Verlet leap-frog algorithm - Revision history

Carl McBride: Undo revision 10860 by DannySaylor (talk) Spam

2010-11-30T11:54:35Z

Undo revision 10860 by DannySaylor (talk) Spam

← Older revision		Revision as of 13:54, 30 November 2010
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	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]		*[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]
	*[http://www.online-casino-gaming.org/online-slots/ online slots]
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

DannySaylor at 11:52, 30 November 2010

2010-11-30T11:52:59Z

← Older revision		Revision as of 13:52, 30 November 2010
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	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]		*[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]
			*[http://www.online-casino-gaming.org/online-slots/ online slots]
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

Carl McBride at 14:47, 26 November 2010

2010-11-26T14:47:29Z

← Older revision		Revision as of 16:47, 26 November 2010
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	The '''Verlet leap-frog algorithm''' is a variant of the original Verlet scheme <ref>[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98-103 (1967)]</ref> for use in [[molecular dynamics]] simulations. The algorithm is given by:		The '''Verlet leap-frog algorithm''' <ref>R. W. Hockney "The potential calculation and some applications", Methods in Computational Physics vol. '''9''' pp. 135-211 Academic Press, New York (1970)</ref> is a variant of the original Verlet scheme <ref>[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98-103 (1967)]</ref> for use in [[molecular dynamics]] simulations. The algorithm is given by:

	:<math>r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)</math>		:<math>r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)</math>
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	<references/>		<references/>
	'''Related reading'''		'''Related reading'''
	*R. W. Hockney "The potential calculation and some applications", Methods in Computational Physics vol. '''9''' pp. 135-211 Academic Press, New York (1970)
	*[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]		*[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

Carl McBride: /* References */ Added title of a publication

2010-11-26T14:46:44Z

References: Added title of a publication

← Older revision		Revision as of 16:46, 26 November 2010
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	<references/>		<references/>
	'''Related reading'''		'''Related reading'''
	*R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York ~~pp. 135–211~~ (1970)		*R. W. Hockney "The potential calculation and some applications", Methods in Computational Physics vol. '''9''' pp. 135-211 Academic Press, New York (1970)
	*[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]		*[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

Carl McBride: Slight tidy

2010-11-26T14:04:46Z

Slight tidy

← Older revision		Revision as of 16:04, 26 November 2010
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	The '''Verlet leap-frog algorithm''' is a variant of the original Verlet scheme (~~Ref~~. 1)		The '''Verlet leap-frog algorithm''' is a variant of the original Verlet scheme <ref>[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98-103 (1967)]</ref> for use in [[molecular dynamics]] simulations. The algorithm is given by:

	:<math>r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)</math>		:<math>r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)</math>
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	:<math>v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a (t)</math>		:<math>v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a (t)</math>

	where ''r'' is the position, ''v'' is the velocity, ''a'' is the acceleration and ''t'' is the time.		where ''r'' is the position, ''v'' is the velocity, ''a'' is the acceleration and ''t'' is the time. <math>\delta t</math> is known as the [[time step]].
	==See also==		==See also==
	*[[Velocity Verlet algorithm]]		*[[Velocity Verlet algorithm]]
	==References==		==References==
	~~#[http:~~/~~/dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review~~ '''~~159~~''' ~~pp. 98 - 103 (1967)]~~		<references/>
	#R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York pp. 135–211 (1970)		'''Related reading'''
	#[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]		*R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York pp. 135–211 (1970)
			*[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

Carl McBride: /* References */ Add a Ref.

2007-11-15T10:39:41Z

References: Add a Ref.

← Older revision		Revision as of 12:39, 15 November 2007
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	#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98 - 103 (1967)]		#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98 - 103 (1967)]
	#R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York pp. 135–211 (1970)		#R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York pp. 135–211 (1970)
			#[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

Carl McBride at 17:52, 13 August 2007

2007-08-13T17:52:04Z

← Older revision		Revision as of 19:52, 13 August 2007
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	where ''r'' is the position, ''v'' is the velocity, ''a'' is the acceleration and ''t'' is the time.		where ''r'' is the position, ''v'' is the velocity, ''a'' is the acceleration and ''t'' is the time.
			==See also==
			*[[Velocity Verlet algorithm]]
	==References==		==References==
	#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98 - 103 (1967)]		#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98 - 103 (1967)]
	#R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York pp. 135–211 (1970)		#R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York pp. 135–211 (1970)
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

Carl McBride at 10:29, 10 July 2007

2007-07-10T10:29:13Z

← Older revision		Revision as of 12:29, 10 July 2007
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	:<math>v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a (t)</math>		:<math>v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a (t)</math>

			where ''r'' is the position, ''v'' is the velocity, ''a'' is the acceleration and ''t'' is the time.
	==References==		==References==
	#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98 - 103 (1967)]		#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98 - 103 (1967)]
	#R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York pp. 135–211 (1970)		#R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York pp. 135–211 (1970)
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

Carl McBride at 11:01, 15 June 2007

2007-06-15T11:01:05Z

← Older revision		Revision as of 13:01, 15 June 2007
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			The '''Verlet leap-frog algorithm''' is a variant of the original Verlet scheme (Ref. 1)

	:<math>r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)</math>		:<math>r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)</math>

Carl McBride: New page: : $r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)$ : $v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a ...$

2007-06-15T10:52:44Z

New page: :<math>r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)</math> :<math>v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a ...

New page

:<math>r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)</math>

:<math>v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a (t)</math>
==References==
#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98 - 103 (1967)]
#R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York pp. 135–211 (1970)
[[category: Molecular dynamics]]