pybilt.diffusion package¶
Submodules¶
pybilt.diffusion.diffusion_coefficients module¶
Estimate self diffusion coefficients from MSD(t) data.
This module provides a set of functions to estimate self diffusion coefficients from mean squared displacement (MSD) time trajectories.
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pybilt.diffusion.diffusion_coefficients.diffusion_coefficient_Einstein(times, msd_vals, dim=2, time_range=None)[source]¶ Estimate diffusion coefficient from MSD(t) via Einstein relation.
A function to estimate the diffusion constant from a mean squared displacement time series. This function uses the long time mean squared displacement approximation (Einstein relation):
MSD = lim_(t->inf) <||r_i(t) - r_i(0)||**2>_(nsels) = 2*dim*D*t
where D is the diffusion coefficient.
- Parameters
times (numpy.array) – Array of the simulation times of each MSD point.
msd_vals (numpy.array) – Array of the MSD values.
dim (Optional[int]) – Set the dimension of the data and fit function: 1 for 1-dimensional , 2 for 2-dimensional, or 3 for 3-dimensional. Defaults to 2.
time_range (Optional[list]) – Specify a time range via a list with format [time_start, time_end]; the range should be given in the same units as the time data in the Arg times. Defaults to None, which uses the whole time range in Args times.
- Returns
The value of the diffusion coefficient.
- Return type
float
References
- Preston B. Moore, Carlos F. Lopez, Michael L. Klein, Dynamical
Properties of a Hydrated Lipid Bilayer from a Multinanosecond Molecular Dynamics Simulation, Biophysical Journal, Volume 81, Issue 5, 2001, Pages 2484-2494, ISSN 0006-3495, http://dx.doi.org/10.1016/S0006-3495(01)75894-8. (http://www.sciencedirect.com/science/article/pii/S0006349501758948)
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pybilt.diffusion.diffusion_coefficients.diffusion_coefficient_anomalous_fit(times, msd_vals, dim=2, time_range=None)[source]¶ Fit MSD time series data to an anomalous diffusion model.
- The anomalous diffusion function has the form:
MSD(t) = 2 * dim * D_alpha * t**alpha
For alpha values 0 < alpha < 1 corresponds to subdiffusion, while 1 < alpha < 2 corresponds to superdiffusion.
- Parameters
times (numpy.array) – Array of the simulation times of each MSD point.
msd_vals (numpy.array) – Array of the MSD values.
dim (Optional[int]) – Set the dimension of the data and fit function: 1 for 1-dimensional , 2 for 2-dimensional, or 3 for 3-dimensional. Defaults to 2.
time_range (Optional[list]) – Specify a time range via a list with format [time_start, time_end]; the range should be given in the same units as the time data in the Arg times. Defaults to None, which uses the whole time range in Args times.
- Returns
The return is a tuple with values (D_alpha, alpha) where D_alpha is the anomalous diffusion coefficent and alpha is the anomalous diffusion power.
- Return type
tuple
References
- Gerald R. Kneller, Krzysztof Baczynski, and Marta
Pasenkiewicz-Gierula, Consistent picture of lateral subdiffusion in lipid bilayers: Molecular dynamics simulation and exact results, The Journal of Chemical Physics 135, 141105 (2011); doi: http://dx.doi.org/10.1063/1.3651800
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pybilt.diffusion.diffusion_coefficients.diffusion_coefficient_linear_fit(times, msd_vals, dim=2, time_range=None)[source]¶ Estimate the diffusion coefficent via linear least squares fit of MSD(t) data.
- Assumes the MSD data has the linear form,
MSD(t) = 2*dim*D*t ,
and uses a linear least squares fit to estimate the diffusion coefficent D.
- Parameters
times (numpy.array) – Array of the simulation times of each MSD point.
msd_vals (numpy.array) – Array of the MSD values.
dim (Optional[int]) – Set the dimension of the data and fit function: 1 for 1-dimensional , 2 for 2-dimensional, or 3 for 3-dimensional. Defaults to 2.
time_range (Optional[list]) – Specify a time range via a list with format [time_start, time_end]; the range should be given in the same units as the time data in the Arg times. Defaults to None, which uses the whole time range in Args times.
- Returns
Returns a tuple with format (D, Error_D), where D is the estimated diffusion coefficent and Error_D is the estimated error for D.
- Return type
tuple
References
- Preston B. Moore, Carlos F. Lopez, Michael L. Klein, Dynamical
Properties of a Hydrated Lipid Bilayer from a Multinanosecond Molecular Dynamics Simulation, Biophysical Journal, Volume 81, Issue 5, 2001, Pages 2484-2494, ISSN 0006-3495; http://dx.doi.org/10.1016/S0006-3495(01)75894-8 (http://www.sciencedirect.com/science/article/pii/S0006349501758948)