Ballone-Pastore-Galli-Gazzillo: Difference between revisions
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The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986) (Eq. 3.8 Ref. 1), developed for hard sphere mixtures, is given by | The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986) (Eq. 3.8 Ref. 1), originally developed for hard sphere mixtures, is given by | ||
<math>B(r)=\left[ 1-s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left( | <math>B(r)=\left[ 1-s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left( | ||
r\right) </math> | r\right) </math> | ||
where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). Notice that for s = 1 | where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). The value of s can be determined by a self-consistency condition. | ||
Notice that for s = 1 the BPGG approximation reduces to the hypernetted chain closure. | |||
== References == | |||
P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 275 (1986) | P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 275 (1986) | ||
Category: Integral equations | Category: Integral equations | ||
Revision as of 14:11, 20 February 2008
The Ballone-Pastore-Galli-Gazzillo (BPGG) closure relation (1986) (Eq. 3.8 Ref. 1), originally developed for hard sphere mixtures, is given by
![{\displaystyle B(r)=\left[1-s\gamma \left(r\right)\right]^{1/s}-1-\gamma \left(r\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/43ba6461880b0729dccda09431ad7433f5470d28)
where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). The value of s can be determined by a self-consistency condition. Notice that for s = 1 the BPGG approximation reduces to the hypernetted chain closure.
References
P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 275 (1986)
Category: Integral equations