Martynov Vompe - Revision history

Carl McBride: typo

2012-02-16T11:43:57Z

typo

← Older revision		Revision as of 13:43, 16 February 2012
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	[[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>#[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>[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==

Carl McBride: Updated internal link

2012-02-16T11:43:39Z

Updated internal link

← Older revision		Revision as of 13:43, 16 February 2012
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	The '''Martynov-Vompe''' ~~(Refs. 1 and 2)~~ [[Closure relations \| closure relation]] is given by:		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]]

Carl McBride at 16:57, 26 June 2007

2007-06-26T16:57:58Z

← Older revision		Revision as of 18:57, 26 June 2007
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	The '''Martynov-Vompe''' (Refs. 1 and 2) closure		The '''Martynov-Vompe''' (Refs. 1 and 2) [[Closure relations \| closure relation]] 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>

Nice and Tidy at 13:15, 21 June 2007

2007-06-21T13:15:39Z

← Older revision		Revision as of 15:15, 21 June 2007
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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 [[~~WCA~~ separation]] for the		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
	[[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]]

Carl McBride at 12:13, 7 June 2007

2007-06-07T12:13:59Z

← Older revision		Revision as of 14:13, 7 June 2007
Line 7:		Line 7:
	:<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 pair potential (Note: in the [[WCA separation]] for the		where <math>\Phi_p</math> is the perturbative part of the [[Intermolecular pair potential \| pair potential]] (Note: in the [[WCA 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]]

Carl McBride at 08:37, 29 May 2007

2007-05-29T08:37:43Z

← Older revision		Revision as of 10:37, 29 May 2007
Line 9:		Line 9:
	where <math>\Phi_p</math> is the perturbative part of the pair potential (Note: in the [[WCA 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 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]]s		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. 3).

Carl McBride at 13:13, 21 March 2007

2007-03-21T13:13:58Z

← Older revision		Revision as of 15:13, 21 March 2007
Line 8:		Line 8:

	where <math>\Phi_p</math> is the perturbative part of the pair potential (Note: in the [[WCA 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]] 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 ~~consistency~~]]s		Martynov and Vompe have used the <math>dp_v-dP_c</math> and <math>dU-dP</math> [[thermodynamic consistencies]]s
	in constructing their closures (Ref. 3).		in constructing their closures (Ref. 3).

Carl McBride at 12:09, 21 March 2007

2007-03-21T12:09:19Z

← Older revision		Revision as of 14:09, 21 March 2007
Line 9:		Line 9:
	where <math>\Phi_p</math> is the perturbative part of the pair potential (Note: in the [[WCA 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]] 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 ~~consistencie~~]]s		Martynov and Vompe have used the <math>dp_v-dP_c</math> and <math>dU-dP</math> [[thermodynamic consistency]]s
	in constructing their closures (Ref. 3).		in constructing their closures (Ref. 3).

Nice and Tidy at 11:41, 27 February 2007

2007-02-27T11:41:33Z

← Older revision		Revision as of 13:41, 27 February 2007
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	#[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)]		#[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)]
	#[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/10.1063/1.467189 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/		#[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)]
	~~#[JCP_1994_100_05249~~]
	~~#[JCP_1996_104_08058]~~
	[[Category:Integral equations]]		[[Category:Integral equations]]

Nice and Tidy at 11:37, 27 February 2007

2007-02-27T11:37:44Z

← Older revision		Revision as of 13:37, 27 February 2007
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	==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)]		#[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)]
	#[http://dx.doi.org/		#[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/		#[http://dx.doi.org/
	#[JCP_1994_100_05249]		#[JCP_1994_100_05249]
	#[JCP_1996_104_08058]		#[JCP_1996_104_08058]
	[[Category:Integral equations]+		[[Category:Integral equations]]