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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
International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2025)
April 27–30, 2025
Denver, CO|The Westin Denver Downtown
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!
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Latest News
Argonne’s METL gears up to test more sodium fast reactor components
Argonne National Laboratory has successfully swapped out an aging cold trap in the sodium test loop called METL (Mechanisms Engineering Test Loop), the Department of Energy announced April 23. The upgrade is the first of its kind in the United States in more than 30 years, according to the DOE, and will help test components and operations for the sodium-cooled fast reactors being developed now.
Hao Li, Ganglin Yu, Shanfang Huang, Mengfei Zhou, Guanlin Shi, Kan Wang
Nuclear Science and Engineering | Volume 193 | Number 11 | November 2019 | Pages 1186-1218
Technical Paper | doi.org/10.1080/00295639.2019.1614800
Articles are hosted by Taylor and Francis Online.
Geometric sensitivity analyses of the -eigenvalue have many applications in analyses of geometric uncertainty, calculations of differential control rod worth, and searches for critical geometry. The adjoint-weighted first-order geometric sensitivity theory is widely used and has continuously evolved with the Monte Carlo methods. However, the existing adjoint-weighted algorithm can do only uniform isotropic expansions or contractions of surfaces. The adjoint-weighted algorithm also requires computation of adjoint-weighted scattering and fission reaction rates exactly at material interfaces, which has an infinitesimal probability in reality. This paper presents an improved geometry adjoint-weighted perturbation algorithm that is incorporated into the continuous-energy Reactor Monte Carlo (RMC) code. The improvement of the adjoint-weighted algorithm is decomposed into three steps for constructing a cross-section function of geometric parameters using logical expressions, calculating the derivative of the cross-section function, and estimating the adjoint-weighted surface reaction rates. The improved algorithm can accommodate common one-parameter geometric perturbations of internal interfaces or boundary surfaces as well as those of cells as long as the perturbed cells can be described by logical expressions of spatial surface equations. The perturbation algorithm is compared with a direct difference method, the linear least-squares fitting method with central differences, for several typical geometric perturbations including translation, fixed-axis rotation, and uniform isotropic/anisotropic expansion transformations of planar, spherical, cylindrical, and conical surfaces. The differences between the two methods are not more than 3% and not more than 3 for the majority of the test examples. Even though the perturbation algorithm has higher figures of merit than the direct difference method for the majority of the test examples, there is no guarantee that the former can always be more efficient than the latter. The limitation in the efficiency of the perturbation algorithm was demonstrated by the totally reflecting light water reactor pin model.