PyDDM.ddm_calc.get_MSD_from_DDM_data
PyDDM.ddm_calc.get_MSD_from_DDM_data¶
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get_MSD_from_DDM_data(q, A, D, B, qrange_to_avg)¶ Finds the mean squared displacement (MSD) from the DDM matrix as well as values for the amplitude (A) and background (B). Uses the method described in the papers below. 1 2
\[MSD(\Delta t) = \frac{4}{q^2} \ln \left[ \frac{A(q)}{A(q)-D(q,\Delta t)+B(q)} \right]\]- Parameters
q (array) – 1D array of the magnitudes of wavevectors
A (array) – Array of same size as q of the amplitude
D (array) – 2D array containing the DDM matrix
B (array or float) – Background
qrange_to_avg (array_like) – 2-element array or list.
- Returns
msd_mean (array) – Mean squared displacment, averaged over the range of q values specified
msd_stddev (array) – Standard deviation of the mean squared displacements
References
- 1
Bayles, A. V., Squires, T. M. & Helgeson, M. E. Probe microrheology without particle tracking by differential dynamic microscopy. Rheol Acta 56, 863–869 (2017).
- 2
Edera, P., Bergamini, D., Trappe, V., Giavazzi, F. & Cerbino, R. Differential dynamic microscopy microrheology of soft materials: A tracking-free determination of the frequency-dependent loss and storage moduli. Phys. Rev. Materials 1, 073804 (2017).