•   Wikis

# Root mean square fluctuation: Wikis

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

# Encyclopedia

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

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

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, ie. $\overline{x}_i$

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.