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
2026 ANS Annual Conference
May 31–June 3, 2026
Denver, CO|Sheraton Denver
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
Dec 2025
Jul 2025
Latest Journal Issues
Nuclear Science and Engineering
January 2026
Nuclear Technology
December 2025
Fusion Science and Technology
November 2025
Latest News
AI at work: Southern Nuclear’s adoption of Copilot agents drives fleet forward
Southern Nuclear is leading the charge in artificial intelligence integration, with employee-developed applications driving efficiencies in maintenance, operations, safety, and performance.
The tools span all roles within the company, with thousands of documented uses throughout the fleet, including improved maintenance efficiency, risk awareness in maintenance activities, and better-informed decision-making. The data-intensive process of preparing for and executing maintenance operations is streamlined by leveraging AI to put the right information at the fingertips for maintenance leaders, planners, schedulers, engineers, and technicians.
Donald J. Dudziak
Nuclear Science and Engineering | Volume 47 | Number 2 | February 1972 | Pages 230-234
Technical Note | doi.org/10.13182/NSE72-A22402
Articles are hosted by Taylor and Francis Online.
A derivation of the time-dependent forward stochastic equation is sketched for a point reactor with linear feedback and an arbitrary finite fission neutron frequency distribution. Certain pathological characteristics of possible stochastic trajectories are discussed, and limiting conjectures are made based on physical considerations. The time-independent forward stochastic equation with negative reactivity feedback is solved in the classical manner, leading to a recursion relation for the long-run probabilities. Next, all factorial moments of the long-run distribution are shown to be finite, and the corresponding probabilities, P(N,∞), are thus o(N-k) for any integer k. Following this, a more tractable recursion relation is presented for the simpler case of binary fission. For this simpler model, the equivalence to an independent analysis of the Kolmogorov forward matrix equations, as presented in a previous paper, is demonstrated. Finally, a simple recursion relation among factorial moments of the long-run distribution is derived for the binary fission model.