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. 2017 Oct 3;7:12614. doi: 10.1038/s41598-017-12737-1

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Symbols, initial part of the mean square displacement, normalized with the square mean free path, vs. the normalized time $t / τ_{1}$ , for a range of particle concentrations. Solid line, master equation 4. Long- and short-dashed lines are fits to a quadratic and a linear functions of time, respectively, offset for clarity. The inset shows the MSD for the same systems, but at a long time scale where the levelling off of the curves is observed due to the field of view’s finite size.