.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/validation/percus_yevick_vs_tsang_2001.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_gallery_validation_percus_yevick_vs_tsang_2001.py>`
        to download the full example code.

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

.. _sphx_glr_gallery_validation_percus_yevick_vs_tsang_2001.py:


PackLab Percus--Yevick versus the Tsang et al. reference
=========================================================

This validation example compares PackLab's Percus--Yevick (PY) solution for a
binary hard-sphere mixture with manually digitised PY curves from Figure 8.3.4
of Tsang, Kong, Ding, and Ao (2001).  The book uses radii
:math:`a_2 = 2a_1`, partial volume fractions :math:`f_1=0.2` and
:math:`f_2=0.1`, and reduced separation :math:`r/(2a_1)`.

The digitised values originate from a printed figure, rather than the source
numerical data, so this is a visual reference comparison rather than a
high-precision error benchmark.

.. GENERATED FROM PYTHON SOURCE LINES 15-26

.. code-block:: Python


    import os
    from pathlib import Path

    import matplotlib.pyplot as plt
    from matplotlib.lines import Line2D
    import numpy as np

    from PackLab import analytical, ureg









.. GENERATED FROM PYTHON SOURCE LINES 27-29

Load the digitised reference data
---------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 29-44

.. code-block:: Python


    if "PACKLAB_DOCS_ROOT" in os.environ:
        docs_root = Path(os.environ["PACKLAB_DOCS_ROOT"])
    else:
        docs_root = Path(__file__).resolve().parents[2]
    data_path = (
        docs_root
        / "manuscript"
        / "softwareX"
        / "data"
        / "tsang_2001_figure_8_3_4_digitized.csv"
    )
    digitized = np.genfromtxt(data_path, delimiter=",", names=True, dtype=None, encoding="utf-8")









.. GENERATED FROM PYTHON SOURCE LINES 45-47

Match the mixture and calculate PackLab's PY solution
------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 47-70

.. code-block:: Python


    radii = np.array([1.0, 2.0]) * ureg.micrometer
    partial_volume_fractions = np.array([0.2, 0.1])

    # The book reports partial *volume* fractions. Convert them to the number
    # fractions required by the mixture solver, n_i proportional to f_i/a_i^3.
    number_fractions = partial_volume_fractions / radii.to("micrometer").magnitude**3
    number_fractions /= number_fractions.sum()

    domain = analytical.PercusYevickDomain(
        size=100_000 * ureg.micrometer,
        radii=radii,
        volume_fraction=partial_volume_fractions.sum(),
        number_fractions=number_fractions,
    )
    reduced_separation = np.linspace(0.0, 5.0, 500)
    result = analytical.PercusYevickSolver(
        densities=domain.particle_densities_per_radius,
        radii=domain.radii,
        wavenumber="auto",
    ).compute(reduced_separation * 2.0 * radii[0])









.. GENERATED FROM PYTHON SOURCE LINES 71-73

Compare all three partial correlations
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 73-125

.. code-block:: Python


    figure, axis = plt.subplots(figsize=(8, 4.5))
    curves = (
        (r"$g_{11}$", "g11", (0, 0), "C0", "-.", "^"),
        (r"$g_{12}$", "g12", (0, 1), "C1", "--", "s"),
        (r"$g_{22}$", "g22", (1, 1), "C4", "-", "o"),
    )

    for label, component_pair, indices, colour, line_style, marker in curves:
        _ = axis.plot(
            reduced_separation,
            result.g[indices],
            color=colour,
            linestyle=line_style,
            linewidth=2,
        )
        reference = digitized[digitized["component_pair"] == component_pair]
        _ = axis.plot(
            reference["reduced_separation"],
            reference["g_ij"],
            linestyle="none",
            marker=marker,
            markersize=4.5,
            markerfacecolor="white",
            markeredgecolor="black",
            markeredgewidth=0.9,
        )

    _ = axis.axhline(1.0, color="0.65", linestyle=":", linewidth=1)
    _ = axis.set(
        xlim=(0.0, 5.0),
        ylim=(0.0, 3.5),
        xlabel=r"reduced separation $r/(2a_1)$",
        ylabel=r"partial correlation $g_{ij}(r)$",
        title="PackLab and digitised Tsang et al. PY reference",
    )
    axis.grid(alpha=0.2)
    _ = axis.legend(
        handles=[
            Line2D([], [], color=colour, linestyle=line_style, label=f"PackLab {label}")
            for label, _, _, colour, line_style, _ in curves
        ]
        + [
            Line2D(
                [], [], color="black", linestyle="none", marker="o", markerfacecolor="white",
                label="digitised Tsang PY",
            )
        ],
        ncol=2,
    )
    figure.tight_layout()
    plt.show()



.. image-sg:: /gallery/validation/images/sphx_glr_percus_yevick_vs_tsang_2001_001.png
   :alt: PackLab and digitised Tsang et al. PY reference
   :srcset: /gallery/validation/images/sphx_glr_percus_yevick_vs_tsang_2001_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.201 seconds)


.. _sphx_glr_download_gallery_validation_percus_yevick_vs_tsang_2001.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: percus_yevick_vs_tsang_2001.ipynb <percus_yevick_vs_tsang_2001.ipynb>`

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

      :download:`Download Python source code: percus_yevick_vs_tsang_2001.py <percus_yevick_vs_tsang_2001.py>`

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

      :download:`Download zipped: percus_yevick_vs_tsang_2001.zip <percus_yevick_vs_tsang_2001.zip>`


.. only:: html

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

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