Percus Yevick - Revision history

Carl McBride: Added internal link

2008-03-14T10:53:58Z

Added internal link

← Older revision		Revision as of 12:53, 14 March 2008
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	Note: the restriction <math>-1 < \gamma (r) \leq 1</math> arising from the logarithmic term Ref. 6.		Note: the restriction <math>-1 < \gamma (r) \leq 1</math> arising from the logarithmic term Ref. 6.
	A critical look at the PY was undertaken by Zhou and Stell in Ref. 7.		A critical look at the PY was undertaken by Zhou and Stell in Ref. 7.
			==See also==
			*[[Exact solution of the Percus Yevick integral equation for hard spheres]]
	==References==		==References==
	#[http://dx.doi.org/10.1088/0034-4885/28/1/306 J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics '''28''' pp. 169-199 (1965)]		#[http://dx.doi.org/10.1088/0034-4885/28/1/306 J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics '''28''' pp. 169-199 (1965)]

Carl McBride at 17:09, 26 June 2007

2007-06-26T17:09:45Z

← Older revision		Revision as of 19:09, 26 June 2007
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	:<math>\left.D(r)\right. = y(r) + c(r) -g(r)</math>		:<math>\left.D(r)\right. = y(r) + c(r) -g(r)</math>

	one has the exact integral equation		one has the exact [[integral equations \| integral equation]]

	:<math>y(r_{12}) - D(r_{12}) = 1 + n \int (f(r_{13})y(r_{13})+D(r_{13})) h(r_{23})~dr_3</math>		:<math>y(r_{12}) - D(r_{12}) = 1 + n \int (f(r_{13})y(r_{13})+D(r_{13})) h(r_{23})~dr_3</math>
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	:<math>\left.h-c\right.=y-1</math>		:<math>\left.h-c\right.=y-1</math>

	The ~~''PY''~~ closure can be written as (Ref. 3 Eq. 61)		The Percus-Yevick [[Closure relations \| closure relation]] can be written as (Ref. 3 Eq. 61)

	:<math>\left.f [ \gamma (r) ]\right. = [e^{-\beta \Phi} -1][\gamma (r) +1]</math>		:<math>\left.f [ \gamma (r) ]\right. = [e^{-\beta \Phi} -1][\gamma (r) +1]</math>

Nice and Tidy at 13:18, 21 June 2007

2007-06-21T13:18:03Z

← Older revision		Revision as of 15:18, 21 June 2007
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	:<math>\left.g(r)\right. = e^{-\beta \Phi} (1+ \gamma(r))</math>		:<math>\left.g(r)\right. = e^{-\beta \Phi} (1+ \gamma(r))</math>

	~~or in~~ terms of the [[bridge function]]		where <math>\Phi(r)</math> is the [[intermolecular pair potential]].

			In terms of the [[bridge function]]

	:<math>\left.B(r)\right.= \ln (1+\gamma(r) ) - \gamma(r)</math>		:<math>\left.B(r)\right.= \ln (1+\gamma(r) ) - \gamma(r)</math>

Carl McBride at 12:59, 8 June 2007

2007-06-08T12:59:13Z

← Older revision		Revision as of 14:59, 8 June 2007
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	If one defines a class of diagrams by the linear combination (Eq. 5.18 Ref.1)		If one defines a class of [[cluster diagrams \| diagrams]] by the linear combination (Eq. 5.18 Ref.1)
	(See G. Stell in Ref. 2)		(See G. Stell in Ref. 2)

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	:<math>\left.g(r)\right. = e^{-\beta \Phi} (1+ \gamma(r))</math>		:<math>\left.g(r)\right. = e^{-\beta \Phi} (1+ \gamma(r))</math>

	or in terms of the bridge function		or in terms of the [[bridge function]]

	:<math>\left.B(r)\right.= \ln (1+\gamma(r) ) - \gamma(r)</math>		:<math>\left.B(r)\right.= \ln (1+\gamma(r) ) - \gamma(r)</math>

Carl McBride: /* References */

2007-02-28T11:05:57Z

References

← Older revision		Revision as of 13:05, 28 February 2007
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	#[http://dx.doi.org/10.1103/PhysRevA.30.999 Forrest J. Rogers and David A. Young "New, thermodynamically consistent, integral equation for simple fluids", Physical Review A '''30''' pp. 999 - 1007 (1984)]		#[http://dx.doi.org/10.1103/PhysRevA.30.999 Forrest J. Rogers and David A. Young "New, thermodynamically consistent, integral equation for simple fluids", Physical Review A '''30''' pp. 999 - 1007 (1984)]
	#[http://dx.doi.org/10.1063/1.1467894 Niharendu Choudhury and Swapan K. Ghosh "Integral equation theory of Lennard-Jones fluids: A modified Verlet bridge function approach", Journal of Chemical Physics, '''116''' pp. 8517-8522 (2002)]		#[http://dx.doi.org/10.1063/1.1467894 Niharendu Choudhury and Swapan K. Ghosh "Integral equation theory of Lennard-Jones fluids: A modified Verlet bridge function approach", Journal of Chemical Physics, '''116''' pp. 8517-8522 (2002)]
	#[http://dx.doi.org/		#[http://dx.doi.org/10.1007/BF01011655 Yaoqi Zhou and George Stell "The hard-sphere fluid: New exact results with applications", Journal of Statistical Physics '''52''' 1389-1412 (1988)]
	~~#[JSP_1988_52_1389_nolotengoSpringer]~~

	[[Category: Integral equations]]		[[Category: Integral equations]]

Carl McBride: /* References */

2007-02-28T11:03:18Z

References

← Older revision		Revision as of 13:03, 28 February 2007
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	#[http://dx.doi.org/10.1080/00268978300102111 G. A. Martynov and G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' pp. 1495-1504 (1983)]		#[http://dx.doi.org/10.1080/00268978300102111 G. A. Martynov and G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' pp. 1495-1504 (1983)]
	#[http://dx.doi.org/10.1103/PhysRevA.30.999 Forrest J. Rogers and David A. Young "New, thermodynamically consistent, integral equation for simple fluids", Physical Review A '''30''' pp. 999 - 1007 (1984)]		#[http://dx.doi.org/10.1103/PhysRevA.30.999 Forrest J. Rogers and David A. Young "New, thermodynamically consistent, integral equation for simple fluids", Physical Review A '''30''' pp. 999 - 1007 (1984)]
			#[http://dx.doi.org/10.1063/1.1467894 Niharendu Choudhury and Swapan K. Ghosh "Integral equation theory of Lennard-Jones fluids: A modified Verlet bridge function approach", Journal of Chemical Physics, '''116''' pp. 8517-8522 (2002)]
	#[http://dx.doi.org/		#[http://dx.doi.org/
	~~#[http://dx.doi.org/~~
	~~#[JCP_2002_116_08517]~~
	#[JSP_1988_52_1389_nolotengoSpringer]		#[JSP_1988_52_1389_nolotengoSpringer]

	[[Category: Integral equations]]		[[Category: Integral equations]]

Carl McBride: /* References */

2007-02-28T11:01:08Z

References

← Older revision		Revision as of 13:01, 28 February 2007
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	# G. Stell "PERCUS-YEVICK EQUATION FOR RADIAL DISTRIBUTION FUNCTION OF A FLUID", Physica '''29''' pp. 517- (1963)		# G. Stell "PERCUS-YEVICK EQUATION FOR RADIAL DISTRIBUTION FUNCTION OF A FLUID", Physica '''29''' pp. 517- (1963)
	#[http://dx.doi.org/10.1103/PhysRev.110.1 Jerome K. Percus and George J. Yevick "Analysis of Classical Statistical Mechanics by Means of Collective Coordinates", Physical Review '''110''' pp. 1 - 13 (1958)]		#[http://dx.doi.org/10.1103/PhysRev.110.1 Jerome K. Percus and George J. Yevick "Analysis of Classical Statistical Mechanics by Means of Collective Coordinates", Physical Review '''110''' pp. 1 - 13 (1958)]
	#[http://dx.doi.org/		#[http://dx.doi.org/10.1080/00268978300102111 G. A. Martynov and G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' pp. 1495-1504 (1983)]
	#[http://dx.doi.org/10.1103/PhysRevA.30.999 Forrest J. Rogers and David A. Young "New, thermodynamically consistent, integral equation for simple fluids", Physical Review A '''30''' pp. 999 - 1007 (1984)]		#[http://dx.doi.org/10.1103/PhysRevA.30.999 Forrest J. Rogers and David A. Young "New, thermodynamically consistent, integral equation for simple fluids", Physical Review A '''30''' pp. 999 - 1007 (1984)]
	#[http://dx.doi.org/		#[http://dx.doi.org/
	#[http://dx.doi.org/		#[http://dx.doi.org/
	~~#[http://dx.doi.org/~~





	~~#[MP_1983_49_1495]~~

	#[JCP_2002_116_08517]		#[JCP_2002_116_08517]
	#[JSP_1988_52_1389_nolotengoSpringer]		#[JSP_1988_52_1389_nolotengoSpringer]

	[[Category: Integral equations]]		[[Category: Integral equations]]

Carl McBride: /* References */

2007-02-28T10:57:59Z

References

← Older revision		Revision as of 12:57, 28 February 2007
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	==References==		==References==
	#[http://dx.doi.org/10.1088/0034-4885/28/1/306 J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics '''28''' pp. 169-199 (1965)]		#[http://dx.doi.org/10.1088/0034-4885/28/1/306 J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics '''28''' pp. 169-199 (1965)]
	#~~[http://dx~~.~~doi~~.~~org/~~		# G. Stell "PERCUS-YEVICK EQUATION FOR RADIAL DISTRIBUTION FUNCTION OF A FLUID", Physica '''29''' pp. 517- (1963)
	#[http://dx.doi.org/10.1103/PhysRev.110.1 Jerome K. Percus and George J. Yevick "Analysis of Classical Statistical Mechanics by Means of Collective Coordinates", Physical Review '''110''' pp. 1 - 13 (1958)]		#[http://dx.doi.org/10.1103/PhysRev.110.1 Jerome K. Percus and George J. Yevick "Analysis of Classical Statistical Mechanics by Means of Collective Coordinates", Physical Review '''110''' pp. 1 - 13 (1958)]
	#[http://dx.doi.org/		#[http://dx.doi.org/
			#[http://dx.doi.org/10.1103/PhysRevA.30.999 Forrest J. Rogers and David A. Young "New, thermodynamically consistent, integral equation for simple fluids", Physical Review A '''30''' pp. 999 - 1007 (1984)]
	#[http://dx.doi.org/		#[http://dx.doi.org/
	#[http://dx.doi.org/		#[http://dx.doi.org/
	#[http://dx.doi.org/		#[http://dx.doi.org/
	~~#[http://dx.doi.org/~~



	~~#[P_1963_29_0517_nolotengoElsevier]~~

	#[MP_1983_49_1495]		#[MP_1983_49_1495]
	~~#[PRA_1984_30_000999]~~
	#[JCP_2002_116_08517]		#[JCP_2002_116_08517]
	#[JSP_1988_52_1389_nolotengoSpringer]		#[JSP_1988_52_1389_nolotengoSpringer]

	[[Category: Integral equations]]		[[Category: Integral equations]]

Carl McBride: /* References */

2007-02-28T10:54:52Z

References

← Older revision		Revision as of 12:54, 28 February 2007
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	==References==		==References==
			#[http://dx.doi.org/10.1088/0034-4885/28/1/306 J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics '''28''' pp. 169-199 (1965)]
			#[http://dx.doi.org/
			#[http://dx.doi.org/10.1103/PhysRev.110.1 Jerome K. Percus and George J. Yevick "Analysis of Classical Statistical Mechanics by Means of Collective Coordinates", Physical Review '''110''' pp. 1 - 13 (1958)]
			#[http://dx.doi.org/
			#[http://dx.doi.org/
			#[http://dx.doi.org/
			#[http://dx.doi.org/
			#[http://dx.doi.org/



	~~#[RPP_1965_28_0169]~~
	#[P_1963_29_0517_nolotengoElsevier]		#[P_1963_29_0517_nolotengoElsevier]
	~~#[PR_1958_110_000001]~~
	#[MP_1983_49_1495]		#[MP_1983_49_1495]
	#[PRA_1984_30_000999]		#[PRA_1984_30_000999]

Nice and Tidy at 11:19, 27 February 2007

2007-02-27T11:19:41Z

← Older revision		Revision as of 13:19, 27 February 2007
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	#[JCP_2002_116_08517]		#[JCP_2002_116_08517]
	#[JSP_1988_52_1389_nolotengoSpringer]		#[JSP_1988_52_1389_nolotengoSpringer]

			[[Category: Integral equations]]