# Root mean square fluctuation

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Root mean square fluctuation

The mean square fluctuation (MSF) is a measure of the deviation between the position of particle i and some reference position.

$MSF=frac\left\{1\right\}\left\{T\right\}sum_\left\{t_j=1\right\}^\left\{T\right\}\left(x_i\left(t_j\right) - ilde\left\{x\right\}_i\right)^2$,

where T is the time over which one wants to average, and $ilde\left\{x\right\}_i$ is the reference position of particle i. Typically this reference position will be the time-averaged position of the same particle i, ie. $overline\left\{x\right\}_i$

Note that where the difference between RMSD and MSF is that with the later the average is taken over time, giving a value for each particle i. With RMSD the average is taken over the particles, giving time specific values.

*Root mean square deviation (bioinformatics)
* Root Mean Square Fluctuation calculated by GROMACS [http://www.gromacs.org/documentation/reference/online/g_rmsf.html]

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