.. _sphx_glr_gallery_analytical:

Analytical models
=================

Examples that solve the Percus--Yevick hard-sphere model directly. The
scattering workflow builds on this result and requires the optional
``packlab[scattering]`` installation extra.



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how the radial distribution function of an equilibrium hard-sphere fluid changes with volume fraction.  At higher density, the first neighbour shell becomes more pronounced.  Each curve is an independent Percus--Yevick calculation; it is not an RSA packing trajectory.">

.. only:: html

  .. image:: /gallery/analytical/images/thumb/sphx_glr_01_monodisperse_volume_fraction_thumb.png
    :alt:

  :doc:`/gallery/analytical/01_monodisperse_volume_fraction`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Monodisperse Percus--Yevick fluid at several densities</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Evaluate the three distinct partial pair correlations of a binary hard-sphere mixture.  The hard-core cutoffs occur at the corresponding contact distances 2a_1, a_1+a_2, and 2a_2.">

.. only:: html

  .. image:: /gallery/analytical/images/thumb/sphx_glr_02_binary_mixture_pair_correlations_thumb.png
    :alt:

  :doc:`/gallery/analytical/02_binary_mixture_pair_correlations`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Binary-mixture Percus--Yevick pair correlations</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the complete workflow for computing the radial distribution function g_{ij}(r) of a polydisperse hard sphere mixture using a Percus Yevick style solver.">

.. only:: html

  .. image:: /gallery/analytical/images/thumb/sphx_glr_analytical_poly_disperse_thumb.png
    :alt:

  :doc:`/gallery/analytical/analytical_poly_disperse`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Percus Yevick mixture solver workflow</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of Percus Yevick structure factor computation for a polydisperse mixture and corresponding phase function calculation.">

.. only:: html

  .. image:: /gallery/analytical/images/thumb/sphx_glr_scattering_thumb.png
    :alt:

  :doc:`/gallery/analytical/scattering`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Scattering Example: Percus Yevick Structure Factor and Phase Function</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /gallery/analytical/01_monodisperse_volume_fraction
   /gallery/analytical/02_binary_mixture_pair_correlations
   /gallery/analytical/analytical_poly_disperse
   /gallery/analytical/scattering