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Physical scientists often use the term root mean square as a synonym for standard deviation when it can be assumed the input signal has zero mean, that is, referring to the square root of the mean squared deviation of a signal from a given baseline or fit. [8] [9] This is useful for electrical engineers in calculating the "AC only" RMS of a signal.
In fluid dynamics, normalized root mean square deviation (NRMSD), coefficient of variation (CV), and percent RMS are used to quantify the uniformity of flow behavior such as velocity profile, temperature distribution, or gas species concentration. The value is compared to industry standards to optimize the design of flow and thermal equipment ...
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.
In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable. [ 1 ] It may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value (e.g., may be a mean or an assumed mean of the data), [ 2 ...
Let P and Q be two sets, each containing N points in .We want to find the transformation from Q to P.For simplicity, we will consider the three-dimensional case (=).The sets P and Q can each be represented by N × 3 matrices with the first row containing the coordinates of the first point, the second row containing the coordinates of the second point, and so on, as shown in this matrix:
In statistical mechanics, the mean squared displacement (MSD, also mean square displacement, average squared displacement, or mean square fluctuation) is a measure of the deviation of the position of a particle with respect to a reference position over time.
The qualification of "rms" (root mean square) arises because it is the nuclear cross-section, proportional to the square of the radius, which is determining for electron scattering. This definition of charge radius is often applied to composite hadrons such as a proton, neutron, pion, or kaon, that are made up of more than one quark.
True RMS provides a more correct value that is proportional to the square root of the average of the square of the curve, and not to the average of the absolute value. For any given waveform , the ratio of these two averages is constant and, as most measurements are made on what are (nominally) sine waves, the correction factor assumes this ...