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| The '''Martynov-Vompe''' [[Closure relations | closure relation]] <ref>[http://dx.doi.org/10.1103/PhysRevE.47.1012 G. A. Martynov and A. G. Vompe "Differential condition of thermodynamic consistency as a closure for the Ornstein-Zernike equation", Physical Review E, '''47''' pp. 1012-1017 (1993)]</ref> | | The '''Martynov-Vompe''' (Refs. 1 and 2) closure |
| <ref>[http://dx.doi.org/10.1063/1.467189 A. G. Vompe and G. A. Martynov "The bridge function expansion and the self-consistency problem of the Ornstein–Zernike equation solution", Journal of Chemical Physics '''100''' pp. 5249-5258 (1994)]</ref> is given by:
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| :<math>\left.B\right.=-a(\ln y^*) - b(\ln y^*)^2</math> | | :<math>\left.B\right.=-a(\ln y^*) - b(\ln y^*)^2</math> |
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| :<math>\left.y^*(r)\right. = \ln y(r) - \beta \Phi_p</math> | | :<math>\left.y^*(r)\right. = \ln y(r) - \beta \Phi_p</math> |
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| where <math>\Phi_p</math> is the perturbative part of the [[Intermolecular pair potential | pair potential]] (Note: in the [[Weeks-Chandler-Andersen perturbation theory | Weeks-Chandler-Andersen separation]] for the | | where <math>\Phi_p</math> is the perturbative part of the pair potential (Note: in the [[WCA separation]] for the |
| [[Lennard-Jones model | Lennard-Jones]] system, the `perturbative part' is the attractive part). | | [[Lennard-Jones]] system, the `perturbative part' is the attractive part). |
| Martynov and Vompe have used the <math>dp_v-dP_c</math> and <math>dU-dP</math> [[thermodynamic consistencies]] | | Martynov and Vompe have used the <math>dp_v-dP_c</math> and <math>dU-dP</math> [[thermodynamic consistencie]]s |
| in constructing their closures <ref>[http://dx.doi.org/10.1063/1.471522 Lloyd L. Lee, Dhananjay Ghonasgi, and Enrique Lomba "The fluid structures for soft-sphere potentials via the zero-separation theorems on molecular distribution functions", Journal of Chemical Physics '''104''' pp. 8058-8067 (1996)]</ref>. | | in constructing their closures (Ref. 3). |
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| ==References== | | ==References== |
| <references/>
| | #[PRE_1993_47_001012] |
| | | #[JCP_1994_100_05249] |
| | | #[JCP_1996_104_08058] |
| [[Category:Integral equations]] | |