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), originally developed for hard sphere mixtures, is given by
The '''Ballone-Pastore-Galli-Gazillo''' (BPGG) (1986) (Eq. 3.8 Ref. 1) [[Closure relations | closure relation]],
developed for [[hard sphere model | 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). 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.


 
where <math>s=15/8</math>.
== References ==
It has its origins in the [[Martynov Sarkisov | Martynov-Sarkisov]] closure (<math>s=2</math>).
 
The value of <math>s</math> can be determined by a self-consistency condition.
P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 275 (1986)  
Notice that for <math>s=1</math> the BPGG approximation reduces to the [[HNC| hyper-netted chain]] closure.
 
==References==
Category: Integral equations
#[http://dx.doi.org/10.1080/00268978600102071 P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, '''59''' pp. 275-290 (1986)]
[[Category: Integral equations]]

Revision as of 15:55, 20 February 2008

The Ballone-Pastore-Galli-Gazillo (BPGG) (1986) (Eq. 3.8 Ref. 1) closure relation, developed for hard sphere mixtures, is given by

where . It has its origins in the Martynov-Sarkisov closure (). The value of can be determined by a self-consistency condition. Notice that for the BPGG approximation reduces to the hyper-netted chain closure.

References

  1. P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 pp. 275-290 (1986)