginary terms for the radial distribution function of hard spheres in the Percus-Yevick approximation up to the distance of 4 (though extendable beyond that), where is the hard-sphere diameter. It is shown that a third-order recursive ordinary ...
We present an analytic expression containing no imaginary terms for the radial distribution function of hard spheres in the Percus-Yevick approximation up to the distance of 4σ (though extendable beyond that), where σ is the hard-sphere diameter. It is shown that a third-order recursive ordi...
While well justified for sufficiently soft interactions, it is clearly not applicable to HS like interaction, because an intrinsic length scale – the hard sphere diameter – emerges. Thus, it is legitimate to say that the divergence of the high frequency elastic moduli in the limit of very ...
It has been used to evaluate the function at distances up to 20 times the hard sphere diameter. The same recursive formula can be applied to calculate derivatives of the distribution function which are useful in the thermodynamic analysis of equations of state obtained from perturbation theories. ...
(σij)=G(η,zij),whereGis a common function for all the mixtures of the same dimensionality, regardless of the number of components,ηis the packing fraction of the mixture, andzij=(σiσj/σij)〈σd1〉/〈σd〉is a dimensionless parameter,〈σn〉being thenthmoment of the diameter ...
The isolated pair wave equation is solved for two isolated hydrogen atoms interacting via the 3 危 u + potential, from which a scattering length a = 0.72 is determined and used as an effective hard-core diameter in a dilute hard-sphere Bose-gas model calculation. In the low-density limit,...
2. RESULTS AND DISCUSSION The density used in the hard-sphere crystal is expressed relative to close packing, namely, z = {N/V)ail2m, (1) where σ is a diameter of the hard sphere, V is the volume and Ν is the number of spheres. The entropy of the fee and hep crystals ...