# Difference between revisions of "Kirkwood superposition approximation"

Carl McBride (talk | contribs) m (New page: Kirkwood 1935 (Eq. 40 \cite{JCP_1935_03_00300}, Eq. 5.6 \cite{PRSA_1946_188_0010}) <math>g_N^{(3)}(r_1,r_2,r_3)=g_N^{(2)}(r_1,r_2)g_N^{(2)}(r_2,r_3)g_N^{(2)}(r_3,r_1)</math> It appears t...) |
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− | Kirkwood 1935 (Eq. 40 | + | Kirkwood 1935 (Eq. 40 Ref. 1, Eq. 5.6 Ref. 2) |

<math>g_N^{(3)}(r_1,r_2,r_3)=g_N^{(2)}(r_1,r_2)g_N^{(2)}(r_2,r_3)g_N^{(2)}(r_3,r_1)</math> | <math>g_N^{(3)}(r_1,r_2,r_3)=g_N^{(2)}(r_1,r_2)g_N^{(2)}(r_2,r_3)g_N^{(2)}(r_3,r_1)</math> | ||

It appears that this was used as a basis of a closure for the | It appears that this was used as a basis of a closure for the | ||

− | Kirkwood integral equation | + | Kirkwood integral equation (Ref. 1) and the Yvon, and Born-Green |

− | + | (Ref. 2) until the work of Morita and Hiroike (Ref. 3). | |

− | It was pointed out in Ref.s | + | It was pointed out in Ref.s 4 and 5, that there is an inconsistency between |

− | the pressure and the compressibility equation if this | + | the pressure and the compressibility equation if this superposition approximation is used to generate <math>g(r)</math>. |

− | superposition approximation is used | + | |

− | to generate <math>g(r)</math>. | + | ==References== |

+ | #[JCP_1935_03_00300] | ||

+ | #[PRSA_1946_188_0010] | ||

+ | #[http://dx.doi.org/10.1143/PTP.23.1003 Tohru Morita and Kazuo Hiroike "A New Approach to the Theory of Classical Fluids. I" Progress of Theoretical Physics '''23''' pp. 1003-1027 (1960)] | ||

+ | #[PR_1952_085_000777] | ||

+ | #[PRSA_1953_216_0203] |

## Revision as of 17:42, 19 February 2007

Kirkwood 1935 (Eq. 40 Ref. 1, Eq. 5.6 Ref. 2)

It appears that this was used as a basis of a closure for the Kirkwood integral equation (Ref. 1) and the Yvon, and Born-Green (Ref. 2) until the work of Morita and Hiroike (Ref. 3). It was pointed out in Ref.s 4 and 5, that there is an inconsistency between the pressure and the compressibility equation if this superposition approximation is used to generate .

## References

- [JCP_1935_03_00300]
- [PRSA_1946_188_0010]
- Tohru Morita and Kazuo Hiroike "A New Approach to the Theory of Classical Fluids. I" Progress of Theoretical Physics
**23**pp. 1003-1027 (1960) - [PR_1952_085_000777]
- [PRSA_1953_216_0203]