CosineModel¶

class poreana.model.CosineModel(data_link, n_diff=6, n_df=10, n_diff_radial=6, d0=1.0, is_print=False, coeff=[])¶

This class sets the Cosine Model to calculate the free energy profile and the diffusion profile. The profiles have the typical cosine oscillation. These profiles over the bins are expressed by the following Fourier series. The diffusion profile is calculated between bin i and i+1 over the bin border with

\[\ln \left(D_{i+ \frac{1}{2}}\right)=a_{0}+\sum_{k=1}^{n_b} a_{k} \cdot \cos \left(\frac{2\pi ki}{n}\right).\]

Similarly, the free energy Fourier series can be written:

\[F_{i} = a_{0}+\sum_{k=1}^{n_b} a_{k} \cdot \cos \left(\frac{2\pi ki}{n} \right),\]

with the number of bins \(n\), the index of a bin \(i\), the coefficients \(a_{k}\) of the Fourier series and \(k\) as the number of coefficents. The free energy is calculated in the bin center.

For the free energy the coefficient it is assumed that \(a_{0} = 0\).

Parameters:

data_linkstring: Data link to the pickle data from poreana.sample.Sample.init_diffusion_mc()
n_diffinteger, optional: Number of the Fourier coefficients for the diffusion profile
n_dfinteger, optional: Number of the Fourier coefficients for the free energy profile
n_diff_radialinteger, optional: Number of the Fourier coefficients for the radial diffusion profile
d0double, optional: Initial guess of diffusion coefficient \(\left( 10^{-9} \frac{m^2}{s}\right)\)
is_printbool, optional: True to print output

Methods

`__class__`	alias of `type`
`__delattr__`(name, /)	Implement delattr(self, name).
`__dict__`
`__dir__`(/)	Default dir() implementation.
`__doc__`
`__eq__`(value, /)	Return self==value.
`__format__`(format_spec, /)	Default object formatter.
`__ge__`(value, /)	Return self>=value.
`__getattribute__`(name, /)	Return getattr(self, name).
`__gt__`(value, /)	Return self>value.
`__hash__`(/)	Return hash(self).
`__init__`(data_link[, n_diff, n_df, ...])
`__init_subclass__`	This method is called when a class is subclassed.
`__le__`(value, /)	Return self<=value.
`__lt__`(value, /)	Return self<value.
`__module__`
`__ne__`(value, /)	Return self!=value.
`__new__`(args, *kwargs)
`__reduce__`(/)	Helper for pickle.
`__reduce_ex__`(protocol, /)	Helper for pickle.
`__repr__`(/)	Return repr(self).
`__setattr__`(name, value, /)	Implement setattr(self, name, value).
`__sizeof__`(/)	Size of object in memory, in bytes.
`__str__`(/)	Return str(self).
`__subclasshook__`	Abstract classes can override this to customize issubclass().
`__weakref__`	list of weak references to the object (if defined)
`_calc_profile`(coeff, basis)	This function calculates the diffusion and free energy profile over the bins.
`_cosine_model`()	This function sets a Fourier Cosine Series Model for the MC Diffusion Calculation and determines the initialize profiles.
`_create_basis_border`()	This function creates the basis part in every bin of the Fourier series for the diffusion \(\ln \ (D)\).
`_create_basis_center`()	This function creates the basis part of the Fourier series for the free energy and the radial diffusion profile.
`_init_model`()	This function initializes the coefficient list for the Fourier series and the profile list for the free energy and diffusion profile.
`_init_profiles`()	This function initializes the normal diffusion, radial diffusion and free energy profile over the bins.