Soft-core mean spherical approximation - Revision history

Carl McBride at 12:15, 7 June 2007

2007-06-07T12:15:12Z

← Older revision		Revision as of 14:15, 7 June 2007
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	:<math>B(r) = \beta \~~Phi_2~~ (r) - \gamma (r) + \ln \left( 1 + \gamma (r) - \beta \Phi_2 (r) \right)</math>		:<math>B(r) = \beta \Phi_{12} (r) - \gamma (r) + \ln \left( 1 + \gamma (r) - \beta \Phi_2 (r) \right)</math>

	where <math>\~~Phi_2~~ (r)</math> is the [[~~Pair~~ potential \| pair potential]], <math>\gamma (r)</math> is the [[Indirect correlation function \| indirect correlation function]], and <math> \beta = 1(/k_B T) </math>, where <math>k_B</math>		where <math>\Phi_{12} (r)</math> is the [[Intermolecular pair potential \| pair potential]], <math>\gamma (r)</math> is the [[Indirect correlation function \| indirect correlation function]], and <math> \beta = 1(/k_B T) </math>, where <math>k_B</math>
	is the [[Boltzmann constant]].		is the [[Boltzmann constant]].

Carl McBride at 13:14, 21 March 2007

2007-03-21T13:14:50Z

← Older revision		Revision as of 15:14, 21 March 2007
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	Junzo Chihara (along with Madden and Rice) extended the [[Percus Yevick]] equation for [[Lennard-Jones]] systems to provide a soft-core [[Mean spherical approximation \| mean spherical approximation]],		Junzo Chihara (along with Madden and Rice) extended the [[Percus Yevick]] equation for [[Lennard-Jones model \| Lennard-Jones]] systems to provide a soft-core [[Mean spherical approximation \| mean spherical approximation]],
	the SMSA,		the SMSA,

Carl McBride at 11:19, 28 February 2007

2007-02-28T11:19:41Z

← Older revision		Revision as of 13:19, 28 February 2007
Line 5:		Line 5:
	:<math>B(r) = \beta \Phi_2 (r) - \gamma (r) + \ln \left( 1 + \gamma (r) - \beta \Phi_2 (r) \right)</math>		:<math>B(r) = \beta \Phi_2 (r) - \gamma (r) + \ln \left( 1 + \gamma (r) - \beta \Phi_2 (r) \right)</math>

	where <math>\Phi_2 (r)</math> is the , <math>\gamma (r)</math> is the , and <math> \beta = 1(/k_B T) </math>, where <math>k_B</math>		where <math>\Phi_2 (r)</math> is the [[Pair potential \| pair potential]], <math>\gamma (r)</math> is the [[Indirect correlation function \| indirect correlation function]], and <math> \beta = 1(/k_B T) </math>, where <math>k_B</math>
	is the [[Boltzmann constant]].		is the [[Boltzmann constant]].

Carl McBride at 11:18, 28 February 2007

2007-02-28T11:18:10Z

← Older revision		Revision as of 13:18, 28 February 2007
Line 1:		Line 1:
	Chihara (along with Madden and Rice) extended the [[Percus Yevick]] equation for [[Lennard-Jones]] systems to provide a soft-core [[Mean spherical approximation \| mean spherical approximation]],		Junzo Chihara (along with Madden and Rice) extended the [[Percus Yevick]] equation for [[Lennard-Jones]] systems to provide a soft-core [[Mean spherical approximation \| mean spherical approximation]],
	the SMSA,		the SMSA,

Line 5:		Line 5:
	:<math>B(r) = \beta \Phi_2 (r) - \gamma (r) + \ln \left( 1 + \gamma (r) - \beta \Phi_2 (r) \right)</math>		:<math>B(r) = \beta \Phi_2 (r) - \gamma (r) + \ln \left( 1 + \gamma (r) - \beta \Phi_2 (r) \right)</math>

	where		where <math>\Phi_2 (r)</math> is the , <math>\gamma (r)</math> is the , and <math> \beta = 1(/k_B T) </math>, where <math>k_B</math>
			is the [[Boltzmann constant]].

	==References==		==References==
	#[http://dx.doi.org/10.1143/PTP.50.409 Junzo Chihara "Integral Euqations for Fluids with Long-Range and Short-Range Potentials - Application to a Charged Particle System", Progress of Theoretical Physics, '''50''' pp. 409-423 (1973)]		#[http://dx.doi.org/10.1143/PTP.50.409 Junzo Chihara "Integral Euqations for Fluids with Long-Range and Short-Range Potentials - Application to a Charged Particle System", Progress of Theoretical Physics, '''50''' pp. 409-423 (1973)]
	#[http://dx.doi.org/		#[http://dx.doi.org/10.1143/PTP.50.1156 Junzo Chihara "Integral Equations for Neutral and Charged Quantum Fluids Including Extension of the Percus-Yevick Equation" Progress of Theoretical Physics, '''50''' pp. 1156-1181 (1973)]
	~~#[PTP_1973_050_1156~~]
	#[http://dx.doi.org/10.1063/1.439651 William G. Madden and Stuart A. Rice "The mean spherical approximation and effective pair potentials in liquids", Journal of Chemical Physics '''72''' pp. 4208-4215 (1980)]		#[http://dx.doi.org/10.1063/1.439651 William G. Madden and Stuart A. Rice "The mean spherical approximation and effective pair potentials in liquids", Journal of Chemical Physics '''72''' pp. 4208-4215 (1980)]

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

Carl McBride at 11:14, 28 February 2007

2007-02-28T11:14:38Z

← Older revision		Revision as of 13:14, 28 February 2007
Line 1:		Line 1:
	Chihara (along with Madden and Rice) extended the [[Percus Yevick]] equation for [[Lennard-Jones]] systems to provide a soft-core [[Mean spherical approximation \| mean spherical approximation]],		Chihara (along with Madden and Rice) extended the [[Percus Yevick]] equation for [[Lennard-Jones]] systems to provide a soft-core [[Mean spherical approximation \| mean spherical approximation]],
	the SMSA ~~(Refs 1~~,~~2 and 3)~~		the SMSA,


	:<math>B(r) = \beta \Phi_2 (r) - \gamma (r) + \ln \left( 1 + \gamma (r) - \beta \Phi_2 (r) \right)</math>		:<math>B(r) = \beta \Phi_2 (r) - \gamma (r) + \ln \left( 1 + \gamma (r) - \beta \Phi_2 (r) \right)</math>

			where

	==References==		==References==
	#[~~PTP_1973_050_0409~~]		#[http://dx.doi.org/10.1143/PTP.50.409 Junzo Chihara "Integral Euqations for Fluids with Long-Range and Short-Range Potentials - Application to a Charged Particle System", Progress of Theoretical Physics, '''50''' pp. 409-423 (1973)]
			#[http://dx.doi.org/
	#[PTP_1973_050_1156]		#[PTP_1973_050_1156]
	#[http://dx.doi.org/10.1063/1.439651 William G. Madden and Stuart A. Rice "The mean spherical approximation and effective pair potentials in liquids", Journal of Chemical Physics '''72''' pp. 4208-4215 (1980)]		#[http://dx.doi.org/10.1063/1.439651 William G. Madden and Stuart A. Rice "The mean spherical approximation and effective pair potentials in liquids", Journal of Chemical Physics '''72''' pp. 4208-4215 (1980)]

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

Nice and Tidy at 15:07, 27 February 2007

2007-02-27T15:07:54Z

← Older revision		Revision as of 17:07, 27 February 2007
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	#[PTP_1973_050_0409]		#[PTP_1973_050_0409]
	#[PTP_1973_050_1156]		#[PTP_1973_050_1156]
	#[~~JCP_1980_72_04208~~]		#[http://dx.doi.org/10.1063/1.439651 William G. Madden and Stuart A. Rice "The mean spherical approximation and effective pair potentials in liquids", Journal of Chemical Physics '''72''' pp. 4208-4215 (1980)]

			[[Category: Integral equations]]

Carl McBride: New page: Chihara (along with Madden and Rice) extended the Percus Yevick equation for Lennard-Jones systems to provide a soft-core [[Mean spherical approximation | mean spherical approximat...

2007-02-23T11:59:32Z

New page: Chihara (along with Madden and Rice) extended the Percus Yevick equation for Lennard-Jones systems to provide a soft-core [[Mean spherical approximation | mean spherical approximat...

New page

Chihara (along with Madden and Rice) extended the [[Percus Yevick]] equation for [[Lennard-Jones]] systems to provide a soft-core [[Mean spherical approximation | mean spherical approximation]],
the SMSA (Refs 1,2 and 3)

:<math>B(r) = \beta \Phi_2 (r) - \gamma (r) + \ln \left( 1 + \gamma (r) - \beta \Phi_2 (r) \right)</math>

==References==
#[PTP_1973_050_0409]
#[PTP_1973_050_1156]
#[JCP_1980_72_04208]