Bridge function - Revision history

Carl McBride: Added a recent publication

2012-11-07T15:26:48Z

Added a recent publication

← Older revision		Revision as of 17:26, 7 November 2012
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	where <math>\rho</math> is the density of the fluid.		where <math>\rho</math> is the density of the fluid.
	==Universality of the Bridge functional==		==Universality of the Bridge functional==
	For Rosenfeld's principle of the universality of the bridge functional see ~~Ref~~. 2.		For Rosenfeld's principle of the universality of the bridge functional see <ref>[http://dx.doi.org/10.1063/1.464569 Yaakov Rosenfeld "Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas", Journal of Chemical Physics '''98''' pp. 8126-8148 (1993)]</ref>.

	==References==		==References==
	#[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]		<references/>
	#[http://dx.doi.org/10.1063/1.~~464569 Yaakov Rosenfeld~~ "~~Free energy model for inhomogeneous fluid mixtures: Yukawa~~-~~charged hard spheres, general interactions, and plasmas~~", Journal of Chemical Physics '''98''' ~~pp. 8126-8148~~ (~~1993~~)]		;Related reading
	#[http://dx.doi.org/10.1063/1.~~1860559 Sang Kyu Kwak~~ and ~~David A. Kofke~~ "~~Evaluation of~~ bridge-function ~~diagrams via Mayer-sampling Monte Carlo simulation~~", Journal of Chemical Physics '''~~122~~''' ~~104508~~ (~~2005~~)]		*[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]
			*[http://dx.doi.org/10.1063/1.1860559 Sang Kyu Kwak and David A. Kofke "Evaluation of bridge-function diagrams via Mayer-sampling Monte Carlo simulation", Journal of Chemical Physics '''122''' 104508 (2005)]
			*[http://dx.doi.org/10.1063/1.4766465 Stefan M. Kast and Daniel Tomazic "An exact bound on the bridge function in integral equation theories", Journal of Chemical Physics '''137''' 174502 (2012)]


	[[category: integral equations]]		[[category: integral equations]]

Carl McBride: /* References */ Added a reference.

2008-04-28T13:00:42Z

References: Added a reference.

← Older revision		Revision as of 15:00, 28 April 2008
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	#[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]		#[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]
	#[http://dx.doi.org/10.1063/1.464569 Yaakov Rosenfeld "Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas", Journal of Chemical Physics '''98''' pp. 8126-8148 (1993)]		#[http://dx.doi.org/10.1063/1.464569 Yaakov Rosenfeld "Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas", Journal of Chemical Physics '''98''' pp. 8126-8148 (1993)]
			#[http://dx.doi.org/10.1063/1.1860559 Sang Kyu Kwak and David A. Kofke "Evaluation of bridge-function diagrams via Mayer-sampling Monte Carlo simulation", Journal of Chemical Physics '''122''' 104508 (2005)]
	[[category: integral equations]]		[[category: integral equations]]

Carl McBride at 11:14, 11 June 2007

2007-06-11T11:14:48Z

← Older revision		Revision as of 13:14, 11 June 2007
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	where <math>\rho</math> is the density of the fluid.		where <math>\rho</math> is the density of the fluid.
			==Universality of the Bridge functional==
			For Rosenfeld's principle of the universality of the bridge functional see Ref. 2.

	==References==		==References==
	#[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]		#[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]
	#[http://dx.doi.org/10.1063/1.464569 Yaakov Rosenfeld "Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas", Journal of Chemical Physics '''98''' pp. 8126-8148 (1993)]		#[http://dx.doi.org/10.1063/1.464569 Yaakov Rosenfeld "Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas", Journal of Chemical Physics '''98''' pp. 8126-8148 (1993)]
	[[category: integral equations]]		[[category: integral equations]]

Carl McBride at 11:12, 11 June 2007

2007-06-11T11:12:47Z

← Older revision		Revision as of 13:12, 11 June 2007
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	==References==		==References==
	#[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]		#[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]
			#[http://dx.doi.org/10.1063/1.464569 Yaakov Rosenfeld "Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas", Journal of Chemical Physics '''98''' pp. 8126-8148 (1993)]
	[[category: integral equations]]		[[category: integral equations]]

Carl McBride at 09:28, 8 June 2007

2007-06-08T09:28:04Z

← Older revision		Revision as of 11:28, 8 June 2007
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	The '''bridge functions''' are infinite series of irreducible [[diagrams]] <math>D_i</math>:		The '''bridge functions''' are infinite series of irreducible [[Cluster diagrams \| diagrams]] <math>D_i</math>:

	:<math>B^{(2)}(r) = \rho^2 \frac{1}{2} D_1(r) + \rho^3 [D_2(r) + D_3(r)] + \rho^4[...]+...</math>		:<math>B^{(2)}(r) = \rho^2 \frac{1}{2} D_1(r) + \rho^3 [D_2(r) + D_3(r)] + \rho^4[...]+...</math>
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	:<math>B^{(1)}(r) = \frac{1}{3} B^{(2)}(r) + \rho^3 \left[\frac{1}{6}D_2(r) - \frac{1}{12}D_3(r)\right] + \rho^4[...]+...</math>		:<math>B^{(1)}(r) = \frac{1}{3} B^{(2)}(r) + \rho^3 \left[\frac{1}{6}D_2(r) - \frac{1}{12}D_3(r)\right] + \rho^4[...]+...</math>

	where <math>\rho</math> is the density of the fluid		where <math>\rho</math> is the density of the fluid.
	==References==		==References==
	#[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]		#[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]
	[[category: integral equations]]		[[category: integral equations]]

Carl McBride at 09:25, 8 June 2007

2007-06-08T09:25:37Z

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 ==References==
 #[http://dx.doi.org/10.1063/1.2737046     Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]
 [[category:  integral equations]]

Carl McBride: New page: ==References== #[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids...

2007-06-08T08:40:39Z

New page: ==References== #[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids...

New page

==References==
#[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)]
[[category: integral equations]]