statistical mechanics, the mean squared displacement (MSD), also called mean square displacement, average squared displacement, or mean square fluctuation, is a...

quantization error Reduced chi-squared statistic Mean squared displacement Mean squared prediction error Minimum mean square error Overfitting Peak signal-to-noise...

expression, the mean squared displacement refers to just once Cartesian component ux of the vector u that describes the displacement of atoms from their...

(ARV) Central moment Geometric mean Glossary of mathematical symbols L2 norm Least squares Mean squared displacement Pythagorean addition True RMS converter...

processes. Root mean square Mean absolute error Average absolute deviation Mean signed deviation Mean squared error Squared deviations from the mean Errors and...

diffusion is the Brownian motion of one particle. The particle's Mean squared displacement from its original position is: MSD ≡ ⟨ ( x − x 0 ) 2 ⟩ = 2 n D...

particles, in which the diffusion coefficient is related to the mean squared displacement of a Brownian particle, while the second part consists in relating...

diffusion process with a non-linear relationship between the mean squared displacement (MSD), ⟨ r 2 ( τ ) ⟩ {\displaystyle \langle r^{2}(\tau )\rangle...

{\displaystyle \mathbf {v} (0)\tau } as the system relaxes. The mean squared displacement can be determined similarly: ⟨ r 2 ( t ) ⟩ = v 2 ( 0 ) τ 2 ( 1...

source (for example, one single spray of perfume)—the square root of the mean squared displacement from this point. In Fickian diffusion, this is 2 n D...

respectively, and ⟨ u 2 ⟩ {\displaystyle \langle u^{2}\rangle } is the mean squared displacement. In crystallographic publications, values of U {\displaystyle...

detector, a type of chromatography detector Mean squared displacement, a statistical measure of random motion Mean signed deviation, a measure of statistical...

one-dimensional vibrational mean squared displacement of the j t h {\displaystyle j^{th}} emitter. In the Debye model, the mean squared displacement is calculated in...

{B} }T}}} , where l {\displaystyle l} is the mean bond length. Single-segment mean-squared displacement (MSD) for lag time τ ( τ ≪ τ R {\displaystyle...

For passive diffusion, the law of diffusion states that the mean squared displacement is ⟨ r 2 ⟩ = 2 d D t {\displaystyle \langle r^{2}\rangle =2dDt}...

techniques to account for multiple scattering events. From the mean squared displacement with respect to time (noted MSD or <Δr2> ), one can calculate...

judgment on the question... Einstein derived expressions for the mean squared displacement of particles. Using the kinetic theory of gases, which at the...

Landau–Peierls instability refers to the phenomenon in which the mean square displacements due to thermal fluctuations diverge in the thermodynamic limit...

change with temperature. Random walk statistics describe the mean squared displacement of diffusing species in terms of the number of jumps N and the...

suspended in a (complex) fluid a direct relation between g2-1 and the mean squared displacement of the particles <Δr2> can be established. Let us note P(s) the...

instantaneous displacement of the surface from its average position, the mean squared displacement may be represented with a displacement spectrum G(k)...

logarithmic displacements of lattice sites (which are difficult to quantify for a finite system size), but the magnitude of the mean squared displacement of the...

the mean squared displacement ⟨r(t)2⟩ generically scales as ⟨r(t)2⟩ ~ t2 for small t and ⟨r(t)2⟩ ~ t for large t. In two dimensions, the mean squared displacement...

rs. The criterion states that the crystal melts when the root-mean-square displacement of the electrons ⟨ r 2 ⟩ {\displaystyle {\sqrt {\langle r^{2}\rangle...

sufficiently well-described by the normal diffusion model, where the mean squared displacement (MSD) grows linearly with time. Instead the diffusion may be better...

Dtube = kB T μtube. By then recalling that in 1-dimension the mean squared displacement due to Brownian motion is given by s(t)2 = 2Dtube t, we obtain...

amplitude of the displacement (movements of the air or the diaphragm of a speaker) is described. The logarithm of the amplitude squared is usually quoted...

most famous statistical properties of this process is that the mean squared displacement (MSD) of a particle in the file follows, M S D ≈ t 1 2 {\displaystyle...

positively correlated with the average parasite mean speed, and negatively correlated with the mean square displacement (MSD). Therefore, the motility modifications...

averaged force, elasticity and displacement used to account for stochastic forces. Time-averaged Mean squared displacement, M S D = ⟨ ( X ( t ) ) 2 ⟩ {\displaystyle...