.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/analytical_poly_disperse.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_gallery_analytical_poly_disperse.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_analytical_poly_disperse.py:


Percus Yevick mixture solver workflow
=====================================

This example demonstrates the complete workflow for computing the radial
distribution function :math:`g_{ij}(r)` of a polydisperse hard sphere mixture
using a Percus Yevick style solver.

The example covers the following steps:

1. Define a polydisperse domain (radii, volume fraction, number fractions)
2. Build the Fourier grid :math:`p`
3. Construct the Percus Yevick solver
4. Compute :math:`C_{ij}(p)`, :math:`H_{ij}(p)`, :math:`h_{ij}(r)`, and :math:`g_{ij}(r)`
5. Plot all :math:`g_{ij}(r)` curves on a single figure

The main output is a figure showing all pair correlations :math:`g_{ij}(r)` for
each species pair :math:`(i, j)`.

.. GENERATED FROM PYTHON SOURCE LINES 21-80



.. image-sg:: /gallery/images/sphx_glr_analytical_poly_disperse_001.png
   :alt: Radial distribution functions
   :srcset: /gallery/images/sphx_glr_analytical_poly_disperse_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import numpy as np
    from PackLab import ureg
    from PackLab import analytical, samplers
    import matplotlib.pyplot as plt

    distribution = samplers.Normal(
        mean=1.5 * ureg.micrometer,
        standard_deviation=0.2 * ureg.micrometer,
        bins=6,
    )

    particle_radii, number_fractions = distribution.to_bins()

    domain = analytical.PYDomain(
        size=100 * ureg.micrometer,
        radii=particle_radii,
        volume_fraction=0.3,
        number_fractions=number_fractions,
    )

    domain.print_bins()

    spatial_frequency_max = 1e3 / domain.radii.min()

    spatial_frequency = np.linspace(0, spatial_frequency_max / 2, 30_000)

    solver = analytical.Solver(
        densities=domain.particle_densities_per_radius,
        radii=domain.radii,
        p=spatial_frequency,
    )

    distances = np.linspace(domain.radii.min() * 2, domain.radii.max() * 4, 1500)

    result = solver.compute(distances=distances)


    figure, ax = plt.subplots(1, 1)

    r = result.distances.magnitude
    n = result.g.shape[0]


    for i in range(n):
        for j in range(n):
            ax.plot(
                result.distances.magnitude,
                result.g[i, j, :],
                label=f"g[{i},{j}]"
            )

    ax.set_xlabel("r")
    ax.set_ylabel("g(r)")
    ax.set_title("Radial distribution functions")

    ax.legend()

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 31.660 seconds)


.. _sphx_glr_download_gallery_analytical_poly_disperse.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: analytical_poly_disperse.ipynb <analytical_poly_disperse.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: analytical_poly_disperse.py <analytical_poly_disperse.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: analytical_poly_disperse.zip <analytical_poly_disperse.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_