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In the physics of gas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is calculated using the following equation: v RMS = 3 R T M {\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}}
In bioinformatics, the root mean square deviation of atomic positions is the measure of the average distance between the atoms of superimposed proteins. In structure based drug design , the RMSD is a measure of the difference between a crystal conformation of the ligand conformation and a docking prediction.
The average wavelength a and the root mean square wavelength q are derived from a. When trying to understand a surface that depends on both amplitude and frequency it is not obvious which pair of metrics optimally describes the balance, so a statistical analysis of pairs of measurements can be performed (e.g.: R z and λ {\displaystyle \lambda ...
If is defined as the root mean square of the velocity in any one dimension (i.e. any single direction), then [1] [2] =. If v th {\displaystyle v_{\text{th}}} is defined as the mean of the magnitude of the velocity in any one dimension (i.e. any single direction), then v th = 2 k B T π m . {\displaystyle v_{\text{th}}={\sqrt {\frac {2k_{\text{B ...
The peak-to-average power ratio (PAPR) is the peak amplitude squared (giving the peak power) divided by the RMS value squared (giving the average power). [1] It is the square of the crest factor. When expressed in decibels , crest factor and PAPR are equivalent, due to the way decibels are calculated for power ratios vs amplitude ratios .
The data set [100, 100, 100] has constant values. Its standard deviation is 0 and average is 100, giving the coefficient of variation as 0 / 100 = 0; The data set [90, 100, 110] has more variability. Its standard deviation is 10 and its average is 100, giving the coefficient of variation as 10 / 100 = 0.1
The square root of a mean square is known as the root mean square (RMS or rms), and can be used as an estimate of the standard deviation of a random variable when the random variable is zero-mean. References
When a dynamical system fluctuates about some well-defined average position, the RMSD from the average over time can be referred to as the RMSF or root mean square fluctuation. The size of this fluctuation can be measured, for example using Mössbauer spectroscopy or nuclear magnetic resonance, and can provide important physical information.