Fitting a time averaged MSD with various maximum time lags.

Abstract

<p>A trajectory with <i>α</i> = 0.7, <i>L</i> = 2<sup>9</sup>, <i>σ</i> = 0.5 was simulated (black squares) and fitted for various <i>τ</i><sub><i>M</i></sub> values. While the small <i>τ</i><sub><i>M</i></sub> fitting (red <i>τ</i><sub><i>M</i></sub> = 10 and blue <i>τ</i><sub><i>M</i></sub> = 50) underestimated <i>α</i>, the large <i>τ</i><sub><i>M</i></sub> (green <i>τ</i><sub><i>M</i></sub> = 150) gives an overestimation. Clearly, selecting the optimal <i>τ</i><sub><i>M</i></sub> value is not trivial as both small and large values may lead to erroneous results. Graphically assessing the quality of the fit does not help select the best <i>τ</i><sub><i>M</i></sub> either.</p

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