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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.
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.
The particle's Mean squared displacement from its original position is: =, where is the dimension of the particle's Brownian motion. For example, the diffusion of a molecule across a cell membrane 8 nm thick is 1-D diffusion because of the spherical symmetry; However, the diffusion of a molecule from the membrane to the center of a eukaryotic ...
The log-spectral distance (LSD), also referred to as log-spectral distortion or root mean square log-spectral distance, is a distance measure between two spectra. [1] The log-spectral distance between spectra () and ^ is defined as p-norm:
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 ...
Simulated squared displacements of free Brownian particles (semi-transparent wiggly lines) as a function of time, for three selected choices of initial squared velocity which are 0, 3k B T/m, and 6k B T/m respectively, with 3k B T/m being the equipartition value in thermal equilibrium. The colored solid curves denote the mean squared ...
By measuring the mean squared displacement over a time interval along with the universal gas constant R, the temperature T, the viscosity η, and the particle radius r, the Avogadro constant N A can be determined. The type of dynamical equilibrium proposed by Einstein was not new.
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.