PyDDM.ddm_analysis_and_fitting.newt

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PyDDM.ddm_analysis_and_fitting.newt#

newt(t, s)#

This function is used to determine a new time when a distribution of decay times are present. The new time is the average over all the decay times.

Parameters:

  • t (float) – Decay time (seconds), e.g. tau

  • s (float) – Stretching exponent

Returns:

  • newt (float)- New, average decay time (seconds)

Theory

\[\langle \tau \rangle = \int_{0}^{\infty} e^{\left( \frac{-\Delta t}{\tau}\right)^{s}} \,d \Delta t = \frac{1}{s} \Gamma \left( \frac{1}{s} \right) \tau\]
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