diff --git a/docs/source/methods/index.rst b/docs/source/methods/index.rst index 85e4229d2..947c4b9a1 100644 --- a/docs/source/methods/index.rst +++ b/docs/source/methods/index.rst @@ -7,3 +7,22 @@ Methodology The OpenMC code solves the neutron transport equation using the Monte Carlo method whereby particles are tracked as they randomly move through a geometry, undergoing collisions, and creating secondary particles. + +------------------- +Reflective Surfaces +------------------- + +In general, a surface can be written in the form :math:`f(x,y,z) = 0`. If a +neutron is traveling in direction :math:`\vec{v}` and crosses a reflective +surface of the above form, it can be shown that the velocity vector will then +become + +.. math:: + + \mathbf{v'} = \mathbf{v} - 2 (\mathbf{v} \cdot \hat{\mathbf{n}}) + \hat{\mathbf{n}} + +where :math:`\hat{\mathbf{n}}` is a unit vector normal to the surface at the +point of the surface crossing. The direction of the surface normal will be the +gradient to the surface at the point of crossing, i.e. :math:`\mathbf{n} = +\nabla f(x,y,z)`. diff --git a/docs/source/usersguide/input.rst b/docs/source/usersguide/input.rst index 917a834e5..96e7499cc 100644 --- a/docs/source/usersguide/input.rst +++ b/docs/source/usersguide/input.rst @@ -50,40 +50,40 @@ Geometry Specification -- geometry.xml Types of surfaces: -x-plane - A plane perpendicular to the x axis, i.e. a surface of the form x - x0 - = 0. The coefficients specified are "x0". +``x-plane`` + A plane perpendicular to the x axis, i.e. a surface of the form :math:`x - x_0 + = 0`. The coefficients specified are ":math:`x_0`". -y-plane - A plane perpendicular to the y axis, i.e. a surface of the form y - y0 - = 0. The coefficients specified are "y0". +``y-plane`` + A plane perpendicular to the y axis, i.e. a surface of the form :math:`y - y_0 + = 0`. The coefficients specified are ":math:`y_0`". -z-plane - A plane perpendicular to the z axis, i.e. a surface of the form z - z0 - = 0. The coefficients specified are "z0". +``z-plane`` + A plane perpendicular to the z axis, i.e. a surface of the form :math:`z - z_0 + = 0`. The coefficients specified are ":math:`z_0`". -plane - An arbitrary plane of the form A*x + B*y + C*z = D. The coefficients - specified are "A B C D". +``plane`` + An arbitrary plane of the form :math:`Ax + By + Cz = D`. The coefficients + specified are ":math:`A \: B \: C \: D`". -x-cylinder +``x-cylinder`` An infinite cylinder whose length is paralle to the x-axis. This is a - quadratic surface of the form (y - y0)^2 + (z - z0)^2 = R^2. The coefficients - specified are "y0 z0 R". + quadratic surface of the form :math:`(y - y_0)^2 + (z - z_0)^2 = R^2`. The + coefficients specified are ":math:`y_0 \: z_0 \: R`". -y-cylinder +``y-cylinder`` An infinite cylinder whose length is paralle to the y-axis. This is a - quadratic surface of the form (x - x0)^2 + (z - z0)^2 = R^2. The coefficients - specified are "x0 z0 R". + quadratic surface of the form :math:`(x - x_0)^2 + (z - z_0)^2 = R^2`. The + coefficients specified are ":math:`x_0 \: z_0 \: R`". -z-cylinder +``z-cylinder`` An infinite cylinder whose length is paralle to the z-axis. This is a - quadratic surface of the form (x - x0)^2 + (y - y0)^2 = R^2. The coefficients - specified are "x0 y0 R". + quadratic surface of the form :math:`(x - x_0)^2 + (y - y_0)^2 = R^2`. The + coefficients specified are ":math:`x_0 \: y_0 \: R`". -sphere - A sphere of the form (x - x0)^2 + (y - y0)^2 + (z - z0)^2 = R^2. The - coefficients specified are "x0 y0 z0 R". +``sphere`` + A sphere of the form :math:`(x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 = + R^2`. The coefficients specified are ":math:`x_0 \: y_0 \: z_0 \: R`". ---------------------------------------- Materials Specification -- materials.xml