Velocity Verlet algorithm: Difference between revisions
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The '''Velocity Verlet algorithm''' for use in [[molecular dynamics]] is given by | The '''Velocity Verlet algorithm''', for use in [[molecular dynamics]], is given by <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>: | ||
:<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> | ||
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:<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, <math>a</math> is the acceleration and <math>t</math> is the time. | where <math>r</math> is the position, <math>v</math> is the velocity, <math>a</math> is the acceleration and <math>t</math> is the time. <math>\delta t</math> is known as the [[time step]]. | ||
==See also== | ==See also== | ||
*[[Verlet leap-frog algorithm]] | *[[Verlet leap-frog algorithm]] | ||
==References== | ==References== | ||
<references/> | |||
'''Related reading''' | |||
*[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)] | |||
*[https://doi.org/10.1063/1.5008438 Jaewoon Jung, Chigusa Kobayashi, and Yuji Sugita "Kinetic energy definition in velocity Verlet integration for accurate pressure evaluation", Journal of Chemical Physics '''148''' 164109 (2018)] | |||
==External resources== | ==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)]. | *[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]] | ||
Latest revision as of 11:46, 3 May 2018
The Velocity Verlet algorithm, for use in molecular dynamics, is given by [1]:
![{\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, is the acceleration and is the time. is known as the time step.
See also[edit]
References[edit]
Related reading
- 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)
- Jaewoon Jung, Chigusa Kobayashi, and Yuji Sugita "Kinetic energy definition in velocity Verlet integration for accurate pressure evaluation", Journal of Chemical Physics 148 164109 (2018)
External resources[edit]
- 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).