mc_fit¶

poreana.diffusion.mc_fit(link, len_step=[], section=[], is_std=False, is_print=True, is_plot=True, kwargs_scatter={}, kwargs_line={})¶

This function uses the diffusion profiles over box length which are calculated in the function poreana.mc.MC.run() to estimate the final diffusion coefficient. For that a line is fitted of the averaged diffusion profiles \(D_{\mathrm{mean}}({\Delta t_{\alpha}})\) for the different lag times as a function of \(1/\Delta t_{\alpha}\). The function plots all mean diffusion \(D_\mathrm{mean}({\Delta t_{\alpha}})\) over the inverse lag times and the linear fit. Additionally, the final diffusion coefficient \(D\) for a lag time \(\Delta t_{\alpha} \rightarrow \infty\) is printed. Also, a table of the selected step length and the belonging \(D_{\mathrm{mean}}({\Delta t_{\alpha}})\) can be displayed.

In order to be able to estimate how the choice of lag times affects the result, an additional error estimation is possible. For this all possible fourth tuples of the entire calculated lag times are used to estimate a mean diffusion coefficient \(\langle D \rangle\) which is the mean value of all fourth tuples fitting results. Also, the standard deviation of all fitting results is printed. If there is no big difference between the diffusion coefficient \(D\) and the mean diffusion coefficient \(\langle D \rangle\), all \(D_\mathrm{mean}({\Delta t_{\alpha}})\) are on a straight line. The standard deviation also can be used to check if the result fluctuates strongly at the choice of other lag times. This error estimate is calculated if \(\mathrm{is}\_{\mathrm{std}}=True\).

Parameters:

link: string: Link to the diffusion hdf5 data file generated by the MC Alogrithm poreana.mc.MC.run()
len_step: integer, list, optional: List of the different step length, if it is [] all calculated lag times will be used to fit the diffusion coefficent
sectionlist, string, optional: If \(\mathrm{section} = \mathrm{"pore"}\) the pore section is fitted. If \(\mathrm{section} = \mathrm{"reservoir"}\) the left reservoir area is fitted. If \(\mathrm{section} = \mathrm{[a,b]}\) the box area between a and b is fitted.
is_stdbool, optional: True to calculate a mean diffusion coefficient to assess the dependency of the result on the selected lag time
is_printbool, optional: Print diffusion coefficient
is_plotbool, optional: Show the fitting plot
kwargs_scatter: dict, optional: Dictionary with plotting parameters for the points
kwargs_line: dict, optional: Dictionary with plotting parameters for the fitting line

Returns:

diffusion: float: Diffusion coefficient \(D \ \left( 10^{-9} \frac{m^2}{s}\right)\) for the calculated system
diffusion_mean: float: Mean diffusion coefficient \(\langle D \rangle \ \left(10^{-9} \frac{m^2}{s}\right)\) for the calculated system
diff_tableobj: Table of used lag times with the associated \(D_{\mathrm{mean}}({\Delta t_{\alpha}}) \ \left(10^{-9} \frac{m^2}{s}\right)\)
resfloat: error of intercept \(\left(10^{-9} \frac{m^2}{s}\right)\) for fitting the selected lag times