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Hardbound. speedy advances in chromatographic techniques, spectroscopic thoughts and pharmacological assay equipment have ended in the invention of more and more new and fascinating typical items from terrestrial and marine resources. the current quantity includes finished studies on a number of the significant advances during this box that have taken position in recent times.
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Extra resources for Advances in Chemical Physics (Volume 139)
Obviously, MSA reduces to PY for the HS system and presents an internal inconsistency as well. recent advances in the field of integral equation theories 3. 19 Hypernetted-Chain Approximation An analysis of clusters expansion to higher order (as compared to PY equation) leads to the hypernetted-chain (HNC) approximation [44–46]. In other words, directly solving the OZ relation in conjunction with Eq. (28) is possible, under a drastic assumption on BðrÞ. The total correlation function is given simply by hðrÞ ¼ exp½ÀbuðrÞ þ hðrÞ À cðrÞ À 1 ð37Þ implying that the bridge function BðrÞ is identically equal to 0.
9, calculated with the ODS scheme, compared to MC simulation data . Taken from Ref. . We would like to mention that RHNC is able to reproduce qualitatively accurate bridge functions inside the core, especially when a reference system (RS) of soft spheres is utilized rather than the conventional hard-sphere fluid. However, the prescription used to determine the RS requires a priori knowledge of both the RS and the system under investigation. This feature restricts the applicability of RHNC to sytems for which the EOS is available.
The HMSA has strong theoretical basis since it can be derived from Percus’ functional expansion formalism and its bridge function expresses as a functional of the remormalized indirect correlation function gÃ ðrÞ ¼ gðrÞ À buLR ðrÞ so that expff ðrÞgÃ ðrÞg À 1 BðrÞ ¼ ÀgÃ ðrÞ þ ln 1 þ f ðrÞ ð52Þ where f ðrÞ is the ‘‘switching’’ function defined as: f ðrÞ ¼ 1 À expðÀarÞ ð53Þ The parameter a is varied in a self-consistent manner until virial and compressibility routes for the pressure coincide.