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add more details in documentation of geometry

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Jiankai Yu 2019-09-15 16:57:07 -04:00
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docs/source/methods/geometry.rst
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@ -901,8 +901,39 @@ Dxy + Eyz + Fxz + Gx + Hy + Jz + K = 0`. Thus, the gradient to the surface is
------------------------------
White Boundary Conditions
------------------------------
The white boundary condition is usually applied in deterministic code, where the particle
will hit the surface and travel back with isotropic angular distribution. Essentially, the
change of particle's direction will comply to the cosine distribution instead of uniform
distribution.
The probability distribution function (pdf) for the reflected direction can be expressed
as follows,
.. math::
: label: white-reflection-pdf
where mu is the cosine of the polar angle between reflected direction and the normal to the
surface; and theta is the azimuthal angle.
Thus, the cosine of the polar angle can extracted like this,
.. math::
: label: white-reflection-cosine
and the azimuthal angle is uniform in the range of 2*PI,
.. math::
: label: white-reflection-unifrm
Then, cosine can be obtained by analytical inversion of cumulative probability distribution (cdf)
like this,
.. math::
: label: white-reflection-sqrt-prn
Eventually, the final reflected direction vector can be computed via the rotation of normal to
the surface like this,
.. math::
: label: white-reflection-rotation
The white boundary condition can apply to any kind of surface, as long as the normal to the surface
is known as mentioned above in :ref:`reflection`.
.. _constructive solid geometry: http://en.wikipedia.org/wiki/Constructive_solid_geometry
.. _surfaces: http://en.wikipedia.org/wiki/Surface
.. _MCNP: http://mcnp.lanl.gov