Martynov Vompe: Difference between revisions

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The '''Martynov-Vompe''' (Refs. 1 and 2) closure
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>
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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>


where <math>\Phi_p</math> is the perturbative part of the [[Intermolecular pair potential  | pair potential]] (Note: in the [[Weeks-Chandler-Anderson perturbation theory | Weeks-Chandler-Anderson separation]] for the
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 (Ref. 3).
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==
#[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)]
<references/>
#[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)]
 
#[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)]


[[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]