Verlet leap-frog algorithm: Difference between revisions
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The '''Verlet leap-frog algorithm''' is a variant of the original Verlet scheme ( | 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== | ||
<references/> | |||
'''Related reading''' | |||
*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]] | ||
Revision as of 15:04, 26 November 2010
The Verlet leap-frog algorithm is a variant of the original Verlet scheme [1] for use in molecular dynamics simulations. The algorithm is given by:
where r is the position, v is the velocity, a is the acceleration and t is the time. is known as the time step.
See also
References
Related reading
- R. W. Hockney, Methods in Computational Physics vol. 9, Academic Press, New York pp. 135–211 (1970)
- 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)