Werner KRAUTH - Recent changes [en]

Main Page

2013-05-24T21:55:36Z

/* Upcoming events */

Revision as of 21:55, 24 May 2013		Current revision
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	Current interests are in hard spheres, mainly the melting transition in two-dimensional disks, bosons (in collaboration with the experimental groups at ENS), and the theory of convergence and of coupling in Markov chains.		Current interests are in hard spheres, mainly the melting transition in two-dimensional disks, bosons (in collaboration with the experimental groups at ENS), and the theory of convergence and of coupling in Markov chains.

-	[[Image:Hard disk melting.jpg\|left\|100px\|border\|thumb\|Melting of hard disks]]By the way: the term '''melting of hard disks''' does not relate to the irreversible memory loss when your laptop catches fire (left figure), but to a fundamental phase transition in the model of two-dimensional hard spheres, that is, billiard balls without friction and without inner structure (center and right figures). The possibility that two-dimensional systems with continuous degrees of freedom could melt was discovered in 1962, by Alder and Wainwright, but the nature of the transition remained a mystery for several decades ([[Bernard_Krauth_2011\|but we think we now solved it]]).	+	[[Image:Hard disk melting.jpg\|left\|100px\|border\|thumb\|Melting of hard disks]]By the way: the term '''melting of hard disks''' does not relate to the irreversible memory loss when your '''computer hard disk''' catches fire (left figure), but to a fundamental phase transition in the model of two-dimensional hard spheres, that is, billiard balls without friction and without inner structure (center and right figures). The possibility that two-dimensional systems with continuous degrees of freedom could melt was discovered in 1962, by Alder and Wainwright, but the nature of the transition remained a mystery for several decades ([[Bernard_Krauth_2011\|but we think we now solved it]]).
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	Theoretical Colloquium Utrecht University, March 13, 2013 Utrecht, Netherlands (Invited colloquium)		Theoretical Colloquium Utrecht University, March 13, 2013 Utrecht, Netherlands (Invited colloquium)

-	Seminar "Disorder and Strong Electron Correlations". April 3, 2012, Abdus Salam International Center	+	Seminar "Disorder and Strong Electron Correlations". April 3, 2013, Abdus Salam International Center
	for Theoretical Physics, Trieste, Italy		for Theoretical Physics, Trieste, Italy
		+
		+	Seminar, May 28/29 2013 School of Physics & Engineering Zhongshan (Sun Yat-Sen) University Guangzhou, People's Republic of China
		+
		+	Lecture series and seminaire, May 30-June 5, 2013 Hongkong University of Science and Technology (HKUST)

	[http://www.statphys25.org/ Statphys25, July 22 – 26, 2013, Seoul National University, Seoul, Korea] (Invited talk)		[http://www.statphys25.org/ Statphys25, July 22 – 26, 2013, Seoul National University, Seoul, Korea] (Invited talk)

Special:Log/move

2013-05-06T15:50:52Z

[[Anderson et al 2012]] moved to [[Engel et al 2013]]

Publications WK

2013-05-06T15:49:56Z

/* Recent publications and preprints */

Revision as of 15:49, 6 May 2013		Current revision
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	[[Kapfer_Krauth_2013\|S. C. Kapfer, W. Krauth, ''Sampling from a polytope and hard-disk Monte Carlo'' arXiv:1301.4901 (2013)]]		[[Kapfer_Krauth_2013\|S. C. Kapfer, W. Krauth, ''Sampling from a polytope and hard-disk Monte Carlo'' arXiv:1301.4901 (2013)]]

-	[[Anderson et al 2012\|J. A. Anderson, M. Engel, S. C. Glotzer,	+	[[Engel et al 2013\| M. Engel, J. A. Anderson, S. C. Glotzer,
	M. Isobe, E. P. Bernard, W. Krauth ''Hard-disk equation of state:		M. Isobe, E. P. Bernard, W. Krauth ''Hard-disk equation of state:
-	First-order liquid-hexatic transition in two dimensions with three simulation methods arXiv/11/2012, to appear in Phys. Rev. E]]	+	First-order liquid-hexatic transition in two dimensions with three simulation methods'' Phys. Rev. E 87, 042134 (2013) ]]

	[[Bernard Krauth_b_2011\|E. P. Bernard, W. Krauth ''Addendum to ''Event-chain Monte Carlo algorithms for hard-sphere systems'' Phys. Rev. E86, 017701 (2012)]]		[[Bernard Krauth_b_2011\|E. P. Bernard, W. Krauth ''Addendum to ''Event-chain Monte Carlo algorithms for hard-sphere systems'' Phys. Rev. E86, 017701 (2012)]]

Main Page

2013-05-05T15:33:41Z

/* Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods */

Revision as of 15:33, 5 May 2013		Current revision
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	[[Image:Eqofstate.jpg\|left\|200px\|border\|thumb\|Move of one particle in the Event-driven MC algorithm]] Spring and summer of 2012 was partly spent on a project with colleagues Joshua Anderson, Michael Engel and Sharon Glotzer from the University of Michigan, Masaharu Isobe from the Nagoya Institute of Technology, and Etienne Bernard from MIT. We were interested in checking [[Bernard_Krauth_2011\|our earlier results]] on the melting transition of hard disks in two dimensions which predicted the existence of a first-order liquid-hexatic phase transition - a big surprise after hundreds of other papers had fought over two other scenarios for melting in two dimensions. [[Anderson et al 2012\| Our confirmation preprint]] finally came out in November 2012, and it was published in Physical Review E, in April 2013. Using three completely independent algorithms ([http://arxiv.org/abs/1211.1646v1 massively parallel local Monte Carlo], molecular dynamics, [[Bernard_Krauth_Wilson_2009\|event-chain Monte Carlo]]), we confirmed our earlier data (see figure to the left). We are all happy about this independent verification, and Etienne Bernard and I are quite relieved, as so much can go wrong with numerical simulations, especially if they take an eternity, almost, to run.		[[Image:Eqofstate.jpg\|left\|200px\|border\|thumb\|Move of one particle in the Event-driven MC algorithm]] Spring and summer of 2012 was partly spent on a project with colleagues Joshua Anderson, Michael Engel and Sharon Glotzer from the University of Michigan, Masaharu Isobe from the Nagoya Institute of Technology, and Etienne Bernard from MIT. We were interested in checking [[Bernard_Krauth_2011\|our earlier results]] on the melting transition of hard disks in two dimensions which predicted the existence of a first-order liquid-hexatic phase transition - a big surprise after hundreds of other papers had fought over two other scenarios for melting in two dimensions. [[Anderson et al 2012\| Our confirmation preprint]] finally came out in November 2012, and it was published in Physical Review E, in April 2013. Using three completely independent algorithms ([http://arxiv.org/abs/1211.1646v1 massively parallel local Monte Carlo], molecular dynamics, [[Bernard_Krauth_Wilson_2009\|event-chain Monte Carlo]]), we confirmed our earlier data (see figure to the left). We are all happy about this independent verification, and Etienne Bernard and I are quite relieved, as so much can go wrong with numerical simulations, especially if they take an eternity, almost, to run.

-	The figure to the left shows the equation of state for hard disks (the equilibrium pressure as a function of the density (or the volume), with the characteristic loop which indicates the presence of two phases - a minority phase that forms a bubble inside the majority phase. The three curves stand for the simulation methods: different algorithms, different computers, even continents produce the same equation of state, the one that noone else has produced before! The inset gives the difference between the old data (from last year) and the new ones. Let me note that, if the simulation is nontrivial, the calculation of the pressure is quite tricky also, especially in Monte Carlo calculations, as an extrapolation of the pair-correlation function is involved. Those of us in the team who computed the pressure from Monte Carlo were much relieved to see the nice agreement with the molecular dynamics pressure, obtained with Masaharu Isobe's code, which is computed simply by counting the number of collisions taking place over a months-long simulation. For more details, [[Anderson et al 2012\|see the	+	The figure to the left shows the equation of state for hard disks (the equilibrium pressure as a function of the density (or the volume), with the characteristic loop which indicates the presence of two phases - a minority phase that forms a bubble inside the majority phase. The three curves stand for the simulation methods: different algorithms, different computers, even continents produce the same equation of state, the one that noone else has produced before! The inset gives the difference between the old data (from last year) and the new ones. Let me note that, if the simulation is nontrivial, the calculation of the pressure is quite tricky also, especially in Monte Carlo calculations, as an extrapolation of the pair-correlation function is involved. Those of us in the team who computed the pressure from Monte Carlo were much relieved to see the nice agreement with the molecular dynamics pressure, obtained with Masaharu Isobe's code, which is computed simply by counting the number of collisions taking place over a months-long simulation. For more details, [[Anderson et al 2012\| take a look at the paper]].
-	preprint]].	+

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Anderson et al 2012

2013-05-05T15:16:30Z

Revision as of 15:16, 5 May 2013		Current revision
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-	J. A. Anderson, M. Engel, S. C. Glotzer, M. Isobe, E. P. Bernard, W. Krauth ''Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods'' arXiv/1211.1645	+	M. Engel, J. A. Anderson, S. C. Glotzer, M. Isobe, E. P. Bernard, W. Krauth ''Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods'' Phys. Rev. E 87, 042134 (2013)

	=Paper=		=Paper=
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	phase transition in hard disks.		phase transition in hard disks.

-	[http://arxiv.org/pdf/1211.1645v1 Electronic version (from arXiv)]	+	[http://arxiv.org/pdf/1211.1645v2 Electronic version (from arXiv)]
		+
		+	[http://link.aps.org/doi/10.1103/PhysRevE.87.042134 Paper in Physical Review E (Subscription needed)]

	=Context=		=Context=

Main Page

2013-05-05T15:12:54Z

/* Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods */

Revision as of 15:12, 5 May 2013		Current revision
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-	[[Image:Eqofstate.jpg\|left\|200px\|border\|thumb\|Move of one particle in the Event-driven MC algorithm]] Spring and summer of 2012 was partly spent on a project with colleagues Joshua Anderson, Michael Engel and Sharon Glotzer from the University of Michigan, Masaharu Isobe from the Nagoya Institute of Technology, and Etienne Bernard from MIT. We were interested in checking [[Bernard_Krauth_2011\|our earlier results]] on the melting transition of hard disks in two dimensions which predicted the existence of a first-order liquid-hexatic phase transition - a big surprise after hundreds of other papers had fought over two other scenarios for melting in two dimensions. [[Anderson et al 2012\| Our confirmation preprint]] finally came out in November 2012, and it was accepted for publication in Physical Review E, in April 2013. Using three completely independent algorithms ([http://arxiv.org/abs/1211.1646v1 massively parallel local Monte Carlo], molecular dynamics, [[Bernard_Krauth_Wilson_2009\|event-chain Monte Carlo]]), we confirmed our earlier data (see figure to the left). We are all happy about this independent verification, and Etienne Bernard and I are quite relieved, as so much can go wrong with numerical simulations, especially if they take an eternity, almost, to run.	+	[[Image:Eqofstate.jpg\|left\|200px\|border\|thumb\|Move of one particle in the Event-driven MC algorithm]] Spring and summer of 2012 was partly spent on a project with colleagues Joshua Anderson, Michael Engel and Sharon Glotzer from the University of Michigan, Masaharu Isobe from the Nagoya Institute of Technology, and Etienne Bernard from MIT. We were interested in checking [[Bernard_Krauth_2011\|our earlier results]] on the melting transition of hard disks in two dimensions which predicted the existence of a first-order liquid-hexatic phase transition - a big surprise after hundreds of other papers had fought over two other scenarios for melting in two dimensions. [[Anderson et al 2012\| Our confirmation preprint]] finally came out in November 2012, and it was published in Physical Review E, in April 2013. Using three completely independent algorithms ([http://arxiv.org/abs/1211.1646v1 massively parallel local Monte Carlo], molecular dynamics, [[Bernard_Krauth_Wilson_2009\|event-chain Monte Carlo]]), we confirmed our earlier data (see figure to the left). We are all happy about this independent verification, and Etienne Bernard and I are quite relieved, as so much can go wrong with numerical simulations, especially if they take an eternity, almost, to run.

	The figure to the left shows the equation of state for hard disks (the equilibrium pressure as a function of the density (or the volume), with the characteristic loop which indicates the presence of two phases - a minority phase that forms a bubble inside the majority phase. The three curves stand for the simulation methods: different algorithms, different computers, even continents produce the same equation of state, the one that noone else has produced before! The inset gives the difference between the old data (from last year) and the new ones. Let me note that, if the simulation is nontrivial, the calculation of the pressure is quite tricky also, especially in Monte Carlo calculations, as an extrapolation of the pair-correlation function is involved. Those of us in the team who computed the pressure from Monte Carlo were much relieved to see the nice agreement with the molecular dynamics pressure, obtained with Masaharu Isobe's code, which is computed simply by counting the number of collisions taking place over a months-long simulation. For more details, [[Anderson et al 2012\|see the		The figure to the left shows the equation of state for hard disks (the equilibrium pressure as a function of the density (or the volume), with the characteristic loop which indicates the presence of two phases - a minority phase that forms a bubble inside the majority phase. The three curves stand for the simulation methods: different algorithms, different computers, even continents produce the same equation of state, the one that noone else has produced before! The inset gives the difference between the old data (from last year) and the new ones. Let me note that, if the simulation is nontrivial, the calculation of the pressure is quite tricky also, especially in Monte Carlo calculations, as an extrapolation of the pair-correlation function is involved. Those of us in the team who computed the pressure from Monte Carlo were much relieved to see the nice agreement with the molecular dynamics pressure, obtained with Masaharu Isobe's code, which is computed simply by counting the number of collisions taking place over a months-long simulation. For more details, [[Anderson et al 2012\|see the

Hard disk annotated bibliography

2013-04-25T10:48:45Z

New page

Hard-disk annotated bibliography.

Hikaru KAWAMURA, Department of Physics, University of Tohyo, Tohyo 113
Progress of Theoretical Physics, Vol. 61, No. 6, June 1979
A Simple Theory of Hard Disk Transition