PyDDM.ddm_calc.get_MSD_from_DDM_data

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).