Calculation of time-dependent orientation correlation and MSDs of moving cells
We computed the average temporal correlation as follows:\(\left\langle\cos{\theta}\right\rangle\left(t\right)\equiv\left\langle\hat{\mathbf{v}}\left(t+t\right)\bullet\hat{\mathbf{v}}\left(t\right)\right\rangle\), where \(\hat{\mathbf{v}}\) is the unit vector of velocity and calculated the mean square displacement via\(\text{MSD}(t)=\left\langle\left|\mathbf{r}\left(t+t\right)-\mathbf{r}(t)\right|^{2}\right\rangle\).
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