BOYER, Denis; DEAN, David S.; MEJÍA-MONASTERIO, Carlos; OSHANIN, Gleb

doi:10.1103/PhysRevE.85.031136

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BOYER, Denis
Instituto de Fisica

DEAN, David S.
Laboratoire Ondes et Matière d'Aquitaine [LOMA]

MEJÍA-MONASTERIO, Carlos
Laboratory of Physical Properties

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Physical Review E : Statistical, Nonlinear, and Soft Matter Physics. 2012, vol. 85, n° 3, p. 031136

American Physical Society

Résumé en anglais

Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way of extracting diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least squares estimate. Furthermore we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.< Réduire

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Brownian motion

Path-integral methods

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Optimal estimates of the diffusion coefficient of a single Brownian trajectory

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