SklogWiki - Recent changes [en]

WikiNode

2010-09-08T10:16:31Z

Changed an external link for an internal link

Buckingham potential

2010-09-07T09:01:35Z

Added a See also section

← Older revision		Revision as of 09:01, 7 September 2010
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	The Buckingham potential describes the exchange repulsion, which originates from the Pauli exclusion principle, by a more realistic exponential function of distance, in contrast to the inverse twelfth power used by the [[Lennard-Jones model \|Lennard-Jones potential]]. However, since the Buckingham potential remains finite even at very small distances, it runs the risk of an un-physical "Buckingham catastrophe" at short range when used in simulations of charged systems. This occurs when the electrostatic attraction artificially overcomes the repulsive barrier. The Lennard-Jones potential is also about 4 times quicker to compute <ref>[http://dx.doi.org/10.1023/A:1007911511862 David N. J. White "A computationally efficient alternative to the Buckingham potential for molecular mechanics calculations", Journal of Computer-Aided Molecular Design '''11''' pp.517-521 (1997)]</ref> and so is more frequently used in [[Computer simulation techniques \| computer simulations]].		The Buckingham potential describes the exchange repulsion, which originates from the Pauli exclusion principle, by a more realistic exponential function of distance, in contrast to the inverse twelfth power used by the [[Lennard-Jones model \|Lennard-Jones potential]]. However, since the Buckingham potential remains finite even at very small distances, it runs the risk of an un-physical "Buckingham catastrophe" at short range when used in simulations of charged systems. This occurs when the electrostatic attraction artificially overcomes the repulsive barrier. The Lennard-Jones potential is also about 4 times quicker to compute <ref>[http://dx.doi.org/10.1023/A:1007911511862 David N. J. White "A computationally efficient alternative to the Buckingham potential for molecular mechanics calculations", Journal of Computer-Aided Molecular Design '''11''' pp.517-521 (1997)]</ref> and so is more frequently used in [[Computer simulation techniques \| computer simulations]].
-		+	==See also==
		+	*[[Exp-6 potential]]
	==References==		==References==
	<references/>		<references/>
	[[category: models]]		[[category: models]]

User:Fr GuidoSarducci

2010-09-06T16:58:55Z

New user account

Exp-6 potential

2010-09-06T14:54:58Z

References: Added a paper

← Older revision		Revision as of 14:54, 6 September 2010
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	<references/>		<references/>
	'''Related reading'''		'''Related reading'''
-	*[http://dx.doi.org/10.1063/1.440106 M. Ross and F. H. Ree "Repulsive forces of simple molecules and mixtures at high density and temperature", Journal of Chemical Physics '''73''' pp. 6146-6152 (1980)]	+	*[http://dx.doi.org/10.1063/1.1840523 Marvin Ross and Berni Alder "Shock Compression of Argon. II. Nonadditive Repulsive Potential", Journal of Chemical Physics '''46''' pp. 4203-4210 (1967)]
		+	*[http://dx.doi.org/10.1063/1.440106 Marvin Ross and F. H. Ree "Repulsive forces of simple molecules and mixtures at high density and temperature", Journal of Chemical Physics '''73''' pp. 6146-6152 (1980)]
	[[category: models]]		[[category: models]]

Lennard-Jones model

2010-09-06T14:47:30Z

Added mention of the exp-6 potential

← Older revision		Revision as of 14:47, 6 September 2010
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	the Lennard-Jones potential frequently forms one of 'building blocks' of many [[force fields]]. It is worth mentioning that the 12-6 Lennard-Jones model is not the		the Lennard-Jones potential frequently forms one of 'building blocks' of many [[force fields]]. It is worth mentioning that the 12-6 Lennard-Jones model is not the
	most faithful representation of the potential energy surface, but rather its use is widespread due to its computational expediency.		most faithful representation of the potential energy surface, but rather its use is widespread due to its computational expediency.
		+	For example, the repulsive term is maybe better described with the [[exp-6 potential]].
	One of the first [[Computer simulation techniques \|computer simulations]] using the Lennard-Jones model was undertaken by Rahman in 1964 <ref>[http://dx.doi.org/10.1103/PhysRev.136.A405 A. Rahman "Correlations in the Motion of Atoms in Liquid Argon", Physical Review '''136''' pp. A405–A411 (1964)]</ref> in a study of liquid [[argon]].		One of the first [[Computer simulation techniques \|computer simulations]] using the Lennard-Jones model was undertaken by Rahman in 1964 <ref>[http://dx.doi.org/10.1103/PhysRev.136.A405 A. Rahman "Correlations in the Motion of Atoms in Liquid Argon", Physical Review '''136''' pp. A405–A411 (1964)]</ref> in a study of liquid [[argon]].
	== Functional form ==		== Functional form ==

Exp-6 potential

2010-09-06T14:43:45Z

Created page with "The '''exp-6 potential''' is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six)..."

New page

The '''exp-6 potential''' is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics '''22''' pp. 169-186 (1954)]</ref>):

:<math> \Phi_{12}(r) = \frac{\epsilon}{1-6/\alpha} \left[ \left( \frac{6}{\alpha} \right)
\exp \left[ \alpha \frac{1-r}{\sigma} \right] - \left( \frac{\sigma}{r}\right)^6 \right] </math>

where
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>
* <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles or ''sites''
* <math> \sigma </math> is the value of <math>r</math> at which <math> \Phi_{12}(r)=0</math>
* <math> \epsilon </math> is the well depth (energy)
* <math>\alpha</math> is the "steepness" of the repulsive energy
==See also==
*[[Buckingham potential]]
*[[Lennard-Jones model]]
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1063/1.440106 M. Ross and F. H. Ree "Repulsive forces of simple molecules and mixtures at high density and temperature", Journal of Chemical Physics '''73''' pp. 6146-6152 (1980)]
[[category: models]]

Idealised models

2010-09-06T12:04:25Z

'Soft' models: Added an internal link

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	*[[Continuous shouldered well model]]		*[[Continuous shouldered well model]]
	*[[Durian foam bubble model]]		*[[Durian foam bubble model]]
		+	*[[Exp-6 potential]]
	*[[Flexible molecules\|Flexible molecules (intramolecular interactions)]]		*[[Flexible molecules\|Flexible molecules (intramolecular interactions)]]
	*[[Fomin potential]]		*[[Fomin potential]]
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	*[[Single site anisotropic soft-core potential]]		*[[Single site anisotropic soft-core potential]]
	*[[Soft sphere potential]]		*[[Soft sphere potential]]
		+
	==Patchy models==		==Patchy models==
	*[[Patchy particles]]		*[[Patchy particles]]

Conferences

2010-09-06T09:07:58Z

Update w.r.t. date

← Older revision		Revision as of 09:07, 6 September 2010
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	===2010===		===2010===
	====September====		====September====
-	*[http://neptuno.unizar.es/events/constraints2010/ Constraints in molecular simulation] September 2-4, 2010 at ZCAM, Zaragoza, (Spain)
	*[http://ergodic.ugr.es/cp 11th Granada Seminar: Foundations of Nonequilibrium Statistical Physics — From Basic Science to Future Challenges] 13-17 September, (2010). La Herradura, Granada (Spain)		*[http://ergodic.ugr.es/cp 11th Granada Seminar: Foundations of Nonequilibrium Statistical Physics — From Basic Science to Future Challenges] 13-17 September, (2010). La Herradura, Granada (Spain)
	*[http://www.ccp5.ac.uk/AGM/agm_2010.shtml CCP5 Annual Meeting 2010] 13-15 September 2010, Sheffield (UK)		*[http://www.ccp5.ac.uk/AGM/agm_2010.shtml CCP5 Annual Meeting 2010] 13-15 September 2010, Sheffield (UK)
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	*[http://www.vallico.net/tti/tti.html Quantum Monte Carlo and the CASINO program V] 1st-8th August 2010, Vallico Sotto (Italy)		*[http://www.vallico.net/tti/tti.html Quantum Monte Carlo and the CASINO program V] 1st-8th August 2010, Vallico Sotto (Italy)
	*[http://ipht.cea.fr/Meetings/BegRohu2010/ Concepts and Methods of Statistical Mechanics] 23 August - 4 September 2010 Saint Pierre Quiberon (France)		*[http://ipht.cea.fr/Meetings/BegRohu2010/ Concepts and Methods of Statistical Mechanics] 23 August - 4 September 2010 Saint Pierre Quiberon (France)
-		+	*[http://neptuno.unizar.es/events/constraints2010/ Constraints in molecular simulation] September 2-4, 2010 at ZCAM, Zaragoza, (Spain)


	__NOTOC__		__NOTOC__
	[[category: Miscellaneous]]		[[category: Miscellaneous]]

Researchers and research groups

2010-09-02T15:20:32Z

Germany: Added Stephan A. Baeurle group

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	*[http://www2.thphy.uni-duesseldorf.de/~hlowen/ Prof. Dr. Hartmut Löwen] Heinrich-Heine-Universität Düsseldorf		*[http://www2.thphy.uni-duesseldorf.de/~hlowen/ Prof. Dr. Hartmut Löwen] Heinrich-Heine-Universität Düsseldorf
	*[http://www.theochem.ruhr-uni-bochum.de/research/marx/index.en.html Dominik Marx Group] Ruhr-Universitaet Bochum		*[http://www.theochem.ruhr-uni-bochum.de/research/marx/index.en.html Dominik Marx Group] Ruhr-Universitaet Bochum
		+	*[http://www-dick.chemie.uni-regensburg.de/group/stephan_baeurle/ Theory & Computation of Advanced Materials and Sensors] (Dir. Dr. Stephan A. Baeurle) Universität Regensburg

	==Greece==		==Greece==
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	*[http://www.ccp5.ac.uk/ Collaborative Computational Project 5 - The Computer Simulation of Condensed Phases]		*[http://www.ccp5.ac.uk/ Collaborative Computational Project 5 - The Computer Simulation of Condensed Phases]
	*[http://www.uwethiele.de/ Uwe Thiele] Loughborough University		*[http://www.uwethiele.de/ Uwe Thiele] Loughborough University
-	*[http://www.soton.ac.uk/~chemphys/jessex/index.html Prof J W Essex Research Group] University of Southampton	+	*[http://www.soton.ac.uk/~chemphys/jessex/index.html Prof. J. W. Essex Research Group] University of Southampton
		+	*[http://azsoftmatter.wordpress.com/ Computational Physics Group] (Dir. Andrei V. Zvelindovsky) University of Central Lancashire

	== United States of America ==		== United States of America ==

Computer simulation techniques

2010-09-02T14:47:37Z

← Older revision		Revision as of 14:47, 2 September 2010
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-	The two predominant '''computer simulation techniques''' used in the ~~simulation of phases~~ of condensed matter are:	+	The two predominant '''computer simulation techniques''' used in the study of soft condensed matter are:
	*[[Molecular dynamics]]		*[[Molecular dynamics]]
	and		and

Carbon disulfide

2010-09-02T13:40:56Z

Created page with "{{stub-general}} '''Carbon disulfide''' (CS<sub>2</sub>) ==Models== <ref>[http://dx.doi.org/10.1080/00268978100100861 D. J. Tildesley and P. A. Madden "An effective pair potentia..."

New page

{{stub-general}}
'''Carbon disulfide''' (CS<sub>2</sub>)
==Models==
<ref>[http://dx.doi.org/10.1080/00268978100100861 D. J. Tildesley and P. A. Madden "An effective pair potential for liquid carbon disulphide", Molecular Physics '''42''' pp. 1137-1156 (1981)]</ref>
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1080/00268978300100091 D. J. Tildesley and P. A. Madden "Time correlation functions for a model of liquid carbon disulphide", Molecular Physics '''48''' pp. 129-152 (1983)]
[[category: models]]

Realistic models

2010-09-02T13:29:31Z

Added an internal link

← Older revision		Revision as of 13:29, 2 September 2010
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	*[[Ammonia]]		*[[Ammonia]]
	*[[Benzene]]		*[[Benzene]]
-	*[[Carbon]]
	*[[C60]]		*[[C60]]
		+	*[[Carbon]]
	*[[Carbon dioxide]]		*[[Carbon dioxide]]
		+	*[[Carbon disulfide]]
	*[[Difluoroethane]]		*[[Difluoroethane]]
	*[[Ethylene glycol]]		*[[Ethylene glycol]]

Idealised models

2010-09-02T12:53:17Z

Added an internal link

← Older revision		Revision as of 12:53, 2 September 2010
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-	'''Idealised models''' usually consist of a simple [[Intermolecular pair potential\|intermolecular pair potential]], whose purpose is often to study underlying physical phenomena, such as generalised [[phase diagrams]] and the study of [[phase transitions]]. It is entirely possible that a number of the models bear little or no resemblance to real molecular fluids.	+	'''Idealised models''' usually consist of a simple [[Intermolecular pair potential\|intermolecular pair potential]], whose purpose is often to study underlying physical phenomena, such as generalised [[phase diagrams]] and the study of [[phase transitions]]. It is entirely possible that a number of the models bear little or no resemblance to [[Realistic models \| real molecular fluids]].
	==Lattice models==		==Lattice models==
	*[[Barker-Fock model]]		*[[Barker-Fock model]]

Ornstein-Zernike relation

2010-09-02T12:50:11Z

Added an internal link

Magnesium

2010-09-01T10:43:09Z

Made a stub page

New page

{{stub-general}}
'''Magnesium'''
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1063/1.3479392 P. Li, W. Xie, and K. T. Tang "The van der Waals potential of the magnesium dimer", Journal of Chemical Physics '''133''' 084308 (2010)]
[[category: models]]
[[category: metals]]

Realistic models

2010-09-01T10:37:37Z

Added an internal link to magnesium

← Older revision		Revision as of 10:37, 1 September 2010
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	*[[Germanium]]		*[[Germanium]]
	*[[Lithium]]		*[[Lithium]]
		+	*[[Magnesium]]
	*[[Potassium]]		*[[Potassium]]
	*[[Sodium]]		*[[Sodium]]

Conferences

2010-09-01T08:14:57Z

September: Added 23rd Marian Smoluchowski Symposium on Statistical Physics

← Older revision		Revision as of 08:14, 1 September 2010
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	*[http://www.matgas.com/saft2010/ 20 YEARS OF THE SAFT EQUATION: RECENT ADVANCES AND CHALLENGES] September 19-21, 2010, Barcelona (Spain)		*[http://www.matgas.com/saft2010/ 20 YEARS OF THE SAFT EQUATION: RECENT ADVANCES AND CHALLENGES] September 19-21, 2010, Barcelona (Spain)
	*[http://tnt.phys.uniroma1.it/~transport/ Anomalous Transport: from Billiards to Nanosystems] 20-24 September 2010 Sperlonga (Italy)		*[http://tnt.phys.uniroma1.it/~transport/ Anomalous Transport: from Billiards to Nanosystems] 20-24 September 2010 Sperlonga (Italy)
		+	*[http://th-www.if.uj.edu.pl/zfs/smoluchowski/index.html Random Matrices, Statistical Physics and Information Theory] 26-30 September, Kraków (Poland)

	====October====		====October====

SklogWiki:About

2010-09-01T08:02:12Z

← Older revision		Revision as of 08:02, 1 September 2010
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	[[Image:Zentralfriedhof.jpg\|thumb\|200px\|Ludwig Boltzmann's grave, with S= k log W seen at the top. (Photo: Daderot)]]		[[Image:Zentralfriedhof.jpg\|thumb\|200px\|Ludwig Boltzmann's grave, with S= k log W seen at the top. (Photo: Daderot)]]
	'''SklogWiki''' is a [[wiki]] for anyone interested in [[Classical thermodynamics \| thermodynamics]], [[statistical mechanics]] and the [[Computer simulation techniques \| computer simulation]] of simple liquids, [[complex fluids]], and soft condensed matter.		'''SklogWiki''' is a [[wiki]] for anyone interested in [[Classical thermodynamics \| thermodynamics]], [[statistical mechanics]] and the [[Computer simulation techniques \| computer simulation]] of simple liquids, [[complex fluids]], and soft condensed matter.
-	This site can be viewed as a collaborative inter- and ~~[http://www.w3.org/History/19921103-hypertext/hypertext/WWW/WhatIs.html~~ hyper-linked] electronic encyclopaedia that is instantly up-dateable with the latest research results. It also serves as an important access point to the traditional peer-reviewed scientific literature. SklogWiki is part of the "Science 2.0" movement.	+	This site can be viewed as a collaborative inter- and hyper-linked electronic encyclopaedia that is instantly up-dateable with the latest research results. It also serves as an important access point to the traditional peer-reviewed scientific literature. SklogWiki is part of the "Science 2.0" movement.

	SklogWiki derives its name from a concatenation, or portmanteau, of the the word Wiki and the famous equation for [[entropy]]:		SklogWiki derives its name from a concatenation, or portmanteau, of the the word Wiki and the famous equation for [[entropy]]:
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	Currently SklogWiki has {{NUMBEROFARTICLES}} articles, in various stages of development.		Currently SklogWiki has {{NUMBEROFARTICLES}} articles, in various stages of development.
	SklogWiki was started in February 2007 by [http://www.ucm.es/info/molecsim/carlmcbride.html Carl McBride] and is hosted by the [http://emoles.quim.ucm.es/ Grupo de Termodinámica Estadística de Fluidos Moleculares] of the [http://www.ucm.es Universidad Complutense de Madrid].		SklogWiki was started in February 2007 by [http://www.ucm.es/info/molecsim/carlmcbride.html Carl McBride] and is hosted by the [http://emoles.quim.ucm.es/ Grupo de Termodinámica Estadística de Fluidos Moleculares] of the [http://www.ucm.es Universidad Complutense de Madrid].
-	SklogWiki would especially like to thank the [http://www.icmm.csic.es/mossnoho/ MOSSNOHO] research ~~grant~~ for financial assistance.	+	SklogWiki would especially like to thank the [http://www.icmm.csic.es/mossnoho/ MOSSNOHO] and [http://www.modelico.es/ MODELICO-CM] research grants for financial assistance.

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	! class="unsortable" \| Wiki name !!class="unsortable" \| field !! class="unsortable" \| notes !! \| page count !! \| [http://arxiv.org/abs/0902.3439 wikiFactor]		! class="unsortable" \| Wiki name !!class="unsortable" \| field !! class="unsortable" \| notes !! \| page count !! \| [http://arxiv.org/abs/0902.3439 wikiFactor]
	\|-		\|-
-	\|[~~http://www.SklogWiki.org/~~ SklogWiki]	+	\|[[Main Page \| SklogWiki]]
	\|[[statistical mechanics]], [[Classical thermodynamics \|thermodynamics]]		\|[[statistical mechanics]], [[Classical thermodynamics \|thermodynamics]]
	\|This wiki		\|This wiki
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	\|[[statistical mechanics]], [[Classical thermodynamics \|thermodynamics]]		\|[[statistical mechanics]], [[Classical thermodynamics \|thermodynamics]]
	\|dedicated to the book "Statistical Mechanics: Algorithms and Computations" by [http://www.lps.ens.fr/~krauth/ Werner Krauth]		\|dedicated to the book "Statistical Mechanics: Algorithms and Computations" by [http://www.lps.ens.fr/~krauth/ Werner Krauth]
-	\|[http://www.smac.lps.ens.fr/index.php/Special:Statistics 61 ]	+	\|[http://www.smac.lps.ens.fr/index.php/Special:Statistics 60 ]
-	\|[http://www.smac.lps.ens.fr/index.php/Special:Popularpages 3]	+	\|[http://www.smac.lps.ens.fr/index.php/Special:Popularpages 4]
	\|-		\|-
	\|[http://www.gromacs.org/ GROMACS wiki]		\|[http://www.gromacs.org/ GROMACS wiki]
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	\|deals with [[GROMACS]], a versatile package to perform [[molecular dynamics]]		\|deals with [[GROMACS]], a versatile package to perform [[molecular dynamics]]
	\|unknown		\|unknown
-	\|[http://www.gromacs.org/Special:Popularpages 11]	+	\|[http://www.gromacs.org/Special:Popularpages 13]
	\|-		\|-
	\|[http://matdl.org/matdlwiki/index.php/Main_Page NSDL MatDL Pathway] including [http://matdl.org/matdlwiki/index.php/softmatter:Main_Page The Soft Matter Wiki]		\|[http://matdl.org/matdlwiki/index.php/Main_Page NSDL MatDL Pathway] including [http://matdl.org/matdlwiki/index.php/softmatter:Main_Page The Soft Matter Wiki]
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	\|computational fluid dynamics		\|computational fluid dynamics
	\|		\|
-	\|[http://www.cfd-online.com/Wiki/Special:Statistics ~~434~~]	+	\|[http://www.cfd-online.com/Wiki/Special:Statistics 433]
-	\|[http://www.cfd-online.com/Wiki/Special:PopularPages 28]	+	\|[http://www.cfd-online.com/Wiki/Special:PopularPages 30]
	\|-		\|-
	\|[http://qwiki.stanford.edu/wiki/Main_Page Qwiki]		\|[http://qwiki.stanford.edu/wiki/Main_Page Qwiki]
	\|quantum mechanics		\|quantum mechanics
-	\|~~devoted to the collective creation of technical content for practising scientists. [http://qwiki.stanford.edu/wiki/Wikis~~ (~~WikiNode~~)]	+	\|(site apparently no longer on-line)
	\|[http://qwiki.stanford.edu/wiki/Special:Statistics 960]		\|[http://qwiki.stanford.edu/wiki/Special:Statistics 960]
	\|[http://qwiki.stanford.edu/wiki/Special:Popularpages 20]		\|[http://qwiki.stanford.edu/wiki/Special:Popularpages 20]
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	\|quantum mechanics		\|quantum mechanics
	\| a free-content WWW resource in quantum information science		\| a free-content WWW resource in quantum information science
-	\|[http://www.quantiki.org/wiki/Special:Statistics ~~219~~]	+	\|[http://www.quantiki.org/wiki/Special:Statistics 221]
-	\|[http://www.quantiki.org/wiki/index.php/Special:PopularPages 12]	+	\|[http://www.quantiki.org/wiki/index.php/Special:PopularPages 13]
	\|-		\|-
	\|[http://www.physics.thetangentbundle.net/wiki/Main_Page The Tangent Bundle]		\|[http://www.physics.thetangentbundle.net/wiki/Main_Page The Tangent Bundle]
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	\|a repository of ideas in physics		\|a repository of ideas in physics
	\|[http://www.physics.thetangentbundle.net/wiki/Special:Statistics 644]		\|[http://www.physics.thetangentbundle.net/wiki/Special:Statistics 644]
-	\|[http://www.physics.thetangentbundle.net/wiki/Special:Popularpages 4]	+	\|[http://www.physics.thetangentbundle.net/wiki/Special:Popularpages 5]
	\|-		\|-
	\|[http://www.plasma-universe.com/index.php/Plasma-Universe.com Plasma-Universe.com]		\|[http://www.plasma-universe.com/index.php/Plasma-Universe.com Plasma-Universe.com]
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	\|chemistry		\|chemistry
	\|an open source science project in chemistry led by the Bradley Laboratory at Drexel University		\|an open source science project in chemistry led by the Bradley Laboratory at Drexel University
-	\|[http://usefulchem.wikispaces.com/space/pagelist ~~491~~]	+	\|[http://usefulchem.wikispaces.com/space/pagelist 492]
	\|[http://usefulchem.wikispaces.com/space/stats/page?orderBy=total&orderDir=desc 1]		\|[http://usefulchem.wikispaces.com/space/stats/page?orderBy=total&orderDir=desc 1]
	\|-		\|-
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	\|chemistry		\|chemistry
	\|Chemistry Department Wiki, Imperial College London (editing restricted to Imperial College users)		\|Chemistry Department Wiki, Imperial College London (editing restricted to Imperial College users)
-	\|[http://www.ch.ic.ac.uk/wiki/index.php/Special:Statistics ~~928~~]	+	\|[http://www.ch.ic.ac.uk/wiki/index.php/Special:Statistics 931]
	\|[http://www.ch.ic.ac.uk/wiki/index.php/Special:Popularpages 10]		\|[http://www.ch.ic.ac.uk/wiki/index.php/Special:Popularpages 10]
	\|-		\|-
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	\|A free 'General Chemistry textbook' (Chemistry department at UC Davis)		\|A free 'General Chemistry textbook' (Chemistry department at UC Davis)
	\| unknown		\| unknown
-	\|[http://chemwiki.ucdavis.edu/Special:Popularpages 8]	+	\|[http://chemwiki.ucdavis.edu/Special:Popularpages 10]
	\|-		\|-
	\|[http://nmrwiki.org NMRWiki]		\|[http://nmrwiki.org NMRWiki]
	\|chemistry		\|chemistry
	\|Magnetic Resonance-themed wiki (NMR,EPR,MRI). ([http://nmrwiki.org/wiki/index.php?title=Scientific_Wiki_Sites wikiNode])		\|Magnetic Resonance-themed wiki (NMR,EPR,MRI). ([http://nmrwiki.org/wiki/index.php?title=Scientific_Wiki_Sites wikiNode])
-	\|[http://nmrwiki.org/wiki/index.php?title=Special:Statistics ~~601~~]	+	\|[http://nmrwiki.org/wiki/index.php?title=Special:Statistics 650]
-	\|[http://nmrwiki.org/wiki/index.php?title=Special:Popularpages 6]	+	\|[http://nmrwiki.org/wiki/index.php?title=Special:Popularpages 7]
	\|-		\|-
	\|[http://www.mathematics.thetangentbundle.net/wiki/Main_Page The Tangent Bundle Mathematics Project]		\|[http://www.mathematics.thetangentbundle.net/wiki/Main_Page The Tangent Bundle Mathematics Project]
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	\|a repository of ideas in mathematics		\|a repository of ideas in mathematics
	\|[http://www.mathematics.thetangentbundle.net/wiki/Special:Statistics 264]		\|[http://www.mathematics.thetangentbundle.net/wiki/Special:Statistics 264]
-	\|[http://www.mathematics.thetangentbundle.net/wiki/Special:Popularpages 2]	+	\|[http://www.mathematics.thetangentbundle.net/wiki/Special:Popularpages 3]
	\|-		\|-
	\|[http://www.maths.tcd.ie/~mathsoc/w/index.php?title=Main_Page mathsoc]		\|[http://www.maths.tcd.ie/~mathsoc/w/index.php?title=Main_Page mathsoc]
	\|[[mathematics]]		\|[[mathematics]]
	\|Dublin University Mathematical Society		\|Dublin University Mathematical Society
-	\|[http://www.maths.tcd.ie/~mathsoc/wiki/Special:Statistics ~~121~~]	+	\|[http://www.maths.tcd.ie/~mathsoc/wiki/Special:Statistics 122]
	\|[http://www.maths.tcd.ie/~mathsoc/wiki/Special:Popularpages 10]		\|[http://www.maths.tcd.ie/~mathsoc/wiki/Special:Popularpages 10]
	\|-		\|-
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	\|[[mathematics]]		\|[[mathematics]]
	\|group theory wiki		\|group theory wiki
-	\|[http://groupprops.subwiki.org/wiki/Special:Statistics ~~4135~~]	+	\|[http://groupprops.subwiki.org/wiki/Special:Statistics 4412]
	\|[http://groupprops.subwiki.org/wiki/Special:PopularPages 6]		\|[http://groupprops.subwiki.org/wiki/Special:PopularPages 6]
	\|-		\|-
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	\|[[proteins]] and biology		\|[[proteins]] and biology
	\|a community annotated knowledge base of biological molecular structures		\|a community annotated knowledge base of biological molecular structures
-	\|[http://pdbwiki.org/index.php/Special:Statistics ~~62285~~]	+	\|[http://pdbwiki.org/index.php/Special:Statistics 63562]
-	\|[http://pdbwiki.org/index.php/Special:Popularpages 4]	+	\|[http://pdbwiki.org/index.php/Special:Popularpages 5]
	\|-		\|-
	\|[http://openwetware.org/wiki/Main_Page OpenWetWare]		\|[http://openwetware.org/wiki/Main_Page OpenWetWare]
	\|[[proteins]] and biology		\|[[proteins]] and biology
	\|for groups who are working in biology & biological engineering [http://openwetware.org/wiki/Sister_Wiki's (Sister wikis)]		\|for groups who are working in biology & biological engineering [http://openwetware.org/wiki/Sister_Wiki's (Sister wikis)]
-	\|[http://openwetware.org/wiki/Special:Statistics ~~15261~~]	+	\|[http://openwetware.org/wiki/Special:Statistics 16974]
-	\|[http://openwetware.org/wiki/Special:PopularPages 33]	+	\|[http://openwetware.org/wiki/Special:PopularPages 35]
	\|-		\|-
	\|[http://www.yourlabdata.com/ Your Lab Data]		\|[http://www.yourlabdata.com/ Your Lab Data]
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	\|[[proteins]] and biology		\|[[proteins]] and biology
	\|a collaborative, 3-dimensional encyclopaedia of proteins and other molecules. ([http://dx.doi.org/10.1186/gb-2008-9-8-r121 Publication in Genome Biology])		\|a collaborative, 3-dimensional encyclopaedia of proteins and other molecules. ([http://dx.doi.org/10.1186/gb-2008-9-8-r121 Publication in Genome Biology])
-	\|[http://www.proteopedia.org/wiki/index.php/Special:Statistics ~~66997~~]	+	\|[http://www.proteopedia.org/wiki/index.php/Special:Statistics 69501]
-	\|[http://www.proteopedia.org/wiki/index.php/Special:Popularpages 8]	+	\|[http://www.proteopedia.org/wiki/index.php/Special:Popularpages 9]
	\|-		\|-
	\|[http://plastics.inwiki.org/Main_Page Plastics Wiki]		\|[http://plastics.inwiki.org/Main_Page Plastics Wiki]
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	\|an encyclopaedia of plastic materials. [http://plastics.inwiki.org/Plastics_Wiki:TourBusStop (TourBusStop)]		\|an encyclopaedia of plastic materials. [http://plastics.inwiki.org/Plastics_Wiki:TourBusStop (TourBusStop)]
	\|[http://plastics.inwiki.org/Special:Statistics 1546]		\|[http://plastics.inwiki.org/Special:Statistics 1546]
-	\|[http://plastics.inwiki.org/Special:Popularpages 13]	+	\|[http://plastics.inwiki.org/Special:Popularpages 14]
	\|-		\|-
	\|[http://www.palaeos.org/Main_Page Palaeos.org]		\|[http://www.palaeos.org/Main_Page Palaeos.org]
	\|evolutionary biology		\|evolutionary biology
	\|A multi-authored Encyclopedia on the history of life on Earth		\|A multi-authored Encyclopedia on the history of life on Earth
-	\|[http://www.palaeos.org/Special:Statistics ~~3631~~]	+	\|[http://www.palaeos.org/Special:Statistics 3732]
-	\|[http://www.palaeos.org/Special:PopularPages 13]	+	\|[http://www.palaeos.org/Special:PopularPages 14]
	\|}		\|}

	__NOTOC__		__NOTOC__
	[[category: Miscellaneous]]		[[category: Miscellaneous]]

← Older revision		Revision as of 12:50, 2 September 2010
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	</div>		</div>

-	The '''Ornstein-Zernike relation''' ~~(OZ)~~ integral equation <ref>L. S. Ornstein and F. Zernike "Accidental deviations of density and opalescence at the critical point of a single substance", Koninklijke Nederlandse Akademie van Wetenschappen Amsterdam Proc. Sec. Sci. '''17''' pp. 793- (1914)</ref> is given by:	+	The '''Ornstein-Zernike relation''' integral equation <ref>L. S. Ornstein and F. Zernike "Accidental deviations of density and opalescence at the critical point of a single substance", Koninklijke Nederlandse Akademie van Wetenschappen Amsterdam Proc. Sec. Sci. '''17''' pp. 793- (1914)</ref> is given by:
	:<math>h=h\left[c\right]</math>		:<math>h=h\left[c\right]</math>
	where <math>h[c]</math> denotes a functional of <math>c</math>. This relation is exact.		where <math>h[c]</math> denotes a functional of <math>c</math>. This relation is exact.
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	Because of this <math>h</math> must be determined self-consistently.		Because of this <math>h</math> must be determined self-consistently.
	This need for self-consistency is characteristic of all many-body problems.		This need for self-consistency is characteristic of all many-body problems.
-	(Hansen and McDonald, section 5.2 p. 106) For a system in an external field, the OZ has the form (5.2.7)	+	(Hansen and McDonald, section 5.2 p. 106) For a system in an external field, the Ornstein-Zernike relation has the form (5.2.7)
	:<math>h(1,2) = c(1,2) + \int \rho^{(1)}(3) c(1,3)h(3,2) d3</math>		:<math>h(1,2) = c(1,2) + \int \rho^{(1)}(3) c(1,3)h(3,2) d3</math>
-	If the system is both homogeneous and isotropic, the OZ relation becomes (Eq. 6 of Ref. 1)	+	If the system is both homogeneous and isotropic, the Ornstein-Zernike relation becomes (Eq. 6 of Ref. 1)

	:<math>\gamma ({\mathbf r}) \equiv h({\mathbf r}) - c({\mathbf r}) = \rho \int h({\mathbf r'})~c(\|{\mathbf r} - {\mathbf r'}\|) {\rm d}{\mathbf r'}</math>		:<math>\gamma ({\mathbf r}) \equiv h({\mathbf r}) - c({\mathbf r}) = \rho \int h({\mathbf r'})~c(\|{\mathbf r} - {\mathbf r'}\|) {\rm d}{\mathbf r'}</math>
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	where the bold lines connecting root points denote <math>c</math> functions, the blobs denote <math>h</math> functions.		where the bold lines connecting root points denote <math>c</math> functions, the blobs denote <math>h</math> functions.
	An arrow pointing from left to right indicates an uphill path from one root		An arrow pointing from left to right indicates an uphill path from one root
-	point to another. An `uphill path' is a sequence of Mayer bonds passing through increasing	+	point to another. An `uphill path' is a sequence of [[Mayer f-function \|Mayer bonds]] passing through increasing
	particle labels.		particle labels.
-	The OZ relation can be derived by performing a functional differentiation	+	The Ornstein-Zernike relation can be derived by performing a functional differentiation
-	of the grand canonical distribution function ~~(HM check this)~~.	+	of the [[Grand canonical ensemble \|grand canonical]] distribution function.
-	==~~OZ equation~~ in Fourier space==	+	==Ornstein-Zernike relation in Fourier space==
	The Ornstein-Zernike equation may be written in [[Fourier analysis \|Fourier space]] as (<ref>[http://dx.doi.org/10.1063/1.470724 Der-Ming Duh and A. D. J. Haymet "Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function", Journal of Chemical Physics '''103''' pp. 2625-2633 (1995)]</ref> Eq. 5):		The Ornstein-Zernike equation may be written in [[Fourier analysis \|Fourier space]] as (<ref>[http://dx.doi.org/10.1063/1.470724 Der-Ming Duh and A. D. J. Haymet "Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function", Journal of Chemical Physics '''103''' pp. 2625-2633 (1995)]</ref> Eq. 5):