Tarazona's weighted density approximation - Revision history

Carl McBride: Changed references to Cite format

2010-08-18T13:32:54Z

Changed references to Cite format

← Older revision		Revision as of 15:32, 18 August 2010
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	~~{{Stub-general}}~~

	Inspired by the exact solution known for the system of [[1-dimensional hard rods]],		Inspired by the exact solution known for the system of [[1-dimensional hard rods]],
	Pedro Tarazona proposed a series of models in the 1980's (~~Refs~~. 1-4), in which the		Pedro Tarazona proposed a series of models in the 1980's
	dependence of the [[Helmholtz energy function]] is weighted:		<ref>[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1984)]</ref>
			<ref>[http://dx.doi.org/10.1103/PhysRevA.31.2672 P. Tarazona "Free-energy density functional for hard spheres", Physical Review A '''31''' pp. 2672-2679 (1985)]</ref>
			<ref>[http://dx.doi.org/10.1103/PhysRevA.32.3148 P. Tarazona "Erratum: Free-energy density functional for hard spheres", Physical Review A '''32''' p. 3148 (1985)]</ref>
			<ref>[http://dx.doi.org/10.1080/00268978700100381 P. Tarazona, U. Marini Bettolo Marconi and R. Evans "Phase equilibria of fluid interfaces and confined fluids: Non-local versus local density functionals" Molecular Physics '''60''' pp. 573-595 (1987)]</ref>
			in which the dependence of the [[Helmholtz energy function]] is weighted:
	:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>,		:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>,
	where <math>\overline\rho ({\mathbf r})</math> is an average of the		where <math>\overline\rho ({\mathbf r})</math> is an average of the
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	==References==		==References==
	~~#[http:~~/~~/dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1984)]~~		<references/>
	~~#[http://dx.doi.org/10.1103/PhysRevA.31.2672 P. Tarazona "Free-energy density functional for hard spheres", Physical Review A '''31''' pp. 2672 - 2679 (1985)]~~
	~~#[http://dx.doi.org/10.1103/PhysRevA.32.3148 P. Tarazona "Erratum: Free-energy density functional for hard spheres", Physical Review A '''32''' p. 3148 (1985)]~~
	#[http://dx.doi.org/10.1080/00268978700100381 P. Tarazona, U. Marini Bettolo Marconi and R. Evans "Phase equilibria of fluid interfaces and confined fluids: Non-local versus local density functionals" Molecular Physics '''60''' pp. 573 - 595 (1987)]

	[[category:density-functional theory]]		[[category:density-functional theory]]
	[[category:hard sphere]]		[[category:hard sphere]]

Nice and Tidy at 13:03, 19 February 2008

2008-02-19T13:03:32Z

← Older revision		Revision as of 15:03, 19 February 2008
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	{{Stub-general}}		{{Stub-general}}

	Inspired by the exact solution known for the system of [[~~hard rods \|~~ 1-dimensional hard rods]],		Inspired by the exact solution known for the system of [[1-dimensional hard rods]],
	Pedro Tarazona proposed a series of models in the 1980's (Refs. 1-4), in which the		Pedro Tarazona proposed a series of models in the 1980's (Refs. 1-4), in which the
	dependence of the [[Helmholtz energy function]] is weighted:		dependence of the [[Helmholtz energy function]] is weighted:

Nice and Tidy at 11:31, 9 October 2007

2007-10-09T11:31:39Z

← Older revision		Revision as of 13:31, 9 October 2007
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	Inspired by the exact solution known for the system of [[hard rods \| 1-dimensional hard rods]],		Inspired by the exact solution known for the system of [[hard rods \| 1-dimensional hard rods]],
	Pedro Tarazona proposed a series of models in the 1980's, in which the		Pedro Tarazona proposed a series of models in the 1980's (Refs. 1-4), in which the
	dependence of the [[Helmholtz energy function]] is weighted:		dependence of the [[Helmholtz energy function]] is weighted:
	:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>,		:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>,

Carl McBride at 10:22, 9 October 2007

2007-10-09T10:22:31Z

← Older revision		Revision as of 12:22, 9 October 2007
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	{{Stub-general}}		{{Stub-general}}

	Inspired by the exact solution known for the system of 1D hard rods,		Inspired by the exact solution known for the system of [[hard rods \| 1-dimensional hard rods]],
	Pedro Tarazona proposed a series of models in the ~~80s~~, in which the		Pedro Tarazona proposed a series of models in the 1980's, in which the
	dependence of the ~~free~~ energy is weighted:		dependence of the [[Helmholtz energy function]] is weighted:
	:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>,		:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>,
	where <math>\overline\rho ({\mathbf r})</math> is an average of the		where <math>\overline\rho ({\mathbf r})</math> is an average of the

Dduque at 10:14, 9 October 2007

2007-10-09T10:14:43Z

← Older revision		Revision as of 12:14, 9 October 2007
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	{{Stub-general}}		{{Stub-general}}
	~~:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>~~

	where ''A'' is the [[Helmholtz energy function]].		Inspired by the exact solution known for the system of 1D hard rods,
			Pedro Tarazona proposed a series of models in the 80s, in which the
			dependence of the free energy is weighted:
			:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>,
			where <math>\overline\rho ({\mathbf r})</math> is an average of the
			density distribution and where ''A'' is the [[Helmholtz energy function]].
			The function <math>a(x)</math> should vanish at low values of
			its argument (so that the excess vanishes and one is left with
			the ideal case), and diverge at some saturation density corresponding
			to complete packing.

	==References==		==References==
	#[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1984)]		#[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1984)]

Carl McBride at 10:09, 9 October 2007

2007-10-09T10:09:52Z

← Older revision		Revision as of 12:09, 9 October 2007
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			{{Stub-general}}
	:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>		:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>

			where ''A'' is the [[Helmholtz energy function]].
	==References==		==References==
	#[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1984)]		#[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1984)]

Carl McBride: Tarazona moved to Tarazona's weighted density approximation

2007-10-09T10:05:58Z

Tarazona moved to Tarazona's weighted density approximation

← Older revision	Revision as of 12:05, 9 October 2007
(No difference)

Carl McBride at 09:55, 9 October 2007

2007-10-09T09:55:15Z

← Older revision		Revision as of 11:55, 9 October 2007
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	~~Pedro Tarazona~~ (~~Universidad Autónoma de Madrid~~)		:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>

	==References==		==References==

Carl McBride at 16:00, 24 August 2007

2007-08-24T16:00:45Z

← Older revision		Revision as of 18:00, 24 August 2007
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	==References==		==References==
	#[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (~~1985~~)]		#[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1984)]
	#[http://dx.doi.org/10.1103/PhysRevA.31.2672 P. Tarazona "Free-energy density functional for hard spheres", Physical Review A '''32''' pp. 2672 - 2679 (1985)]		#[http://dx.doi.org/10.1103/PhysRevA.31.2672 P. Tarazona "Free-energy density functional for hard spheres", Physical Review A '''31''' pp. 2672 - 2679 (1985)]
			#[http://dx.doi.org/10.1103/PhysRevA.32.3148 P. Tarazona "Erratum: Free-energy density functional for hard spheres", Physical Review A '''32''' p. 3148 (1985)]
			#[http://dx.doi.org/10.1080/00268978700100381 P. Tarazona, U. Marini Bettolo Marconi and R. Evans "Phase equilibria of fluid interfaces and confined fluids: Non-local versus local density functionals" Molecular Physics '''60''' pp. 573 - 595 (1987)]

	[[category:density-functional theory]]		[[category:density-functional theory]]
	[[category:hard sphere]]		[[category:hard sphere]]

Carl McBride at 11:54, 29 March 2007

2007-03-29T11:54:33Z

← Older revision		Revision as of 13:54, 29 March 2007
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	#[http://dx.doi.org/10.1103/PhysRevA.31.2672 P. Tarazona "Free-energy density functional for hard spheres", Physical Review A '''32''' pp. 2672 - 2679 (1985)]		#[http://dx.doi.org/10.1103/PhysRevA.31.2672 P. Tarazona "Free-energy density functional for hard spheres", Physical Review A '''32''' pp. 2672 - 2679 (1985)]

	[[category:~~dft~~]]		[[category:density-functional theory]]
	[[category:hard sphere]]		[[category:hard sphere]]