Velocity Verlet algorithm: Difference between revisions
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The '''Velocity Verlet algorithm''' for use in [[molecular dynamics]] is given by | |||
:<math>r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)</math> | :<math>r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)</math> | ||
:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math> | :<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math> | ||
where <math>r</math> is the position, <math>v</math> is the velocity and <math>t</math> is the time. | |||
==See also== | ==See also== | ||
*[[Verlet leap-frog algorithm]] | *[[Verlet leap-frog algorithm]] | ||
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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)] | ||
#[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)] | #[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)] | ||
==External resources== | |||
*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.04 Velocity version of Verlet algorithm ] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)]. | |||
[[category: Molecular dynamics]] | [[category: Molecular dynamics]] | ||
Revision as of 18:10, 8 February 2009
The Velocity Verlet algorithm for use in molecular dynamics is given by
![{\displaystyle v\left(t+\delta t\right)=v(t)+{\frac {1}{2}}\delta t[a(t)+a(t+\delta t)]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37487fb90cb334d0566a9595100c022963cc19bd)
where is the position, is the velocity and is the time.
See also
References
- Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review 159 pp. 98-103 (1967)
- William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics 76 pp. 637-649 (1982)
External resources
- Velocity version of Verlet algorithm sample FORTRAN computer code from the book M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989).