Threshold graph - Revision history

131.123.61.2: /* External links */ Updated link to ISGCI.

2014-10-19T16:20:01Z

External links: Updated link to ISGCI.

← Older revision		Revision as of 18:20, 19 October 2014
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	A '~~''Verlet list''' (named after [[Loup Verlet]]) is a data structure~~ in ~~[[molecular dynamics]] simulations~~ to ~~efficiently maintain a list of all particles within~~ a ~~given cut-off distance of each other~~.~~<ref name="Verlet1967">{{cite journal \|author=Verlet, L~~. ~~\|title=Computer 'experiments' on classical fluids. I~~. ~~Thermodynamical properties of Lennard-Jones molecules \|journal=Phys~~. ~~Rev~~. ~~\|volume=159 \|page=98–103 \|year=1967}}<~~/~~ref>~~		Andrew Simcox is the name his mothers and fathers gave him and he completely loves this title. Mississippi is the only place I've been residing in but I will have to transfer in a yr or two. To climb is some thing I truly appreciate doing. accurate psychic readings ([http://www.weddingwall.com.au/groups/easy-advice-for-successful-personal-development-today/ www.weddingwall.com.au]) Office supervising is where her primary earnings comes from but she's already applied for an additional 1.<br><br>Look into my homepage :: love [http://www.seekavideo.com/playlist/2199/video/ telephone psychic] ([http://Www.Aseandate.com/index.php?m=member_profile&p=profile&id=13352970 my webpage])

	~~This method may easily be applied to Monte Carlo simulations. For short~~-~~range interactions, a cut~~-off radius is typically used, beyond which particle interactions are considered "close enough" to zero to be safely ignored. For each particle, a Verlet list is constructed that lists all other particles within the potential cut-off distance, plus some extra distance so that the list may be used for several consecutive [[Monte Carlo method\|Monte Carlo]] "sweeps" before being updated. If we wish to use the same Verlet list n times before updating, then the cut-~~off distance for inclusion in the Verlet list should be <math>R_c + 2nd</math>, where <math>R_c</math> is the cut~~-~~off distance of the potential, and <math>d<~~/~~math> is the maximum Monte Carlo step of a single particle~~. ~~Thus, we will spend of order <math>N^2</math> time to compute the Verlet lists (<math>N</math>~~ is ~~the total number of particles),~~ but ~~are rewarded with~~ <~~math~~>n<~~/math~~> ~~Monte Carlo "sweeps" of order <math>Nn^2<~~/~~math> (instead of <math>NN<~~/~~math>)~~. ~~Optimizing our choice of <math>n<~~/~~math>, it can be shown that the <math>O(N^2)<~~/~~math> problem of Monte Carlo sweeps has been converted to an <math>O(N^{5~~/~~3})<~~/~~math> problem by using Verlet lists.~~

	~~Using [[cell lists]~~] ~~to identify the nearest neighbors in <math>O~~(~~N)</math> further reduces the computational cost.~~

	~~==See also==~~
	*[[Cell lists]]
	*[[Verlet integration]]
	*[[Fast multipole method]]

	~~==References==~~
	~~{{reflist}}~~

	~~==External links==~~
	*[http://~~www.physics~~.~~helsinki~~.~~fi/courses/s/atomistiset/lecturenotes/2004~~/~~landscape3a~~.~~pdf Constructing a Neighbour List]~~ &~~mdash; from ''Introduction to Atomistic Simulations'' course at the [[University of Helsinki~~]].

	~~[[Category:Molecular dynamics]]~~
	~~[[Category:Computational chemistry]]~~


	~~{{Comp-sci-stub}}~~

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q943345

2013-03-17T02:17:57Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q943345

← Older revision		Revision as of 04:17, 17 March 2013
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	~~Wilber Berryhill~~ is ~~what his wife enjoys~~ to ~~call him and he totally enjoys this~~ title. ~~Invoicing is my occupation~~. ~~Playing badminton is~~ a ~~factor that he~~ is ~~totally addicted~~ to. ~~Kentucky~~ is ~~exactly~~ where ~~I've usually been living~~.<br><br>~~Here~~ is ~~my web-site: phone psychic~~ ([http://www.~~khuplaza~~.~~com~~/~~dent~~/~~14869889 www~~.~~khuplaza~~.~~com~~])		A '''Verlet list''' (named after [[Loup Verlet]]) is a data structure in [[molecular dynamics]] simulations to efficiently maintain a list of all particles within a given cut-off distance of each other.<ref name="Verlet1967">{{cite journal \|author=Verlet, L. \|title=Computer 'experiments' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules \|journal=Phys. Rev. \|volume=159 \|page=98–103 \|year=1967}}</ref>

			This method may easily be applied to Monte Carlo simulations. For short-range interactions, a cut-off radius is typically used, beyond which particle interactions are considered "close enough" to zero to be safely ignored. For each particle, a Verlet list is constructed that lists all other particles within the potential cut-off distance, plus some extra distance so that the list may be used for several consecutive [[Monte Carlo method\|Monte Carlo]] "sweeps" before being updated. If we wish to use the same Verlet list n times before updating, then the cut-off distance for inclusion in the Verlet list should be <math>R_c + 2nd</math>, where <math>R_c</math> is the cut-off distance of the potential, and <math>d</math> is the maximum Monte Carlo step of a single particle. Thus, we will spend of order <math>N^2</math> time to compute the Verlet lists (<math>N</math> is the total number of particles), but are rewarded with <math>n</math> Monte Carlo "sweeps" of order <math>Nn^2</math> (instead of <math>NN</math>). Optimizing our choice of <math>n</math>, it can be shown that the <math>O(N^2)</math> problem of Monte Carlo sweeps has been converted to an <math>O(N^{5/3})</math> problem by using Verlet lists.

			Using [[cell lists]] to identify the nearest neighbors in <math>O(N)</math> further reduces the computational cost.

			==See also==
			*[[Cell lists]]
			*[[Verlet integration]]
			*[[Fast multipole method]]

			==References==
			{{reflist}}

			==External links==
			*[http://www.physics.helsinki.fi/courses/s/atomistiset/lecturenotes/2004/landscape3a.pdf Constructing a Neighbour List] — from ''Introduction to Atomistic Simulations'' course at the [[University of Helsinki]].

			[[Category:Molecular dynamics]]
			[[Category:Computational chemistry]]


			{{Comp-sci-stub}}

en>David Eppstein: not really a graph operation; add :Category:Perfect graphs

2012-08-07T07:27:42Z

not really a graph operation; add Category:Perfect graphs

New page

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