Hard hyperspheres - Revision history

Carl McBride: Added a recent publication

2011-09-01T10:38:48Z

Added a recent publication

← Older revision		Revision as of 12:38, 1 September 2011
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	==References==		==References==
	<references/>		<references/>
			;Related reading
			*[http://dx.doi.org/10.1063/1.3622597 Jarosław Piasecki, Piotr Szymczak, and John J. Kozak "Structural transitions in hypersphere fluids: Predictions of Kirkwood's approximation", Journal of Chemical Physics '''135''' 084509 (2011)]
	[[category: models]]		[[category: models]]

Carl McBride: Slight tidy + new publication

2011-02-01T10:45:04Z

Slight tidy + new publication

← Older revision		Revision as of 12:45, 1 February 2011
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	~~{{Stub-general}}~~		'''Hard hyperspheres''' are [[hard sphere model \| hard spheres]] in more than three dimensions (<math>D</math>).
	'''Hard hyperspheres''' are [[hard sphere model \| hard spheres]] in more than three dimensions.		==Volume==
	The volume of an ''n''-sphere of unit diameter is given by		The volume of an ''n''-sphere of unit diameter is given by

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	where <math>\Gamma(m)</math> is the [[Gamma function]].		where <math>\Gamma(m)</math> is the [[Gamma function]].
	==~~See also~~==		==Structure factor==
	*[[Hard sphere: virial coefficients]]		[[Structure factor]] <ref>[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)]</ref>
			==Liquid-solid transition==
			The [[Solid-liquid phase transitions \|liquid-solid]] transition for <math>D=4, 5</math> and <math>6</math> <ref>[http://dx.doi.org/10.1063/1.3530780 C. D. Estrada and M. Robles "Fluid–solid transition in hard hypersphere systems", Journal of Chemical Physics '''134''' 044115 (2011)]</ref>.
			==Virial coefficients==
			[[Hard sphere: virial coefficients]] for odd dimensions <ref>[http://dx.doi.org/10.1063/1.2951456 René D. Rohrmann, Miguel Robles, Mariano López de Haro, and Andrés Santos "Virial series for fluids of hard hyperspheres in odd dimensions", Journal of Chemical Physics '''129''' 014510 (2008)]</ref>
			==Percus–Yevick equation==
			The [[Percus Yevick]] equation <ref>[http://dx.doi.org/10.1063/1.2991338 M. Adda-Bedia, E. Katzav, and D. Vella "Solution of the Percus–Yevick equation for hard hyperspheres in even dimensions", Journal of Chemical Physics '''129''' 144506 (2008)]</ref>
	==References==		==References==
	~~#[http:~~//dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)]		<references/>
	#[http://dx.doi.org/10.1063/1.2951456 René D. Rohrmann, Miguel Robles, Mariano López de Haro, and Andrés Santos "Virial series for fluids of hard hyperspheres in odd dimensions", Journal of Chemical Physics '''129''' 014510 (2008)]
	#[http://dx.doi.org/10.1063/1.2991338 M. Adda-Bedia, E. Katzav, and D. Vella "Solution of the Percus–Yevick equation for hard hyperspheres in even dimensions", Journal of Chemical Physics '''129''' 144506 (2008)]
	[[category: models]]		[[category: models]]

Carl McBride: Trivial tidy.

2008-10-16T09:45:34Z

Trivial tidy.

← Older revision		Revision as of 11:45, 16 October 2008
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	{{Stub-general}}		{{Stub-general}}
	~~==Volume==~~		'''Hard hyperspheres''' are [[hard sphere model \| hard spheres]] in more than three dimensions.
	The volume of ~~a <math>d</math>~~ sphere of unit diameter is given by		The volume of an ''n''-sphere of unit diameter is given by

	:<math>~~v_d~~=\frac{(\pi / 4)^{d/2}}{\Gamma(1+ d/2)}</math>		:<math>v_n=\frac{(\pi / 4)^{n/2}}{\Gamma(1+ n/2)}</math>

	where <math>\Gamma(m)</math> is the [[Gamma function]].		where <math>\Gamma(m)</math> is the [[Gamma function]].

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

2008-10-15T10:32:36Z

References: Added a new reference

← Older revision		Revision as of 12:32, 15 October 2008
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	#[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)]		#[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)]
	#[http://dx.doi.org/10.1063/1.2951456 René D. Rohrmann, Miguel Robles, Mariano López de Haro, and Andrés Santos "Virial series for fluids of hard hyperspheres in odd dimensions", Journal of Chemical Physics '''129''' 014510 (2008)]		#[http://dx.doi.org/10.1063/1.2951456 René D. Rohrmann, Miguel Robles, Mariano López de Haro, and Andrés Santos "Virial series for fluids of hard hyperspheres in odd dimensions", Journal of Chemical Physics '''129''' 014510 (2008)]
			#[http://dx.doi.org/10.1063/1.2991338 M. Adda-Bedia, E. Katzav, and D. Vella "Solution of the Percus–Yevick equation for hard hyperspheres in even dimensions", Journal of Chemical Physics '''129''' 144506 (2008)]
	[[category: models]]		[[category: models]]

Carl McBride at 09:33, 7 July 2008

2008-07-07T09:33:31Z

← Older revision		Revision as of 11:33, 7 July 2008
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	{{Stub-general}}		{{Stub-general}}
			==Volume==
			The volume of a <math>d</math> sphere of unit diameter is given by

			:<math>v_d=\frac{(\pi / 4)^{d/2}}{\Gamma(1+ d/2)}</math>

			where <math>\Gamma(m)</math> is the [[Gamma function]].
			==See also==
			*[[Hard sphere: virial coefficients]]
	==References==		==References==
	#[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)]		#[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)]
			#[http://dx.doi.org/10.1063/1.2951456 René D. Rohrmann, Miguel Robles, Mariano López de Haro, and Andrés Santos "Virial series for fluids of hard hyperspheres in odd dimensions", Journal of Chemical Physics '''129''' 014510 (2008)]
	[[category: models]]		[[category: models]]

Nice and Tidy at 11:29, 26 September 2007

2007-09-26T11:29:15Z

← Older revision		Revision as of 13:29, 26 September 2007
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			{{Stub-general}}
	==References==		==References==
	#[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)]		#[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)]
	[[category: models]]		[[category: models]]

Carl McBride: New page: ==References== #[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chem...

2007-06-13T11:04:58Z

New page: ==References== #[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chem...

New page

==References==
#[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)]
[[category: models]]