Geometric buckling from neutron flux
====================================

Geometric buckling can be found if the neutron flux density is known as a function of
position. The smaller the reactor is, more "buckled" the curvature of the neutron flux
is and the higher geometric buckling of the reactor is.

**Links:**

#. `Wikipedia, see fourth equation <https://en.wikipedia.org/wiki/Geometric_and_material_buckling#Derivation>`__.

.. py:currentmodule:: symplyphysics.laws.nuclear.buckling.geometric_buckling_from_neutron_flux

.. py:data:: position

    :attr:`~symplyphysics.symbols.classical_mechanics.position`.

Symbol:
    :code:`x`

Latex:
    :math:`x`

Dimension:
    :code:`length`


.. py:data:: neutron_flux

    :attr:`~symplyphysics.symbols.nuclear.neutron_flux` as a function of :attr:`~position`

Symbol:
    :code:`Phi(x)`

Latex:
    :math:`\Phi{\left(x \right)}`

Dimension:
    :code:`1/(area*time)`


.. py:data:: geometric_buckling

    :attr:`~symplyphysics.symbols.nuclear.geometric_buckling`.

Symbol:
    :code:`B_g^2`

Latex:
    :math:`B_\text{g}^2`

Dimension:
    :code:`1/area`


.. py:data:: neutron_flux_laplacian

    Laplacian of the :attr:`~neutron_flux` as a function of :attr:`~position`.

Symbol:
    :code:`Laplace(Phi)(x)`

Latex:
    :math:`\nabla^{2} \Phi{\left(x \right)}`

Dimension:
    :code:`1/(length**4*time)`


.. py:data:: law

    :code:`B_g^2 = -Laplace(Phi)(x) / Phi(x)`


    Latex:
        .. math::
            B_\text{g}^2 = - \frac{\nabla^{2} \Phi{\left(x \right)}}{\Phi{\left(x \right)}}