Calculating diffusion coefficient from jump statistics
If we have a random process, such as when looking at Brownian Motion, we can look at the individual displacements $\Delta x$, and we'll get[@catipovic2013Improving the quantification of Brownian motion]
$$\textrm{Var}(\Delta x) = \left< \Delta x^2\right> - \left<\Delta x\right>^2$$
For standard Brownian processes, we also have $\left<\Delta x\right> = 0$
And from here, we have that the variance is equal to the mean-squared displacement, which can be re-written as the known equation:
$$\left<\Delta x^2\right> = 2Dt$$
In this case $t$ is the time between frames in the measurement (which is given as constant).
Backlinks
These are the other notes that link to this one.
Comment
Share your thoughts on this note. Comments are not public, they are
messages sent directly to my inbox.
Aquiles Carattino
This note you are reading is part
of my digital garden. Follow the
links to learn more, and remember that these notes evolve over time. After all,
this website is not a
blog.