.. _sphx_glr_gallery_monte_carlo:

Monte-Carlo hard-sphere workflows
=================================

Examples that generate explicit random sequential adsorption configurations.
They cover the basic simulation setup, periodic boundary conditions, radius
distributions, visualisation, and pair-correlation estimates. The Metropolis
example starts from an RSA configuration but then uses a separate equilibrium
hard-sphere workflow with fixed particle count and radii.



.. raw:: html

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

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example creates a small periodic RSA packing from a uniform radius distribution. It then visualises a central two-dimensional slice of the accepted sphere configuration.">

.. only:: html

  .. image:: /gallery/monte_carlo/images/thumb/sphx_glr_01_minimal_rsa_thumb.png
    :alt:

  :doc:`/gallery/monte_carlo/01_minimal_rsa`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Minimal random sequential adsorption</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Periodic boundaries identify opposite faces of the simulation box. They are a good default when measuring bulk quantities because a sphere near one face interacts with spheres near the opposing face.">

.. only:: html

  .. image:: /gallery/monte_carlo/images/thumb/sphx_glr_02_periodic_boundaries_thumb.png
    :alt:

  :doc:`/gallery/monte_carlo/02_periodic_boundaries`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Periodic-boundary RSA packing</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Radius samplers are explicit physical inputs to an RSA simulation. Their to_bins method converts a continuous distribution into radius classes and number fractions for use by the analytical Percus--Yevick model.">

.. only:: html

  .. image:: /gallery/monte_carlo/images/thumb/sphx_glr_03_radius_samplers_thumb.png
    :alt:

  :doc:`/gallery/monte_carlo/03_radius_samplers`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Comparing radius samplers</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Random sequential addition (RSA) creates a valid hard-sphere packing, but it is irreversible and does not sample the equilibrium hard-sphere ensemble. This example uses that RSA configuration only as an initial state for single-particle Metropolis moves. The Metropolis sampler keeps every radius, class label, and the particle count fixed; it only changes sphere centres.">

.. only:: html

  .. image:: /gallery/monte_carlo/images/thumb/sphx_glr_04_metropolis_equilibration_thumb.png
    :alt:

  :doc:`/gallery/monte_carlo/04_metropolis_equilibration`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Equilibrating an RSA configuration with Metropolis moves</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the complete workflow of using PackLab to perform a Random Sequential Addition (RSA) simulation in three dimensions.">

.. only:: html

  .. image:: /gallery/monte_carlo/images/thumb/sphx_glr_monte_carlo_poly_disperse_thumb.png
    :alt:

  :doc:`/gallery/monte_carlo/monte_carlo_poly_disperse`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">A full workflow example with PackLab</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /gallery/monte_carlo/01_minimal_rsa
   /gallery/monte_carlo/02_periodic_boundaries
   /gallery/monte_carlo/03_radius_samplers
   /gallery/monte_carlo/04_metropolis_equilibration
   /gallery/monte_carlo/monte_carlo_poly_disperse