PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheoryExpAndBallistic_ISF

PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheoryExpAndBallistic_ISF

dTheoryExpAndBallistic_ISF(lagtime, tau1, s, tau2, a, Z)

Diffusive and ballistic motion

This model for the ISF can be used to fit dynamics where there is diffusive motion as well as ballistic motion. The ballistic component is assumed to follow a Schulz distribution of velocities. This model was shown to work for characterizing the motion of bacteria 1 .

Parameters

  • lagtime (array) – 1D array of the lag times

  • tau1 (float) – Characteristic decay time for the exponential term of the ISF

  • s (float) – Stretching exponent for exponential term

  • tau2 (float) – Characteristic decay time for ballistic component

  • a (float) – Fraction of the dynamics that are ballistic

  • Z (float) – Schulz distribution number

Returns

isf – The intermediate scattering function

Return type

array

References

1

Wilson, L. G. et al. Differential Dynamic Microscopy of Bacterial Motility. Phys. Rev. Lett. 106, 018101 (2011). https://doi.org/10.1103/PhysRevLett.106.018101

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