Hard cube model - Revision history

Carl McBride: Added references to Truncated hard cubes section

2015-02-09T10:38:03Z

Added references to Truncated hard cubes section

← Older revision		Revision as of 12:38, 9 February 2015
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	For two cubes, the overlap check therefore corresponds to the projection of both shapes onto 15 axes: the three edge vectors of both particles (6 in total), and the axes given by the 9 possible cross products of an edge vector of one cube with an edge vector of the other cube. The particles overlap if and only if the projections of the two particles on all 15 axes overlap as well.		For two cubes, the overlap check therefore corresponds to the projection of both shapes onto 15 axes: the three edge vectors of both particles (6 in total), and the axes given by the 9 possible cross products of an edge vector of one cube with an edge vector of the other cube. The particles overlap if and only if the projections of the two particles on all 15 axes overlap as well.

			==Truncated hard cubes==
			<ref>[http://dx.doi.org/10.1103/PhysRevLett.111.015501 Anjan P. Gantapara, Joost de Graaf, René van Roij, and Marjolein Dijkstra "Phase Diagram and Structural Diversity of a Family of Truncated Cubes: Degenerate Close-Packed Structures and Vacancy-Rich States", Physical Review Letters '''111''' 015501 (2013)]</ref><ref>[http://dx.doi.org/10.1063/1.4906753 Anjan P. Gantapara, Joost de Graaf, René van Roij and Marjolein Dijkstra "Phase behavior of a family of truncated hard cubes", Journal of Chemical Physics '''142''' 054904 (2015)]</ref>

	==References==		==References==

Carl McBride: Slight tidy

2013-12-12T17:47:41Z

Slight tidy

← Older revision		Revision as of 19:47, 12 December 2013
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	[[Image:cube.png\|thumb\|right]]		[[Image:cube.png\|thumb\|right]]
	The '''~~Hard~~ cube model''' models cube-shaped particles interacting purely through excluded-volume interactions. The phase behavior has been studied ~~extensively~~		The '''hard cube model''' models cube-shaped particles interacting purely through excluded-volume interactions. The phase behavior has been studied, for example see <ref>[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials '''10''' pp. 230-235 (2011)]</ref>
	<ref>[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials '''10''' pp. 230-235 (2011)]</ref>		<ref>[http://dx.doi.org/10.1073/pnas.1211784109 F. Smallenburg, L. Filion, M. Marechal, and M. Dijkstra "Vacancy-stabilized crystalline order in hard cubes", Proc. Natl. Acad. Sci. USA '''109''' pp. 17886-17891 (2012)]</ref>.
	<ref>[http://dx.doi.org/10.1073/pnas.1211784109 F. Smallenburg, L. Filion, M. Marechal, and M. Dijkstra "Vacancy-stabilized crystalline order in hard cubes", Proc. Natl. Acad. Sci. USA '''109''' pp. 17886-17891 (2012)]</ref>. The simple cubic crystal phase has been shown to contain a high number of mobile, delocalized vacancies, similar to those seen in [[Parallel hard cubes]].		The simple cubic crystal phase has been shown to contain a high number of mobile, delocalized vacancies, similar to those seen in [[Parallel hard cubes]].

	==Implementation==		==Implementation==

Nice and Tidy: Removed stub template

2013-04-29T11:49:40Z

Removed stub template

← Older revision		Revision as of 13:49, 29 April 2013
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	~~{{stub-general}}~~
	[[Image:cube.png\|thumb\|right]]		[[Image:cube.png\|thumb\|right]]
	The '''Hard cube model''' models cube-shaped particles interacting purely through excluded-volume interactions. The phase behavior has been studied extensively		The '''Hard cube model''' models cube-shaped particles interacting purely through excluded-volume interactions. The phase behavior has been studied extensively

FSmallenburg: fixed reference

2013-04-28T13:23:53Z

fixed reference

← Older revision		Revision as of 15:23, 28 April 2013
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	{{stub-general}}		{{stub-general}}
	[[Image:cube.png\|thumb\|right]]		[[Image:cube.png\|thumb\|right]]
	The '''Hard cube model''' models cube-shaped particles interacting purely through excluded-volume interactions. The phase behavior has been studied extensively <ref>[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials '''10''' pp. 230-235 (2011)]</ref>		The '''Hard cube model''' models cube-shaped particles interacting purely through excluded-volume interactions. The phase behavior has been studied extensively
	<ref>[http://dx.doi.org/10.1073/pnas.1211784109 F. Smallenburg, L. Filion, M. Marechal, and M. Dijkstra, "Vacancy-stabilized crystalline order in hard cubes",		<ref>[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials '''10''' pp. 230-235 (2011)]</ref>
	Proc. Natl. Acad. Sci. USA '''109''' 17886 (2012)]</ref>. The simple cubic crystal phase has been shown to contain a high number of mobile, delocalized vacancies, similar to those seen in [[Parallel hard cubes]].		<ref>[http://dx.doi.org/10.1073/pnas.1211784109 F. Smallenburg, L. Filion, M. Marechal, and M. Dijkstra "Vacancy-stabilized crystalline order in hard cubes", Proc. Natl. Acad. Sci. USA '''109''' pp. 17886-17891 (2012)]</ref>. The simple cubic crystal phase has been shown to contain a high number of mobile, delocalized vacancies, similar to those seen in [[Parallel hard cubes]].

	==Implementation==		==Implementation==

FSmallenburg: Added some information and a reference

2013-04-28T13:16:26Z

Added some information and a reference

← Older revision		Revision as of 15:16, 28 April 2013
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	{{stub-general}}		{{stub-general}}
	[[Image:cube.png\|thumb\|right]]		[[Image:cube.png\|thumb\|right]]
	'''Hard cube model'''		The '''Hard cube model''' models cube-shaped particles interacting purely through excluded-volume interactions. The phase behavior has been studied extensively <ref>[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials '''10''' pp. 230-235 (2011)]</ref>
			<ref>[http://dx.doi.org/10.1073/pnas.1211784109 F. Smallenburg, L. Filion, M. Marechal, and M. Dijkstra, "Vacancy-stabilized crystalline order in hard cubes",
			Proc. Natl. Acad. Sci. USA '''109''' 17886 (2012)]</ref>. The simple cubic crystal phase has been shown to contain a high number of mobile, delocalized vacancies, similar to those seen in [[Parallel hard cubes]].

			==Implementation==
			Overlaps between cubes can be checked based on the [http://en.wikipedia.org/wiki/Hyperplane_separation_theorem separating axis theorem], which says that if two convex objects are not interpenetrating, there must be an axis for which the projections of the two objects will not overlap. In the case of two
			convex polyhedral particles, only a finite number of possible separating axes need to be
			checked: in that case, the possible separating axes are either parallel to a normal of one
			of the faces of either of the two particles, or perpendicular to the plane spanned by one
			of the edges of the first particle and one of the edges of the second particle.

			For two cubes, the overlap check therefore corresponds to the projection of both shapes onto 15 axes: the three edge vectors of both particles (6 in total), and the axes given by the 9 possible cross products of an edge vector of one cube with an edge vector of the other cube. The particles overlap if and only if the projections of the two particles on all 15 axes overlap as well.


	==References==		==References==
	<references/>		<references/>

	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials '''10''' pp. 230-235 (2011)]
	*[http://dx.doi.org/10.1063/1.4734021 Umang Agarwal and Fernando A. Escobedo "Effect of quenched size polydispersity on the ordering transitions of hard polyhedral particles", Journal of Chemical Physics '''137''' 024905 (2012)]		*[http://dx.doi.org/10.1063/1.4734021 Umang Agarwal and Fernando A. Escobedo "Effect of quenched size polydispersity on the ordering transitions of hard polyhedral particles", Journal of Chemical Physics '''137''' 024905 (2012)]
	[[category: models]]		[[category: models]]

Carl McBride: Created page with "{{stub-general}} right '''Hard cube model''' ==References== '''Related reading''' *[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and..."

2012-07-12T15:11:27Z

Created page with "{{stub-general}} thumb|right '''Hard cube model''' ==References== <references/> '''Related reading''' *[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and..."

New page

{{stub-general}}
[[Image:cube.png|thumb|right]]
'''Hard cube model'''
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials '''10''' pp. 230-235 (2011)]
*[http://dx.doi.org/10.1063/1.4734021 Umang Agarwal and Fernando A. Escobedo "Effect of quenched size polydispersity on the ordering transitions of hard polyhedral particles", Journal of Chemical Physics '''137''' 024905 (2012)]
[[category: models]]