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
Nuclear Criticality Safety
NCSD provides communication among nuclear criticality safety professionals through the development of standards, the evolution of training methods and materials, the presentation of technical data and procedures, and the creation of specialty publications. In these ways, the division furthers the exchange of technical information on nuclear criticality safety with the ultimate goal of promoting the safe handling of fissionable materials outside reactors.
Meeting Spotlight
2024 ANS Winter Conference and Expo
November 17–21, 2024
Orlando, FL|Renaissance Orlando at SeaWorld
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 2024
Jan 2024
Latest Journal Issues
Nuclear Science and Engineering
October 2024
Nuclear Technology
Fusion Science and Technology
August 2024
Latest News
New laws offer nuclear industry incentives for existing power plant uprates
This year, the U.S. nuclear industry received a much-needed economic boost that could help preserve operating nuclear power plants and incentivize upgrades that extend their lifespan and power output.
Signed into law in 2022, the Inflation Reduction Act offers production tax credits (PTCs) for existing nuclear power plants and either PTCs or investment tax credits (ITCs) for new carbon-free generation. These credits could make power uprates—increasing the maximum power level at which a commercial plant may operate—a much more appealing option for utilities.
Zbigniew Weiss
Nuclear Science and Engineering | Volume 63 | Number 4 | August 1977 | Pages 457-492
Technical Paper | doi.org/10.13182/NSE77-A27062
Articles are hosted by Taylor and Francis Online.
The response matrix equations (RME) are analyzed from two points of view: (a) their computational feasibility, and (b) their consistency with other methods used in reactor analysis. It is shown that RME can be derived directly from the weak form of the diffusion equation without the concept of partial currents, and hence, are also applicable to the description of phenomena, where partial currents have no physical meaning (for example, the conduction of heat). By splitting the high-order RME into a coupled system of single-order equations, the analysis of the convergence properties of the iterative solutions to RME could be greatly simplified. The derived explicit expressions for the convergence ratio were verified by numerical experimentation. As an illustration, the well-known International Atomic Energy Agency benchmark problem has been calculated by two two-dimensional response matrix programs at ASEA-ATOM, CIKADA, and LABAN. In the second part of the paper, the relation of RME to finite difference (FD) equations has been investigated. It was shown that for small mesh sizes, RME are computationally not feasible. For rectangular nodes, an algorithm called the “vectorial model” (VM) was developed, which reduces the amount of unknowns in RME by a factor of 2. This is a generalization to two- and three-dimensional nodes of the author's earlier results. An approximate reduction of VM to scalar equations (one unknown per node) has been discussed, and its relation to recent developments in nodal methods has been emphasized. Several ideas in this paper, such as the improved FD scheme, are far from being completed and therefore should be challenging for further investigation.