Root mean square fluctuation

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

MSF=\sqrt{\frac{1}{T}\sum_{t_j=1}^{T}(x_i(t_j) - \tilde{x}_i)^2},

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

Note that the difference between RMSD and RMSF is that with the latter the average is taken over time, giving a value for each particle i. With RMSD the average is taken over the particles, giving time resolved values.

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