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Confirmation of theoretical predictions using numerical simulations. (a) The measured MSD (normalized to the actual MSD) as a function of time step for 100 separate simulations. Each simulation has two tracked particles, so the MSD is predicted to be half the actual value, as demonstrated by the simulations. (b) Analysing the effect of tracking more particles. For each n, eight different simulations are plotted, and for each simulation, the mean value of the MSD for a time-step of 1 is plotted. As a guide to the eye, the line corresponding to is plotted, showing excellent agreement between the theoretical prediction and the numerical result.
(a) An example frame with circles highlighting the automatically identified and tracked particles. (b) Confirmation of theoretical predictions by experimental data. Because the MSD is dependent on both the particle and the liquid, the data were fitted to a curve given by A(1-1/n) where n is the number of tracked particles and A is the measured MSD with an infinite number of tracked particles. In this case, A = 0.003895.
Comparisons of measured and literature viscosity values.
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