Born-Green equation - Revision history

Carl McBride at 16:49, 6 September 2007

2007-09-06T16:49:41Z

← Older revision		Revision as of 18:49, 6 September 2007
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			The '''Born-Green equation''' is given by:

	:<math>k_B T \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}=		:<math>k_B T \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}=
	\frac{-\partial \Phi(r_{12})}{\partial {\mathbf r}_1}- \rho \int \left[ \frac{\partial \Phi(r_{13})}{\partial {\mathbf r}_1} \right] {\rm g}(r_{13}){\rm g}(r_{23}) ~ {\rm d}{\mathbf r}_3</math>		\frac{-\partial \Phi(r_{12})}{\partial {\mathbf r}_1}- \rho \int \left[ \frac{\partial \Phi(r_{13})}{\partial {\mathbf r}_1} \right] {\rm g}(r_{13}){\rm g}(r_{23}) ~ {\rm d}{\mathbf r}_3</math>

Nice and Tidy at 14:19, 10 July 2007

2007-07-10T14:19:22Z

← Older revision		Revision as of 16:19, 10 July 2007
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	:<math>kT \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}=		:<math>k_B T \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}=
	\frac{-\partial U(r_{12})}{\partial {\mathbf r}_1}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial {\mathbf r}_1} \right] {\rm g}(r_{13}){\rm g}(r_{23}) ~ {\rm d}{\mathbf r}_3</math>		\frac{-\partial \Phi(r_{12})}{\partial {\mathbf r}_1}- \rho \int \left[ \frac{\partial \Phi(r_{13})}{\partial {\mathbf r}_1} \right] {\rm g}(r_{13}){\rm g}(r_{23}) ~ {\rm d}{\mathbf r}_3</math>

			where <math>\Phi(r_{nm})</math> is the [[intermolecular pair potential]], ''T'' is the [[temperature]], and <math>k_B</math> is the [[Boltzmann constant]].
	==References==		==References==
	#[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)]		#[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)]
	[[category:statistical mechanics]]		[[category:statistical mechanics]]

Carl McBride at 13:52, 10 July 2007

2007-07-10T13:52:13Z

← Older revision		Revision as of 15:52, 10 July 2007
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	:<math>kT \frac{\partial \ln g(r_{12})}{\partial ~~r_1~~}=		:<math>kT \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}=
	\frac{-\partial U(r_{12})}{\partial ~~r_1~~}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial ~~r_1~~} \right] g(r_{13})g(r_{23}) ~ d ~~r_3~~</math>		\frac{-\partial U(r_{12})}{\partial {\mathbf r}_1}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial {\mathbf r}_1} \right] {\rm g}(r_{13}){\rm g}(r_{23}) ~ {\rm d}{\mathbf r}_3</math>
	==References==		==References==
	#[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)]		#[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)]
	[[category:statistical mechanics]]		[[category:statistical mechanics]]

Nice and Tidy at 15:54, 25 May 2007

2007-05-25T15:54:09Z

← Older revision		Revision as of 17:54, 25 May 2007
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	:<math>kT \frac{\partial \ln g(r_{12})}{\partial r_1}=		:<math>kT \frac{\partial \ln g(r_{12})}{\partial r_1}=
	\frac{-\partial U(r_{12})}{\partial r_1}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial r_1} \right] g(r_{13})g(r_{23}) ~ d r_3</math>		\frac{-\partial U(r_{12})}{\partial r_1}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial r_1} \right] g(r_{13})g(r_{23}) ~ d r_3</math>

	==References==		==References==

	#[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)]		#[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)]
			[[category:statistical mechanics]]

Carl McBride at 15:49, 24 April 2007

2007-04-24T15:49:50Z

← Older revision		Revision as of 17:49, 24 April 2007
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	==References==		==References==

	#M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences~~, volume~~ 188 p. 10" (1946)		#[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)]

Nice and Tidy at 17:48, 26 February 2007

2007-02-26T17:48:36Z

← Older revision		Revision as of 19:48, 26 February 2007
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	<math>kT \frac{\partial \ln g(r_{12})}{\partial r_1}=		:<math>kT \frac{\partial \ln g(r_{12})}{\partial r_1}=
	\frac{-\partial U(r_{12})}{\partial r_1}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial r_1} \right] g(r_{13})g(r_{23}) ~ d r_3</math>		\frac{-\partial U(r_{12})}{\partial r_1}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial r_1} \right] g(r_{13})g(r_{23}) ~ d r_3</math>

Carl McBride: New page: $kT \frac{\partial \ln g(r_{12})}{\partial r_1}= \frac{-\partial U(r_{12})}{\partial r_1}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial r_1} \right] g(r_{13})g(r_{23}) ~ d r_...$

2007-02-17T18:16:44Z

New page: <math>kT \frac{\partial \ln g(r_{12})}{\partial r_1}= \frac{-\partial U(r_{12})}{\partial r_1}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial r_1} \right] g(r_{13})g(r_{23}) ~ d r_...

New page

<math>kT \frac{\partial \ln g(r_{12})}{\partial r_1}=
\frac{-\partial U(r_{12})}{\partial r_1}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial r_1} \right] g(r_{13})g(r_{23}) ~ d r_3</math>

==References==

#M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, volume 188 p. 10" (1946)