Martynov Vompe: Difference between revisions
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The '''Martynov-Vompe''' | 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> | ||
<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: | |||
:<math>\left.B\right.=-a(\ln y^*) - b(\ln y^*)^2</math> | :<math>\left.B\right.=-a(\ln y^*) - b(\ln y^*)^2</math> | ||
| Line 7: | Line 8: | ||
:<math>\left.y^*(r)\right. = \ln y(r) - \beta \Phi_p</math> | :<math>\left.y^*(r)\right. = \ln y(r) - \beta \Phi_p</math> | ||
where <math>\Phi_p</math> is the perturbative part of the [[Intermolecular pair potential | pair potential]] (Note: in the [[Weeks-Chandler- | 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 | ||
[[Lennard-Jones model | Lennard-Jones]] system, the `perturbative part' is the attractive part). | [[Lennard-Jones model | 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 consistencies]] | ||
in constructing their closures ( | 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>. | ||
==References== | ==References== | ||
<references/> | |||
[[Category:Integral equations]] | [[Category:Integral equations]] | ||
Latest revision as of 12:43, 16 February 2012
The Martynov-Vompe closure relation [1] [2] is given by:
where
where is the perturbative part of the pair potential (Note: in the Weeks-Chandler-Andersen separation for the Lennard-Jones system, the `perturbative part' is the attractive part). Martynov and Vompe have used the and thermodynamic consistencies in constructing their closures [3].
References[edit]
- ↑ 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)
- ↑ 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)
- ↑ 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)