PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheorySingleExp_ISF
PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheorySingleExp_ISF¶
-
dTheorySingleExp_ISF(lagtime, tau, s)¶ Theoretical model for the DDM matrix with one exponential term
- Parameters
lagtime (array) – 1D array of the lagtimes
tau (float) – The characteristic decay time
s (float) – Stretching exponent
- Returns
ISF – 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.
If we use this model to fit our DDM data, we must be able to estimate the amplitude and background terms.
\[\begin{split}\\ f(q, \Delta t) = e^{\left( \frac{-\Delta t}{\tau}\right)^{s}}\end{split}\]