Effect of vibration in diffusion coefficient determination

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In [@catipovic2013Improving the quantification of Brownian motion], the authors added a drift of 200nm/s and vibrational noise with a standard deviation of 100nm to estimate whether it has any effect on the quality of the measurement of the diffusion coefficient. When calculating diffusion coefficient from jump statistics it gives a $D$ 11% larger, while Calculating diffusion coefficient from mean squared displacement data gives a $D$ 18% larger. When the drift is increased to around $1\mu m/s$ then the result can be off by a factor 10 or more!

Therefore, the most important source of uncertainty that people must consider is the drift, which is hard to remove if there is evaporation, or any other kind of fluid flow.

Regarding vibration, in [@ernst2013Measuring a diffusion coefficient by single-particle tracking: statistical analysis of experimental mean squared displacement curves], they observed that the residual vibration of their piezos was generating errors when calculating the mean squared displacement at the minimal time-delay, which forced them to disregard the data with the shortest time-delay.


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Aquiles Carattino
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