Difference between revisions of "Kirkwood superposition approximation"

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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 \cite{JCP_1935_03_00300}, Eq. 5.6 \cite{PRSA_1946_188_0010})
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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 \cite{JCP_1935_03_00300} and the Yvon, and Born-Green
+
Kirkwood integral equation (Ref. 1) and the Yvon, and Born-Green
\cite{PRSA_1946_188_0010} until the work of Morita and Hiroike \cite{PTP_1960_023_1003}.\\
+
(Ref. 2) until the work of Morita and Hiroike (Ref. 3).
It was pointed out in Ref.s \cite{PR_1952_085_000777,PRSA_1953_216_0203} there is an inconsistency between
+
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)

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)

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 g(r).

References

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