SklogWiki - Recent changes [en]

Researchers and research groups

Carl McBride — Thu, 02 Sep 2010 15:20:32 GMT

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

Carl McBride — Thu, 02 Sep 2010 14:47:37 GMT

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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

Carl McBride — Thu, 02 Sep 2010 13:40:56 GMT

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

Carl McBride — Thu, 02 Sep 2010 13:29:31 GMT

Added an internal link

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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

Carl McBride — Thu, 02 Sep 2010 12:53:17 GMT

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

Carl McBride — Thu, 02 Sep 2010 12:50:11 GMT

Added an internal link

Magnesium

Carl McBride — Wed, 01 Sep 2010 10:43:09 GMT

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

Carl McBride — Wed, 01 Sep 2010 10:37:37 GMT

Added an internal link to magnesium

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	*[[Germanium]]		*[[Germanium]]
	*[[Lithium]]		*[[Lithium]]
		+	*[[Magnesium]]
	*[[Potassium]]		*[[Potassium]]
	*[[Sodium]]		*[[Sodium]]

Conferences

Carl McBride — Wed, 01 Sep 2010 08:14:57 GMT

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

Carl McBride — Wed, 01 Sep 2010 08:02:12 GMT

← 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.

Main Page

Carl McBride — Mon, 30 Aug 2010 15:46:34 GMT

Updated internal link

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	__NOTOC__ __NOEDITSECTION__		__NOTOC__ __NOEDITSECTION__
	=Welcome to [[SklogWiki:About \| SklogWiki]]=		=Welcome to [[SklogWiki:About \| SklogWiki]]=
-	'''SklogWiki''' is a "Science 2.0" [[wiki]] site dedicated to thermodynamics and statistical mechanics, especially that <br> of simple liquids, complex fluids, and soft condensed matter. SklogWiki is particularly oriented towards computer <br> simulations and theoretical studies. Currently SklogWiki has {{NUMBEROFARTICLES}} articles, in various stages of development.	+	'''SklogWiki''' is a [[Wikis and Science 2.0 \|"Science 2.0" wiki]] site dedicated to thermodynamics and statistical mechanics, especially that <br> of simple liquids, complex fluids, and soft condensed matter. SklogWiki is particularly oriented towards computer <br> simulations and theoretical studies. Currently SklogWiki has {{NUMBEROFARTICLES}} articles, in various stages of development.
	<!-----------------------Start of two columns table------------------------>		<!-----------------------Start of two columns table------------------------>
	{\|width="75%" style="border-spacing:8px; margin:0px -8px;vertical-align:top"		{\|width="75%" style="border-spacing:8px; margin:0px -8px;vertical-align:top"

Researchers and research groups

Carl McBride — Mon, 30 Aug 2010 15:26:36 GMT

Spain: Added Giancarlo Franzese’s Group

← Older revision		Revision as of 15:26, 30 August 2010
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	*[http://www.icmab.es/molsim/ Lourdes F. Vega Molecular Simulation Group] Instituto de Ciencia de Materiales de Barcelona (ICMAB), CSIC		*[http://www.icmab.es/molsim/ Lourdes F. Vega Molecular Simulation Group] Instituto de Ciencia de Materiales de Barcelona (ICMAB), CSIC
	*[http://grupos.unican.es/GTFE/ Grupo de Termodinámica y Física Estadística] Universidad de Cantabria		*[http://grupos.unican.es/GTFE/ Grupo de Termodinámica y Física Estadística] Universidad de Cantabria
-	*[http://complex.ffn.ub.es/ Physics of Complex Systems Group] Universitat de Barcelona
	*[http://simcon.upc.edu/ Computer Simulation in Condensed Matter Group SIMCON] Universitat Politècnica de Catalunya		*[http://simcon.upc.edu/ Computer Simulation in Condensed Matter Group SIMCON] Universitat Politècnica de Catalunya
	*[http://www-fen.upc.es/cscmcs/index.html Complex Systems. Computer Simulation of Materials and Biological Systems] Universitat Politècnica de Catalunya		*[http://www-fen.upc.es/cscmcs/index.html Complex Systems. Computer Simulation of Materials and Biological Systems] Universitat Politècnica de Catalunya
	*[http://web.ffn.ub.es/node/6&id=1061 Grupo de Física Estadística] Universitat de Barcelona		*[http://web.ffn.ub.es/node/6&id=1061 Grupo de Física Estadística] Universitat de Barcelona
		+	*[http://complex.ffn.ub.es/ Physics of Complex Systems Group] Universitat de Barcelona
		+	*[http://www.ffn.ub.es/gfranzese/Home.html Giancarlo Franzese’s Group] Universitat de Barcelona
	*[http://www.unex.es/eweb/fisteor/index_eng.html Statistical Physics Group at the University of Extremadura (SPHINX)] University of Extremadura		*[http://www.unex.es/eweb/fisteor/index_eng.html Statistical Physics Group at the University of Extremadura (SPHINX)] University of Extremadura
	*[http://www.ual.es/GruposInv/FQM-230/componentes/jcaballe.htm José Baldomero Caballero Moraleda] Universidad de Almería		*[http://www.ual.es/GruposInv/FQM-230/componentes/jcaballe.htm José Baldomero Caballero Moraleda] Universidad de Almería

Continuous shouldered well model

Carl McBride — Mon, 30 Aug 2010 15:17:19 GMT

Added a recent publication

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-	~~{{stub-general}}~~	+	The '''continuous shouldered well model''' is given by (<ref>[http://dx.doi.org/10.1016/j.molliq.2007.08.021 Giancarlo Franzese "Differences between discontinuous and continuous soft-core attractive potentials: The appearance of density anomaly", Journal of Molecular Liquids '''136''' pp. 267-273 (2007)]</ref> Eq. 1):
-	The '''continuous shouldered well model''' is given by (~~Ref~~. 1 Eq. 1):	+

	:<math>\Phi_{12}(r) = \frac{U_R}{1 + \exp [\Delta(r-R_R)/a]} -U_A \exp \left[ -\frac{(r-R_A)^2}{2\delta_A^2} \right] + \left(\frac{a}{r}\right)^{24}</math>		:<math>\Phi_{12}(r) = \frac{U_R}{1 + \exp [\Delta(r-R_R)/a]} -U_A \exp \left[ -\frac{(r-R_A)^2}{2\delta_A^2} \right] + \left(\frac{a}{r}\right)^{24}</math>
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	where <math>\Phi_{12}</math> is the [[intermolecular pair potential]], <math>U_R</math> is the energy of the repulsive shoulder, <math>U_A</math> is the energy of the attractive well, <math>a</math> is the diameter of the particles, and <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>.		where <math>\Phi_{12}</math> is the [[intermolecular pair potential]], <math>U_R</math> is the energy of the repulsive shoulder, <math>U_A</math> is the energy of the attractive well, <math>a</math> is the diameter of the particles, and <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>.
	==References==		==References==
-	~~#[http:~~//dx.doi.org/10.1016/j.molliq.2007.08.021 Giancarlo Franzese "Differences between discontinuous and continuous soft-core attractive potentials: The appearance of density anomaly", Journal of Molecular Liquids '''~~136~~''' ~~pp. 267-273 (2007)]~~	+	<references/>
-	#[http://dx.doi.org/10.1063/1.2830706 Alan Barros de Oliveira, Giancarlo Franzese, Paulo A. Netz, and Marcia C. Barbosa "Waterlike hierarchy of anomalies in a continuous spherical shouldered potential", Journal ofChemical Physics '''128''' 064901 (2008)]	+	'''Related reading'''
		+	*[http://dx.doi.org/10.1063/1.2830706 Alan Barros de Oliveira, Giancarlo Franzese, Paulo A. Netz, and Marcia C. Barbosa "Waterlike hierarchy of anomalies in a continuous spherical shouldered potential", Journal ofChemical Physics '''128''' 064901 (2008)]
		+	*[http://dx.doi.org/10.1063/1.3463424 Pol Vilaseca and Giancarlo Franzese "Softness dependence of the anomalies for the continuous shouldered well potential", Journal of Chemical Physics '''133''' 084507 (2010)]
	[[Category: Models]]		[[Category: Models]]

Argon

Carl McBride — Mon, 30 Aug 2010 15:12:43 GMT

Started a tidy of the introduction

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-	'''Argon''' (Ar) has a ~~mass of 39.948~~ [[~~atomic mass units~~ \| ~~umas~~]]. One of the first computer simulations of liquid argon was that of Rahman in 1964 <ref name="Rahman" >[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>. Sadus and Prausnitz have shown that three-body repulsion makes a significant contribution to [[Idealised models#Three-body potentials\|three-body interactions]] in the liquid phase	+	'''Argon''' (Ar) has long been a popular choice for [[Computer simulation techniques \|computer simulations]] of simple liquids. One of the first computer simulations of liquid argon was that of Rahman in 1964 <ref name="Rahman" >[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>. Sadus and Prausnitz have shown that three-body repulsion makes a significant contribution to [[Idealised models#Three-body potentials\|three-body interactions]] in the liquid phase
	<ref>[http://dx.doi.org/10.1063/1.471172 Richard J. Sadus and J. M. Prausnitz "Three-body interactions in fluids from molecular simulation: Vapor–liquid phase coexistence of argon", Journal of Chemical Physics '''104''' pp. 4784-4787 (1996)]</ref>		<ref>[http://dx.doi.org/10.1063/1.471172 Richard J. Sadus and J. M. Prausnitz "Three-body interactions in fluids from molecular simulation: Vapor–liquid phase coexistence of argon", Journal of Chemical Physics '''104''' pp. 4784-4787 (1996)]</ref>
	(for use of the [[Axilrod-Teller interaction]] see		(for use of the [[Axilrod-Teller interaction]] see
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	[[Radial distribution function]]		[[Radial distribution function]]
	*[http://dx.doi.org/10.1103/PhysRevA.7.2130 J. L. Yarnell, M. J. Katz, R. G. Wenzel and S. H. Koenig "Structure Factor and Radial Distribution Function for Liquid Argon at 85°K", Physical Review A '''7''' pp. 2130-2144 (1973)]		*[http://dx.doi.org/10.1103/PhysRevA.7.2130 J. L. Yarnell, M. J. Katz, R. G. Wenzel and S. H. Koenig "Structure Factor and Radial Distribution Function for Liquid Argon at 85°K", Physical Review A '''7''' pp. 2130-2144 (1973)]
		+	==Nucleation==
		+	*[http://dx.doi.org/10.1063/1.3474945 Matthew J. McGrath, Julius N. Ghogomu, Narcisse T. Tsona, J. Ilja Siepmann, Bin Chen, Ismo Napari1, and Hanna Vehkamäki "Vapor-liquid nucleation of argon: Exploration of various intermolecular potentials", Journal of Chemical Physics '''133''' 084106 (2010)]
	==Quantum simulations==		==Quantum simulations==
	*[http://dx.doi.org/10.1080/00268978900100811 J. R. Melrose and K. Singer "An investigation of supercooled Lennard-Jones argon by quantum mechanical and classical Monte Carlo simulation", Molecular Physics '''66''' 1203-1214 (1989)]		*[http://dx.doi.org/10.1080/00268978900100811 J. R. Melrose and K. Singer "An investigation of supercooled Lennard-Jones argon by quantum mechanical and classical Monte Carlo simulation", Molecular Physics '''66''' 1203-1214 (1989)]

Conferences

Carl McBride — Mon, 30 Aug 2010 14:56:35 GMT

Update w.r.t. date

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	The following is a chronological list of conferences, seminars, or meetings related to thermodynamics, statistical mechanics, soft condensed matter, many-body problems, complex fluids etc.		The following is a chronological list of conferences, seminars, or meetings related to thermodynamics, statistical mechanics, soft condensed matter, many-body problems, complex fluids etc.
	===2010===		===2010===
-	~~====August====~~
-	*[http://ipht.cea.fr/Meetings/BegRohu2010/ Concepts and Methods of Statistical Mechanics] 23 August - 4 September 2010 Saint Pierre Quiberon (France)
	====September====		====September====
	*[http://neptuno.unizar.es/events/constraints2010/ Constraints in molecular simulation] September 2-4, 2010 at ZCAM, Zaragoza, (Spain)		*[http://neptuno.unizar.es/events/constraints2010/ Constraints in molecular simulation] September 2-4, 2010 at ZCAM, Zaragoza, (Spain)
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	*[http://www.vallico.net/tti/tti.html Quantum Monte Carlo in the Apuan Alps VI] 24th-31st July 2010, Vallico Sotto, Italy		*[http://www.vallico.net/tti/tti.html Quantum Monte Carlo in the Apuan Alps VI] 24th-31st July 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://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)
		+


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

Hard sphere model

Carl McBride — Mon, 30 Aug 2010 14:10:38 GMT

Fluid-solid transition: Fixed "broken" reference link

← Older revision		Revision as of 14:10, 30 August 2010
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	<ref>[http://dx.doi.org/10.1063/1.2201699 M. López de Haro, A. Santos and S. B. Yuste "On the radial distribution function of a hard-sphere fluid", Journal of Chemical Physics '''124''' 236102 (2006)]</ref>		<ref>[http://dx.doi.org/10.1063/1.2201699 M. López de Haro, A. Santos and S. B. Yuste "On the radial distribution function of a hard-sphere fluid", Journal of Chemical Physics '''124''' 236102 (2006)]</ref>
	==Fluid-solid transition==		==Fluid-solid transition==
-	The hard sphere system undergoes a [[Solid-liquid phase transitions \|fluid-solid]] [[First-order transitions \|first order transition]] <ref name="HooverRee">[http://dx.doi.org/10.1063/1.1670641 William G. Hoover and Francis H. Ree "Melting Transition and Communal Entropy for Hard Spheres", Journal of Chemical Physics '''49''' pp. 3609-3617 (1968)]</ref>, ~~now~~ referred as the Kirkwood-Alder transition <ref name="GastRussel">[http://dx.doi.org/10.1063/1.882495 Alice P. Gast and William B. Russel	+	The hard sphere system undergoes a [[Solid-liquid phase transitions \|fluid-solid]] [[First-order transitions \|first order transition]] <ref name="HooverRee">[http://dx.doi.org/10.1063/1.1670641 William G. Hoover and Francis H. Ree "Melting Transition and Communal Entropy for Hard Spheres", Journal of Chemical Physics '''49''' pp. 3609-3617 (1968)]</ref>, sometimes referred to as the Kirkwood-Alder transition <ref name="GastRussel">[http://dx.doi.org/10.1063/1.882495 Alice P. Gast and William B. Russel "Simple Ordering in Complex Fluids", Physics Today '''51''' (12) pp. 24-30 (1998)]</ref>.
-	"Simple Ordering in Complex Fluids", Physics Today '''51''' (12) pp. 24-30 (1998)]</ref>.	+
	The fluid-solid coexistence densities (<math>\rho^* = \rho \sigma^3</math>) are given by		The fluid-solid coexistence densities (<math>\rho^* = \rho \sigma^3</math>) are given by
	:{\| border="1"		:{\| border="1"

User:Myrrhman

Carl McBride — Mon, 30 Aug 2010 14:03:35 GMT

blocked [[Myrrhman (Talk | contribs)]] with an expiry time of 3 months (account creation disabled, e-mail blocked) Spamming links to external sites

Critical points

Carl McBride — Mon, 30 Aug 2010 14:03:22 GMT

Reverted edits by Myrrhman (talk) to last revision by Carl McBride

← Older revision		Revision as of 14:03, 30 August 2010
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	*[[Binder cumulant]]		*[[Binder cumulant]]
	*[[Law of corresponding states]]		*[[Law of corresponding states]]
-	*[http://www.mac-how.net Mac How]
-
	==References==		==References==
	<references/>		<references/>

Critical points

Myrrhman — Mon, 30 Aug 2010 08:37:36 GMT

User:Myrrhman

Myrrhman — Mon, 30 Aug 2010 08:29:06 GMT

New user account

Hard sphere model

152.3.169.6 — Thu, 26 Aug 2010 21:09:31 GMT

Fluid-solid transition: include Kirkwood-Alder transition nomenclature

← Older revision		Revision as of 21:09, 26 August 2010
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	<ref>[http://dx.doi.org/10.1063/1.2201699 M. López de Haro, A. Santos and S. B. Yuste "On the radial distribution function of a hard-sphere fluid", Journal of Chemical Physics '''124''' 236102 (2006)]</ref>		<ref>[http://dx.doi.org/10.1063/1.2201699 M. López de Haro, A. Santos and S. B. Yuste "On the radial distribution function of a hard-sphere fluid", Journal of Chemical Physics '''124''' 236102 (2006)]</ref>
	==Fluid-solid transition==		==Fluid-solid transition==
-	The hard sphere system undergoes a [[Solid-liquid phase transitions \|fluid-solid]] [[First-order transitions \|first order transition]] <ref name="HooverRee">[http://dx.doi.org/10.1063/1.1670641 William G. Hoover and Francis H. Ree "Melting Transition and Communal Entropy for Hard Spheres", Journal of Chemical Physics '''49''' pp. 3609-3617 (1968)]</ref>	+	The hard sphere system undergoes a [[Solid-liquid phase transitions \|fluid-solid]] [[First-order transitions \|first order transition]] <ref name="HooverRee">[http://dx.doi.org/10.1063/1.1670641 William G. Hoover and Francis H. Ree "Melting Transition and Communal Entropy for Hard Spheres", Journal of Chemical Physics '''49''' pp. 3609-3617 (1968)]</ref>, now referred as the Kirkwood-Alder transition <ref name="GastRussel">[http://dx.doi.org/10.1063/1.882495 Alice P. Gast and William B. Russel
		+	"Simple Ordering in Complex Fluids", Physics Today '''51''' (12) pp. 24-30 (1998)]</ref>.
	The fluid-solid coexistence densities (<math>\rho^* = \rho \sigma^3</math>) are given by		The fluid-solid coexistence densities (<math>\rho^* = \rho \sigma^3</math>) are given by
	:{\| border="1"		:{\| border="1"
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	\| 4.887(3) \|\| 3.719(8) \|\| <ref name="Miguel"> </ref>		\| 4.887(3) \|\| 3.719(8) \|\| <ref name="Miguel"> </ref>
	\|}		\|}
		+
	==Helmholtz energy function==		==Helmholtz energy function==
	Values for the [[Helmholtz energy function]] (<math>A</math>) are given in the following Table:		Values for the [[Helmholtz energy function]] (<math>A</math>) are given in the following Table:

← 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):

← Older revision		Revision as of 08:37, 30 August 2010
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	*[[Binder cumulant]]		*[[Binder cumulant]]
	*[[Law of corresponding states]]		*[[Law of corresponding states]]
		+	*[http://www.mac-how.net Mac How]
		+
	==References==		==References==
	<references/>		<references/>