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.
Division Spotlight
Mathematics & Computation
Division members promote the advancement of mathematical and computational methods for solving problems arising in all disciplines encompassed by the Society. They place particular emphasis on numerical techniques for efficient computer applications to aid in the dissemination, integration, and proper use of computer codes, including preparation of computational benchmark and development of standards for computing practices, and to encourage the development on new computer codes and broaden their use.
Meeting 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
Jun 2025
Jan 2025
Latest Journal Issues
Nuclear Science and Engineering
August 2025
Nuclear Technology
July 2025
Fusion Science and Technology
Latest News
NRC cuts fees by 50 percent for advanced reactor applicants
The Nuclear Regulatory Commission has announced it has amended regulations for the licensing, inspection, special projects, and annual fees it will charge applicants and licensees for fiscal year 2025.
H. Rief, H. Kschwendt
Nuclear Science and Engineering | Volume 30 | Number 3 | December 1967 | Pages 395-418
Technical Paper | doi.org/10.13182/NSE67-A18401
Articles are hosted by Taylor and Francis Online.
A detailed Monte Carlo analysis in one, two, and three dimensions and with different multigroup scattering kernels is presented for a number of actual reactor systems. Several variance reducing sampling techniques, which we believe to be unusual, are employed and, in addition to the prediction of reactivity, much emphasis is placed on generation time calculations with reference to the “life cycle” point of view. One of the main points of interest in the numerical results obtained is the comparison of the reactivity and time eigenvalues with those obtained from the equivalent SN and jN calculations. The excellent agreement with these two methods establishes the necessary confidence in the Monte Carlo procedure described here. As a further illustration of the method, it was thought to be of interest to compare the numerical results obtained from different scattering kernels (transport approximation, linear anisotropy, and exact anisotropy) with a view to assessing the influence of these different approximations on the reactivity, absorption, leakage, generation time, etc. Simultaneously, an examination of two different Monte Carlo sampling techniques is presented. To apply a physical test to the method, some highly enriched uranium spheres, some cylinders of extreme geometry reflected by a variety of materials, and some cylindrical annuli were analyzed and the results compared with experiments. In addition, some systems requiring the full use of the three-dimensional scope of the method are studied. The efficiency of the Monte Carlo procedure is finally illustrated by listing, for several calculations, the probable errors in the reactor eigenvalues and other parameters after 10 min of IBM-7090 computer time. This analysis proves that statistical methods can be used to carry out threedimensional assessments of reactor assemblies with sufficient accuracy without the expenditure of a prohibitive amount of computer time. Such a goal has not yet been achieved by the numerical or analytical methods which solve the neutron transport equation.
