Ballone-Pastore-Galli-Gazzillo - Revision history

Nice and Tidy at 14:57, 20 February 2008

2008-02-20T14:57:22Z

← Older revision		Revision as of 16:57, 20 February 2008
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	The '''Ballone-Pastore-Galli-Gazillo''' (BPGG) (1986) (Eq. 3.8 Ref. 1) [[Closure relations \| closure relation]],		The '''Ballone-Pastore-Galli-Gazillo''' (BPGG) (1986) (Eq. 3.8 Ref. 1) [[Closure relations \| closure relation]],
	developed for [[~~hard~~ sphere ~~model~~ \| hard ~~sphere~~]] ~~mixtures~~, is given by		developed for [[Hard-sphere mixtures \| mixtures of hard spheres]], is given by

	:<math>B(r)=\left[ 1+s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(r\right) </math>		:<math>B(r)=\left[ 1+s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(r\right) </math>

Nice and Tidy at 14:55, 20 February 2008

2008-02-20T14:55:37Z

← Older revision		Revision as of 16:55, 20 February 2008
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	The '''Ballone-Pastore-Galli-~~Gazzillo~~ (BPGG)~~''' closure relation~~ (1986) (Eq. 3.8 Ref. 1), ~~originally~~ developed for hard sphere mixtures, is given by		The '''Ballone-Pastore-Galli-Gazillo''' (BPGG) (1986) (Eq. 3.8 Ref. 1) [[Closure relations \| closure relation]],
			developed for [[hard sphere model \| hard sphere]] mixtures, is given by

	<math>B(r)=\left[ 1+s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(		:<math>B(r)=\left[ 1+s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(r\right) </math>
	r\right) </math>
	~~where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). The value of s can be determined by a self-consistency condition.~~
	~~Notice that for s = 1 the BPGG approximation reduces to the hypernetted chain closure.~~


			where <math>s=15/8</math>.
	== References ==		It has its origins in the [[Martynov Sarkisov \| Martynov-Sarkisov]] closure (<math>s=2</math>).
			The value of <math>s</math> can be determined by a self-consistency condition.
	P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 275 (1986)		Notice that for <math>s=1</math> the BPGG approximation reduces to the [[HNC\| hyper-netted chain]] closure.
			==References==
	Category: Integral equations		#[http://dx.doi.org/10.1080/00268978600102071 P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, '''59''' pp. 275-290 (1986)]
			[[Category: Integral equations]]

157.138.11.43 at 14:01, 20 February 2008

2008-02-20T14:01:17Z

← Older revision		Revision as of 16:01, 20 February 2008
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	The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986) (Eq. 3.8 Ref. 1), originally developed for hard sphere mixtures, is given by		The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986) (Eq. 3.8 Ref. 1), originally developed for hard sphere mixtures, is given by

	<math>B(r)=\left[ 1-s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(		<math>B(r)=\left[ 1+s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(
	r\right) </math>		r\right) </math>
	where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). The value of s can be determined by a self-consistency condition.		where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). The value of s can be determined by a self-consistency condition.

157.138.11.43 at 13:11, 20 February 2008

2008-02-20T13:11:30Z

← Older revision		Revision as of 15:11, 20 February 2008
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	The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986) (Eq. 3.8 Ref. 1), developed for hard sphere mixtures, is given by		The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986) (Eq. 3.8 Ref. 1), originally developed for hard sphere mixtures, is given by

	<math>B(r)=\left[ 1-s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(		<math>B(r)=\left[ 1-s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(
	r\right) </math>		r\right) </math>
	where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). Notice that for s = 1 ~~this~~ reduces to the ~~hyper-netted~~ chain closure.		where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). The value of s can be determined by a self-consistency condition.
			Notice that for s = 1 the BPGG approximation reduces to the hypernetted chain closure.


	~~[edit]~~

			== References ==

	~~== Headline text ==~~
	~~References~~
	P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 275 (1986)		P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 275 (1986)
	~~Retrieved from "http://www.sklogwiki.org/SklogWiki/index.php/Ballone-Pastore-Galli-Gazillo"~~
	Category: Integral equations		Category: Integral equations

157.138.11.43 at 13:06, 20 February 2008

2008-02-20T13:06:55Z

← Older revision		Revision as of 15:06, 20 February 2008
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	The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986) (Eq. 3.8 Ref. 1), developed for hard sphere mixtures, is given by		The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986) (Eq. 3.8 Ref. 1), developed for hard sphere mixtures, is given by
	<math>B = (1-s \gamma ) - 1 - \gamma</math>
			<math>B(r)=\left[ 1-s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(
			r\right) </math>
	where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). Notice that for s = 1 this reduces to the hyper-netted chain closure.		where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). Notice that for s = 1 this reduces to the hyper-netted chain closure.

	[edit] References		[edit]


			== Headline text ==
			References
	P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 275 (1986)		P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 275 (1986)
	Retrieved from "http://www.sklogwiki.org/SklogWiki/index.php/Ballone-Pastore-Galli-Gazillo"		Retrieved from "http://www.sklogwiki.org/SklogWiki/index.php/Ballone-Pastore-Galli-Gazillo"
	Category: Integral equations		Category: Integral equations

157.138.11.43 at 13:00, 20 February 2008

2008-02-20T13:00:55Z

← Older revision		Revision as of 15:00, 20 February 2008
Line 1:		Line 1:
	The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986)(Eq. 3.8 Ref. 1), developed for hard sphere mixtures, is given by		The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986) (Eq. 3.8 Ref. 1), developed for hard sphere mixtures, is given by
			<math>B = (1-s \gamma ) - 1 - \gamma</math>
			where s = 15 / 8. It has its origin in the Martynov-Sarkisov closure (s = 2). Notice that for s = 1 this reduces to the hyper-netted chain closure.

			[edit] References
			P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 275 (1986)
			Retrieved from "http://www.sklogwiki.org/SklogWiki/index.php/Ballone-Pastore-Galli-Gazillo"
			Category: Integral equations

157.138.11.43 at 12:58, 20 February 2008

2008-02-20T12:58:07Z

← Older revision		Revision as of 14:58, 20 February 2008
Line 1:		Line 1:
	The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' (Eq. 3.8 Ref. 1) ~~closure relation~~, developed for hard sphere mixtures, is given by		The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' closure relation (1986)(Eq. 3.8 Ref. 1), developed for hard sphere mixtures, is given by

157.138.11.43: New page: The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' (Eq. 3.8 Ref. 1) closure relation, developed for hard sphere mixtures, is given by

2008-02-20T12:55:49Z

New page: The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' (Eq. 3.8 Ref. 1) closure relation, developed for hard sphere mixtures, is given by

New page

The '''Ballone-Pastore-Galli-Gazzillo (BPGG)''' (Eq. 3.8 Ref. 1) closure relation, developed for hard sphere mixtures, is given by