http://www.sklogwiki.org/SklogWiki/api.php?action=feedcontributions&feedformat=atom&user=DannySaylor 2026-05-01T02:11:36Z User contributions MediaWiki 1.41.0 http://www.sklogwiki.org/SklogWiki/index.php?title=Verlet_leap-frog_algorithm&diff=10860 2010-11-30T11:52:59Z

<p>DannySaylor: </p> <hr /> <div>The '''Verlet leap-frog algorithm''' &lt;ref&gt;R. W. Hockney &quot;The potential calculation and some applications&quot;, Methods in Computational Physics vol. '''9''' pp. 135-211 Academic Press, New York (1970)&lt;/ref&gt; is a variant of the original Verlet scheme &lt;ref&gt;[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet &quot;Computer &quot;Experiments&quot; on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules&quot;, Physical Review '''159''' pp. 98-103 (1967)]&lt;/ref&gt; for use in [[molecular dynamics]] simulations. The algorithm is given by:<br /> <br /> :&lt;math&gt;r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)&lt;/math&gt;<br /> <br /> :&lt;math&gt;v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a (t)&lt;/math&gt;<br /> <br /> where ''r'' is the position, ''v'' is the velocity, ''a'' is the acceleration and ''t'' is the time. &lt;math&gt;\delta t&lt;/math&gt; is known as the [[time step]].<br /> ==See also==<br /> *[[Velocity Verlet algorithm]]<br /> ==References==<br /> &lt;references/&gt;<br /> '''Related reading'''<br /> *[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren &quot;On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm&quot;, Journal of Chemical Physics '''127''' 184102 (2007)]<br /> *[http://www.online-casino-gaming.org/online-slots/ online slots]<br /> [[category: Molecular dynamics]]</div>

DannySaylor