amep.spatialcor.sf2d#

amep.spatialcor.sf2d(coords: ndarray, box_boundary: ndarray, other_coords: ndarray | None = None, qmax: float = 20.0, njobs: int = 1, mode: str = 'std', Ntot: int | None = None, accuracy: float = 0.1, chunksize: int | None = None, verbose: bool = False) → tuple[ndarray, ndarray, ndarray]#

Calculates the 2d static structure factor.

Notes

The static structure factor is defined by

\[\begin{split}S(\vec{q}) = \frac{1}{N} \left\langle\sum_{j=1}^{N}\sum_{k=1}^{N}\exp\left\lbrace-i\vec{q}\cdot(\vec{r}_j-\vec{r}_k)\right\rbrace\right\rangle\\ = \frac{1}{N} \left\langle\sum_{j=1}^{N}\left\lvert\exp\left\lbrace-i\vec{q}\cdot\vec{r}_j\right\rbrace\right\rvert^2\right\rangle,\end{split}\]

where $rho(vec{q})$ is the Fourier transform of the particle number density (see Ref. [1] for further information).

S(0,0) is set to 0

References

Parameters:

coords (np.ndarray) – Coordinate frame (3D).
box_boundary (np.ndarray of shape (3,2)) – Boundary of the simulation box in the form of np.array([[xmin, xmax], [ymin, ymax], [zmin, zmax]]).
other_coords (np.ndarray, optional) – Coordinate frame of the other species to which the pair correlation is calculated. The default is None (uses coords).
qmax (float, optional) – Maximum wave number to consider. The default is 20.
njobs (int, optional) – Number of jobs used for parallel computation. The default is 4.
mode (str, optional) – Calculation method. Mode ‘fft’ converts the particle coordinates to a density field and uses the continuum method (FFT) to calculate the structure factor. Mode ‘std’ uses the particle coordinates directly, which is much slower. The default is ‘fft’.
Ntot (int, optional) – Total number of particles in the system. This value is needed for the correct normalization of the structure factor. If None, Ntot is calculated from coords. The default is None.
accuracy (float, optional) – Accuracy for fft mode. 0.0 means least accuracy, 1.0 best accuracy. The default is 0.1. Note that a higher accuracy needs more memory for the computation. accuracy must be in (0,1].
verbose (bool, optional) – If True, a progress bar is shown. The default is False.
chunksize (int or None, optional) – Divide calculation into chunks of this size. The default is None.

Returns:

np.ndarray – Two dimensional static structure factor.
np.ndarray – Wave vector’s x component.
np.ndarray – Wave vector’s y component.

Examples

>>> import amep
>>> traj = amep.load.traj("../examples/data/lammps.h5amep")
>>> frame = traj[-1]
>>> sxy, qx, qy = amep.spatialcor.sf2d(
...     frame.coords(), frame.box, verbose=True, mode='std', njobs=4
... )
>>> fig, axs = amep.plot.new(figsize=(3.7,3))
>>> mp = amep.plot.field(axs, sxy, qx, qy)
>>> cax = amep.plot.add_colorbar(
...     fig, axs, mp, label=r'$S(q_x, q_y$'
... )
>>> axs.set_xlabel(r'$q_x$')
>>> axs.set_ylabel(r'$q_y$')
>>> fig.savefig('./figures/spatialcor/spatialcor-sf2d.png')
>>>