Martynov Sarkisov - Revision history

Nice and Tidy: Changed references to Cite format.

2009-11-11T11:38:56Z

Changed references to Cite format.

Nice and Tidy: Corrected spelling mistake

2008-02-20T14:55:28Z

Corrected spelling mistake

← Older revision		Revision as of 16:55, 20 February 2008
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	where <math>\omega(r)</math> is the thermal potential and <math>A_2=1/2</math>. (This closure formed the basis for the		where <math>\omega(r)</math> is the thermal potential and <math>A_2=1/2</math>. (This closure formed the basis for the
	[[Ballone-Pastore-Galli-~~Gazillo~~]] closure for hard sphere mixtures).		[[Ballone-Pastore-Galli-Gazzillo]] closure for hard sphere mixtures).
	Charpentier and Jaske (Ref. 2) have		Charpentier and Jaske (Ref. 2) have
	observed that the value of <math>A_2</math> differs drastically from 0.5 for temperatures		observed that the value of <math>A_2</math> differs drastically from 0.5 for temperatures

Carl McBride at 17:04, 26 June 2007

2007-06-26T17:04:34Z

← Older revision		Revision as of 19:04, 26 June 2007
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	where <math>\phi</math> is the chosen basis function and <math>A_i</math> are the coefficients determined from		where <math>\phi</math> is the chosen basis function and <math>A_i</math> are the coefficients determined from
	[[thermodynamic consistency]] conditions.		[[thermodynamic consistency]] conditions.
	The Martynov-Sarkisov closure is based on		The Martynov-Sarkisov [[Closure relations \| closure]] is based on
	the expansion of the bridge function in powers of the thermal potential.		the expansion of the bridge function in powers of the [[thermal potential]].

	(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for [[hard sphere model \| hard sphere]]s, is		(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for [[hard sphere model \| hard sphere]]s, is

Carl McBride at 15:03, 21 March 2007

2007-03-21T15:03:40Z

← Older revision		Revision as of 17:03, 21 March 2007
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	'''Martynov''' and '''Sarkisov''' proposed		'''Martynov''' and '''Sarkisov''' proposed
	an expansion of the ~~Bridge~~ function in terms of basis functions:		an expansion of the [[bridge function]] in terms of basis functions:

	:<math>B(\rho, T, r)= - \sum_{i=1}^\infty A_i (\rho,T) \phi^i (\rho, T, r)</math>		:<math>B(\rho, T, r)= - \sum_{i=1}^\infty A_i (\rho,T) \phi^i (\rho, T, r)</math>
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	[[thermodynamic consistency]] conditions.		[[thermodynamic consistency]] conditions.
	The Martynov-Sarkisov closure is based on		The Martynov-Sarkisov closure is based on
	the expansion of the ~~[[Bridge~~ function]] in powers of the thermal potential.		the expansion of the bridge function in powers of the thermal potential.

	(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for [[hard sphere model \| hard sphere]]s, is		(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for [[hard sphere model \| hard sphere]]s, is

Carl McBride at 13:26, 21 March 2007

2007-03-21T13:26:34Z

← Older revision		Revision as of 15:26, 21 March 2007
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	the expansion of the [[Bridge function]] in powers of the thermal potential.		the expansion of the [[Bridge function]] in powers of the thermal potential.

	(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for [[hard sphere]]s, is		(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for [[hard sphere model \| hard sphere]]s, is

	:<math>B[\omega(r)]= - A_2 \omega(r_{12})^2 = \sqrt{(1+2\gamma(r))}-\gamma(r) -1</math>		:<math>B[\omega(r)]= - A_2 \omega(r_{12})^2 = \sqrt{(1+2\gamma(r))}-\gamma(r) -1</math>

Nice and Tidy at 11:09, 27 February 2007

2007-02-27T11:09:31Z

← Older revision		Revision as of 13:09, 27 February 2007
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	#[http://dx.doi.org/10.1063/1.478276 G. A. Martynov, G. N. Sarkisov and A. G. Vompe "New closure for the Ornstein–Zernike equation" Journal of Chemical Physics '''110''' pp. 3961-3969 (1999)]		#[http://dx.doi.org/10.1063/1.478276 G. A. Martynov, G. N. Sarkisov and A. G. Vompe "New closure for the Ornstein–Zernike equation" Journal of Chemical Physics '''110''' pp. 3961-3969 (1999)]
	#[http://dx.doi.org/10.1063/1.1365107 Gari Sarkisov "Approximate integral equation theory for classical fluids", Journal of Chemical Physics '''114''' pp. 9496-9505 (2001)]		#[http://dx.doi.org/10.1063/1.1365107 Gari Sarkisov "Approximate integral equation theory for classical fluids", Journal of Chemical Physics '''114''' pp. 9496-9505 (2001)]

			[[Category: Integral equations]]

Carl McBride: /* References */

2007-02-26T15:26:52Z

References

← Older revision		Revision as of 17:26, 26 February 2007
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	#[http://dx.doi.org/10.1080/00268978300102111 G. A. Martynov; G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' 1495-1504 (1983)]		#[http://dx.doi.org/10.1080/00268978300102111 G. A. Martynov; G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' 1495-1504 (1983)]
	#[http://dx.doi.org/10.1063/1.1332808 I. Charpentier and N. Jakse "Exact numerical derivatives of the pair-correlation function of simple liquids using the tangent linear method", Journal of Chemical Physics '''114''' pp. 2284-2292 (2001)]		#[http://dx.doi.org/10.1063/1.1332808 I. Charpentier and N. Jakse "Exact numerical derivatives of the pair-correlation function of simple liquids using the tangent linear method", Journal of Chemical Physics '''114''' pp. 2284-2292 (2001)]
	doi:10.1063/1.~~1332808~~		#[http://dx.doi.org/10.1063/1.466138 G. Sarkisov and D. Tikhonov "Martynov–Sarkisov integral equation for the simple fluids" Journal of Chemical Physics '''99''' pp. 3926-3932 (1993)]
	~~#[JCP_2001_114_02284~~]		#[http://dx.doi.org/10.1063/1.478276 G. A. Martynov, G. N. Sarkisov and A. G. Vompe "New closure for the Ornstein–Zernike equation" Journal of Chemical Physics '''110''' pp. 3961-3969 (1999)]
	#[~~JCP_1993_99_03926~~]		#[http://dx.doi.org/10.1063/1.1365107 Gari Sarkisov "Approximate integral equation theory for classical fluids", Journal of Chemical Physics '''114''' pp. 9496-9505 (2001)]
	#[~~JCP_1999_110_03961]~~
	~~#[JCP_2001_114_09496~~]

Carl McBride: /* References */

2007-02-26T15:20:20Z

References

← Older revision		Revision as of 17:20, 26 February 2007
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	==References==		==References==
	#[~~MP_1983_49_1495~~]		#[http://dx.doi.org/10.1080/00268978300102111 G. A. Martynov; G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' 1495-1504 (1983)]
			#[http://dx.doi.org/10.1063/1.1332808 I. Charpentier and N. Jakse "Exact numerical derivatives of the pair-correlation function of simple liquids using the tangent linear method", Journal of Chemical Physics '''114''' pp. 2284-2292 (2001)]
			doi:10.1063/1.1332808
	#[JCP_2001_114_02284]		#[JCP_2001_114_02284]
	#[JCP_1993_99_03926]		#[JCP_1993_99_03926]
	#[JCP_1999_110_03961]		#[JCP_1999_110_03961]
	#[JCP_2001_114_09496]		#[JCP_2001_114_09496]

Carl McBride at 17:11, 23 February 2007

2007-02-23T17:11:03Z

← Older revision		Revision as of 19:11, 23 February 2007
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	[[thermodynamic consistency]] conditions.		[[thermodynamic consistency]] conditions.
	The Martynov-Sarkisov closure is based on		The Martynov-Sarkisov closure is based on
	the expansion of the Bridge function in powers of the thermal potential.		the expansion of the [[Bridge function]] in powers of the thermal potential.

	(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for [[hard sphere]]s, is		(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for [[hard sphere]]s, is

Carl McBride at 11:55, 23 February 2007

2007-02-23T11:55:20Z

← Older revision		Revision as of 13:55, 23 February 2007
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	Charpentier and Jaske (Ref. 2) have		Charpentier and Jaske (Ref. 2) have
	observed that the value of <math>A_2</math> differs drastically from 0.5 for temperatures		observed that the value of <math>A_2</math> differs drastically from 0.5 for temperatures
	greater than <math>T^*\approx 2.74</math>, thus the MS closure is deficient in the supercritical domain.		greater than <math>T^*\approx 2.74</math>, thus the Martynov-Sarkisov closure is deficient in the supercritical domain.

	==References==		==References==

← Older revision		Revision as of 13:38, 11 November 2009
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	the expansion of the bridge function in powers of the [[thermal potential]].		the expansion of the bridge function in powers of the [[thermal potential]].

	~~(1983 Eq.16 Ref. 1)~~ closure in terms of the bridge function, for [[hard sphere model \| hard sphere]]s, is		The closure in terms of the bridge function (Eq. 16 of <ref>[http://dx.doi.org/10.1080/00268978300102111 G. A. Martynov; G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' 1495-1504 (1983)]</ref>), for [[hard sphere model \| hard sphere]]s, is

	:<math>B[\omega(r)]= - A_2 \omega(r_{12})^2 = \sqrt{(1+2\gamma(r))}-\gamma(r) -1</math>		:<math>B[\omega(r)]= - A_2 \omega(r_{12})^2 = \sqrt{(1+2\gamma(r))}-\gamma(r) -1</math>
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	where <math>\omega(r)</math> is the thermal potential and <math>A_2=1/2</math>. (This closure formed the basis for the		where <math>\omega(r)</math> is the thermal potential and <math>A_2=1/2</math>. (This closure formed the basis for the
	[[Ballone-Pastore-Galli-Gazzillo]] closure for hard sphere mixtures).		[[Ballone-Pastore-Galli-Gazzillo]] closure for hard sphere mixtures).
	Charpentier and Jaske (~~Ref. 2~~) have		Charpentier and Jaske <ref>[http://dx.doi.org/10.1063/1.1332808 I. Charpentier and N. Jakse "Exact numerical derivatives of the pair-correlation function of simple liquids using the tangent linear method", Journal of Chemical Physics '''114''' pp. 2284-2292 (2001)]</ref> have
	observed that the value of <math>A_2</math> differs drastically from 0.5 for temperatures		observed that the value of <math>A_2</math> differs drastically from 0.5 for temperatures
	greater than <math>T^*\approx 2.74</math>, thus the Martynov-Sarkisov closure is deficient in the supercritical domain.		greater than <math>T^*\approx 2.74</math>, thus the Martynov-Sarkisov closure is deficient in the supercritical domain.

	==References==		==References==
	~~#[http:/~~/~~dx.doi.org/10.1080/00268978300102111 G. A. Martynov; G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' 1495-1504 (1983)]~~		<references/>
	#[http://dx.doi.org/10.1063/1.1332808 I. Charpentier and N. Jakse "Exact numerical derivatives of the pair-correlation function of simple liquids using the tangent linear method", Journal of Chemical Physics '''~~114~~''' ~~pp. 2284-2292 (2001)]~~		'''Related reading'''
	#[http://dx.doi.org/10.1063/1.466138 G. Sarkisov and D. Tikhonov "Martynov–Sarkisov integral equation for the simple fluids" Journal of Chemical Physics '''99''' pp. 3926-3932 (1993)]		*[http://dx.doi.org/10.1063/1.466138 G. Sarkisov and D. Tikhonov "Martynov–Sarkisov integral equation for the simple fluids" Journal of Chemical Physics '''99''' pp. 3926-3932 (1993)]
	#[http://dx.doi.org/10.1063/1.478276 G. A. Martynov, G. N. Sarkisov and A. G. Vompe "New closure for the Ornstein–Zernike equation" Journal of Chemical Physics '''110''' pp. 3961-3969 (1999)]		*[http://dx.doi.org/10.1063/1.478276 G. A. Martynov, G. N. Sarkisov and A. G. Vompe "New closure for the Ornstein–Zernike equation" Journal of Chemical Physics '''110''' pp. 3961-3969 (1999)]
	#[http://dx.doi.org/10.1063/1.1365107 Gari Sarkisov "Approximate integral equation theory for classical fluids", Journal of Chemical Physics '''114''' pp. 9496-9505 (2001)]		*[http://dx.doi.org/10.1063/1.1365107 Gari Sarkisov "Approximate integral equation theory for classical fluids", Journal of Chemical Physics '''114''' pp. 9496-9505 (2001)]

	[[Category: Integral equations]]		[[Category: Integral equations]]