PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheorySingleExp_DDM
PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheorySingleExp_DDM¶
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dTheorySingleExp_DDM(lagtime, amplitude, tau, bg, s=1.0)¶ Theoretical model for the DDM matrix with one exponential term
- Parameters
lagtime (array) – 1D array of the lagtimes
amplitude (float) – Amplitude, “A” in equation below
tau (float) – The characteristic decay time
bg (float) – Background term, “B” in equation below
s (float) – Stretching exponent
- Returns
ddm_matrix – DDM matrix as shown in equation below
- Return type
array
Notes
This model assumes a single exponential for the intermediate scattering function. This is often used with diffusive or ballistic motion. If the dynamics are subdiffusive, the stretching exponent may be less than 1.
\[\begin{split}f(q, \Delta t) = e^{\left( \frac{-\Delta t}{\tau}\right)^{s}} \\ D(q, \Delta t) = A \times (1-f(q, \Delta t)) + B\end{split}\]