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Examples

  • If we map the mean-square displacement of the child as a function of time, we could determine the diffusion coefficient of a nine-month-old though the presence of the walls complicates it a bit.

    What babies are up to.

  • In order to avoid an additional procedure of statistical transformation of local tree-ring index series into normalized values of summer temperature variation, each of the local chronologies was normalized to the mean-square deviation in the generalized curve for the Asian subarctic region [23].

    Tree rings and past climate in the Arctic

  • Superimposition of all crystals gave a mean backbone RMSD (root mean-square distance) of ca. 0.5 Å (all-atom RMSD ca. 1.5 Å).

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  • For long three-dimensional chains and strong surface interactions a 3D-to-2D projection model was assumed and a broad distribution of the calculated mean-square end-to-end-distances for long DNA-fragments was reported

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  • The mean-square end-to-end distance on a two-dimensional surface as a function of contour distance

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  • The communication propensity (CP) of any pair of residues is defined as the mean-square fluctuation of the inter-residue distance, defining dij as distance between the Cα atoms of residue

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  • Recent studies demonstrate that proteins show anomalous diffusion - i.e. a mean-square displacement whose time dependence is weaker than linear - in the cytoplasm

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  • Monte Carlo steps were done successively until the chains reached the mean-square end-to-end distance expected for a relaxed chain.

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  • To extract parameters that can be used to compare the fibers quantitatively, we plotted the cosine of the mean-angle, the fourth moment, the mean-square angle and the mean-square end-to-end distance against the filament contour length, and fitted these data with the equations given in the theory part.

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  • The apparent polymer flexibility, expressed as a persistence length, was then calculated from both the experimental and the theoretical data sets using three different procedures as described above: calculation from the mean-square end-to-end distance as function of contour length, from the decay of the average cosine of the bending angle with the contour length, and from the mean-square bending angle as a function of contour length.

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