Add derivations in geometry section. Update publications.

docs/source/methods/geometry.rst

@@ -265,6 +265,8 @@ Again, we need to check whether the denominator is zero. If so, this means that
 the particle's direction of flight is parallel to the plane and it will
 therefore never hit the plane.
 
+.. _cylinder_distance:
+
 Cylinder Parallel to an Axis
 ----------------------------
 
@@ -366,7 +368,74 @@ will then be either both positive or both negative. If they are both positive,
 the smaller (closer) one will be the solution with a negative sign on the square
 root of the discriminant.
 
-.. TODO: Need to add derivation for x-cone, y-cone, and z-cone.
+Cone Parallel to an Axis
+------------------------
+
+The equation for a cone parallel to, for example, the x-axis is :math:`(y -
+y_0)^2 + (z - z_0)^2 = R^2(x - x_0)^2`. Thus, we need to solve :math:`(y + dv -
+y_0)^2 + (z + dw - z_0)^2 = R^2(x + du - x_0)^2`. Let us define :math:`\bar{x} =
+x - x_0`, :math:`\bar{y} = y - y_0`, and :math:`\bar{z} = z - z_0`. We then have
+
+.. math::
+    :label: dist-xcone-1
+
+    (\bar{y} + dv)^2 + (\bar{z} + dw)^2 = R^2(\bar{x} + du)^2
+
+Expanding equation :eq:`dist-xcone-1` and rearranging terms, we obtain
+
+.. math::
+    :label: dist-xcylinder-2
+
+    (v^2 + w^2 - R^2u^2) d^2 + 2 (\bar{y}v + \bar{z}w - R^2\bar{x}u) d +
+    (\bar{y}^2 + \bar{z}^2 - R^2\bar{x}^2) = 0
+
+Defining the terms
+
+.. math::
+    :label: dist-quadric-terms
+
+    a = v^2 + w^2 - R^2u^2
+
+    k = \bar{y}v + \bar{z}w - R^2\bar{x}u
+
+    c = \bar{y}^2 + \bar{z}^2 - R^2\bar{x}^2
+
+we then have the simple quadratic equation :math:`ad^2 + 2kd + c = 0` which can
+be solved as described in :ref:`cylinder_distance`.
+
+General Quadric
+---------------
+
+The equation for a general quadric surface is :math:`Ax^2 + By^2 + Cz^2 + Dxy +
+Eyz + Fxz + Gx + Hy + Jz + K = 0`. Thus, we need to solve the equation
+
+.. math::
+    :label: dist-quadric-1
+
+    A(x+du)^2 + B(y+dv)^2 + C(z+dw)^2 + D(x+du)(y+dv) + E(y+dv)(z+dw) + \\
+    F(x+du)(z+dw) + G(x+du) + H(y+dv) + J(z+dw) + K = 0
+
+Expanding equation :eq:`dist-quadric-1` and rearranging terms, we obtain
+
+.. math::
+    :label: dist-quadric-2
+
+    d^2(uv + vw + uw) + 2d(Aux + Bvy + Cwx + (D(uv + vx) + E(vz + wy) + \\
+    F(wx + uz))/2) + (x(Ax + Dy) + y(By + Ez) + z(Cz + Fx)) = 0
+
+Defining the terms
+
+.. math::
+    :label: dist-quadric-terms
+
+    a = uv + vw + uw
+
+    k = Aux + Bvy + Cwx + (D(uv + vx) + E(vz + wy) + F(wx + uz))/2
+
+    c = x(Ax + Dy) + y(By + Ez) + z(Cz + Fx)
+
+we then have the simple quadratic equation :math:`ad^2 + 2kd + c = 0` which can
+be solved as described in :ref:`cylinder_distance`.
 
 .. _find-cell:
 
@@ -810,6 +879,18 @@ form of the solution:
 
     w' = w + \frac{2 (\bar{x}u + \bar{y}v - R^2\bar{z}w)}{R^2 (1 + R^2) \bar{z}}
 
+General Quadric
+---------------
+
+A general quadric surface has the form :math:`f(x,y,z) = Ax^2 + By^2 + Cz^2 +
+Dxy + Eyz + Fxz + Gx + Hy + Jz + K = 0`. Thus, the gradient to the surface is
+
+.. math::
+    :label: reflection-quadric-grad
+
+    \nabla f = \left ( \begin{array}{c} 2Ax + Dy + Fz + G \\ 2By + Dx + Ez + H
+    \\ 2Cz + Ey + Fx + J \end{array} \right ).
+
 
 .. _constructive solid geometry: http://en.wikipedia.org/wiki/Constructive_solid_geometry
 .. _surfaces: http://en.wikipedia.org/wiki/Surface

docs/source/publications.rst

@@ -53,6 +53,16 @@ Benchmarking
 Coupling and Multi-physics
 --------------------------
 
+- Matthew Ellis, Benoit Forget, Kord Smith, and Derek Gaston, "Continuous
+  Temperature Representation in Coupled OpenMC/MOOSE Simulations," *Proc. PHYSOR
+  2016*, Sun Valley, Idaho, May 1-5, 2016.
+
+- Antonios G. Mylonakis, Melpomeni Varvayanni, and Nicolas Catsaros,
+  "Investigating a Matrix-free, Newton-based, Neutron-Monte
+  Carlo/Thermal-Hydraulic Coupling Scheme", *Proc. Int. Conf. Nuclear Energy for
+  New Europe*, Portoroz, Slovenia, Sep .14-17
+  (2015). `<https://www.researchgate.net/publication/282001032>`_
+
 - Matt Ellis, Benoit Forget, Kord Smith, and Derek Gaston, "Preliminary coupling
   of the Monte Carlo code OpenMC and the Multiphysics Object-Oriented Simulation
   Environment (MOOSE) for analyzing Doppler feedback in Monte Carlo
@@ -80,8 +90,17 @@ Geometry
 Miscellaneous
 -------------
 
+- Yunzhao Li, Qingming He, Liangzhi Cao, Hongchun Wu, and Tiejun Zu, "Resonance
+  Elastic Scattering and Interference Effects Treatments in Subgroup Method,"
+  *Nucl. Eng. Tech.*, **48**, 339-350
+  (2016). `<http://dx.doi.org/10.1016/j.net.2015.12.015>`_
+
 - William Boyd, Sterling Harper, and Paul K. Romano, "Equipping OpenMC for the
-  big data era," Accepted, *PHYSOR 2016*, Sun Valley, Idaho, May 1-5, 2016.
+  big data era," *Proc. PHYSOR*, Sun Valley, Idaho, May 1-5, 2016.
+
+- Michal Kostal, Vojtech Rypar, Jan Milcak, Vlastimil Juricek, Evzen Losa,
+  Benoit Forget, and Sterling Harper, *Ann. Nucl. Energy*, **87**, 601-611
+  (2016). `<http://dx.doi.org/10.1016/j.anucene.2015.10.010>`_
 
 - Qicang Shen, William Boyd, Benoit Forget, and Kord Smith, "Tally precision
   triggers for the OpenMC Monte Carlo code," *Trans. Am. Nucl. Soc.*, **112**,
@@ -95,6 +114,11 @@ Miscellaneous
 Multi-group Cross Section Generation
 ------------------------------------
 
+- Zhaoyuan Liu, Kord Smith, and Benoit Forget, "A Cumulative Migration Method
+  for Computing Rigorous Transport Cross Sections and Diffusion Coefficients for
+  LWR Lattices with Monte Carlo," *Proc. PHYSOR*, Sun Valley, Idaho, May
+  1-5, 2016.
+
 - Adam G. Nelson and William R. Martin, "Improved Monte Carlo tallying of
   multi-group scattering moments using the NDPP code," *Trans. Am. Nucl. Soc.*,
   **113**, 645-648 (2015)
@@ -108,18 +132,43 @@ Multi-group Cross Section Generation
   Computational Methods Applied to Nuclear Science and Engineering*, Sun Valley,
   Idaho, May 5--9 (2013).
 
-------------
-Nuclear Data
-------------
+
+------------------
+Doppler Broadening
+------------------
 
 - Colin Josey, Pablo Ducru, Benoit Forget, and Kord Smith, "Windowed multipole
-  for cross section Doppler broadening," *J. Comput. Phys.*, In Press
+  for cross section Doppler broadening," *J. Comput. Phys.*, **307**, 715-727
   (2016). `<http://dx.doi.org/10.1016/jcp.2015.08.013>`_
 
+- Jonathan A. Walsh, Benoit Forget, Kord S. Smith, and Forrest B. Brown,
+  "On-the-fly Doppler Broadening of Unresolved Resonance Region Cross Sections
+  via Probability Band Interpolation," *Proc. PHYSOR*, Sun Valley, Idaho, May
+  1-5, 2016.
+
 - Colin Josey, Benoit Forget, and Kord Smith, "Windowed multipole sensitivity to
   target accuracy of the optimization procedure," *J. Nucl. Sci. Technol.*,
   **52**, 987-992 (2015). `<http://dx.doi.org/10.1080/00223131.2015.1035353>`_
 
+- Paul K. Romano and Timothy H. Trumbull, "Comparison of algorithms for Doppler
+  broadening pointwise tabulated cross sections," *Ann. Nucl. Energy*, **75**,
+  358--364 (2015). `<http://dx.doi.org/10.1016/j.anucene.2014.08.046>`_
+
+- Tuomas Viitanen, Jaakko Leppanen, and Benoit Forget, "Target motion sampling
+  temperature treatment technique with track-length esimators in OpenMC --
+  Preliminary results," *Proc. PHYSOR*, Kyoto, Japan, Sep. 28--Oct. 3 (2014).
+
+- Benoit Forget, Sheng Xu, and Kord Smith, "Direct Doppler broadening in Monte
+  Carlo simulations using the multipole representation," *Ann. Nucl. Energy*,
+  **64**, 78--85 (2014). `<http://dx.doi.org/10.1016/j.anucene.2013.09.043>`_
+
+------------
+Nuclear Data
+------------
+
+- Paul K. Romano and Sterling M. Harper, "Nuclear data processing capabilities
+  in OpenMC", *Proc. Nuclear Data*, Sep. 11-16, 2016.
+
 - Jonathan A. Walsh, Paul K. Romano, Benoit Forget, and Kord S. Smith,
   "Optimizations of the energy grid search algorithm in continuous-energy Monte
   Carlo particle transport codes", *Comput. Phys. Commun.*, **196**, 134-142
@@ -139,29 +188,17 @@ Nuclear Data
   performance analysis for varying cross section parameter regimes,"
   *Proc. Joint Int. Conf. M&C+SNA+MC*, Nashville, Tennessee, Apr. 19--23 (2015).
 
-- Paul K. Romano and Timothy H. Trumbull, "Comparison of algorithms for Doppler
-  broadening pointwise tabulated cross sections," *Ann. Nucl. Energy*, **75**,
-  358--364 (2015). `<http://dx.doi.org/10.1016/j.anucene.2014.08.046>`_
-
-- Tuomas Viitanen, Jaakko Leppanen, and Benoit Forget, "Target motion sampling
-  temperature treatment technique with track-length esimators in OpenMC --
-  Preliminary results," *Proc. PHYSOR*, Kyoto, Japan, Sep. 28--Oct. 3 (2014).
-
 - Jonathan A. Walsh, Benoit Forget, and Kord S. Smith, "Accelerated sampling
   of the free gas resonance elastic scattering kernel," *Ann. Nucl. Energy*,
   **69**, 116--124 (2014). `<http://dx.doi.org/10.1016/j.anucene.2014.01.017>`_
 
-- Benoit Forget, Sheng Xu, and Kord Smith, "Direct Doppler broadening in Monte
-  Carlo simulations using the multipole representation," *Ann. Nucl. Energy*,
-  **64**, 78--85 (2014). `<http://dx.doi.org/10.1016/j.anucene.2013.09.043>`_
-
 -----------
 Parallelism
 -----------
 
 - Paul K. Romano, John R. Tramm, and Andrew R. Siegel, "Efficacy of hardware
   threading for Monte Carlo particle transport calculations on multi- and
-  many-core systems," Accepted, *PHYSOR 2016*, Sun Valley, Idaho, May 1-5, 2016.
+  many-core systems," *PHYSOR 2016*, Sun Valley, Idaho, May 1-5, 2016.
 
 - David Ozog, Allen D. Malony, and Andrew R. Siegel, "A performance analysis of
   SIMD algorithms for Monte Carlo simulations of nuclear reactor cores,"
@@ -228,3 +265,11 @@ Parallelism
 - Paul K. Romano and Benoit Forget, "Parallel Fission Bank Algorithms in Monte
   Carlo Criticality Calculations," *Nucl. Sci. Eng.*, **170**, 125--135
   (2012). `<http://hdl.handle.net/1721.1/73569>`_
+
+---------
+Depletion
+---------
+
+- Kai Huang, Hongchun Wu, Yunzhao Li, and Liangzhi Cao, "Generalized depletion
+  chain simplification based of significance analysis," *Proc. PHYSOR*, Sun
+  Valley, Idaho, May 1-5, 2016.