ANS is committed to advancing, fostering, and promoting the development and application of nuclear sciences and technologies to benefit society.
Explore the many uses for nuclear science and its impact on energy, the environment, healthcare, food, and more.
Explore membership for yourself or for your organization.
Conference Spotlight
Nuclear Energy Conference & Expo (NECX)
September 8–11, 2025
Atlanta, GA|Atlanta Marriott Marquis
Standards Program
The Standards Committee is responsible for the development and maintenance of voluntary consensus standards that address the design, analysis, and operation of components, systems, and facilities related to the application of nuclear science and technology. Find out What’s New, check out the Standards Store, or Get Involved today!
Latest Magazine Issues
Aug 2025
Jan 2025
Latest Journal Issues
Nuclear Science and Engineering
September 2025
Nuclear Technology
Fusion Science and Technology
August 2025
Latest News
Powering the future: How the DOE is fueling nuclear fuel cycle research and development
As global interest in nuclear energy surges, the United States must remain at the forefront of research and development to ensure national energy security, advance nuclear technologies, and promote international cooperation on safety and nonproliferation. A crucial step in achieving this is analyzing how funding and resources are allocated to better understand how to direct future research and development. The Department of Energy has spearheaded this effort by funding hundreds of research projects across the country through the Nuclear Energy University Program (NEUP). This initiative has empowered dozens of universities to collaborate toward a nuclear-friendly future.
John F. Carew, Gabriel Zamonsky
Nuclear Science and Engineering | Volume 131 | Number 2 | February 1999 | Pages 199-207
Technical Paper | doi.org/10.13182/NSE97-83
Articles are hosted by Taylor and Francis Online.
Mechanical quadratures that allow systematic improvement and solution convergence are derived for application of the discrete ordinates method to the Boltzmann transport equation. The quadrature directions are arranged on n latitudinal levels, are uniformly distributed over the unit sphere, and have positive weights. Both a uniform and equal-weight quadrature set UEn and a uniform and Gauss-weight quadrature set UGn are derived. These quadratures have the advantage over the standard level-symmetric LQn quadrature sets in that the weights are positive for all orders, and the solution may be systematically converged by increasing the order of the quadrature set. As the order of the quadrature is increased the points approach a uniform continuous distribution on the unit sphere and the quadrature is invariant with respect to spatial rotations. The numerical integrals converge for continuous functions as the order of the quadrature is increased.Numerical calculations were performed to evaluate the application of the UEn quadrature set. Comparisons of the exact moments and those calculated using the UEn quadrature set demonstrate that the moment integrals are performed accurately except for distributions that are very sharply peaked along the direction of the polar axis. A series of DORT transport calculations of the >1-MeV neutron flux for a typical reactor core/pressure vessel geometry were also carried out. These calculations employed the UEn (n = 6, 10, 12, 18, and 24) quadratures and indicate that the UEn solutions have converged to within ~0.5%. The UE24 solutions were also found to be more accurate than the calculations performed with the S16 level-symmetric quadratures.