PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheoryPolydisperse_DDM
PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheoryPolydisperse_DDM¶
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dTheoryPolydisperse_DDM(lagtime, amplitude, tau, mu, bg)¶ Theoretical model for the DDM matrix to account for polydisperisty
- Parameters
lagtime (array) – 1D array of the lagtimes
amplitude (float) – Amplitude, “A” in equation below
tau (float) – The characteristic decay time
mu (float) – To account for polydispersity
bg (float) – Background term, “B” in equation below
- Returns
ddm_matrix – DDM matrix as shown in equation below
- Return type
array
Notes
This model is used when polydispersity is present.
\[D(q,\Delta t) = A(q) \left[ 1 - \exp \left( -\frac{\Delta t}{\tau(q)} \right) \left( 1 + \frac{\mu \tau^2}{2} \right) \right] + B(q)\]