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
August 2025
Fusion Science and Technology
Latest News
Chris Wagner: The role of Eden Radioisotopes in the future of nuclear medicine
Chris Wagner has more than 40 years of experience in nuclear medicine, beginning as a clinical practitioner before moving into leadership roles at companies like Mallinckrodt (now Curium) and Nordion. His knowledge of both the clinical and the manufacturing sides of nuclear medicine laid the groundwork for helping to found Eden Radioisotopes, a start-up venture that intends to make diagnostic and therapeutic raw material medical isotopes like molybdenum-99 and lutetium-177.
M. M. R. Williams
Nuclear Science and Engineering | Volume 155 | Number 1 | January 2007 | Pages 109-118
Technical Note | doi.org/10.13182/NSE05-73TN
Articles are hosted by Taylor and Francis Online.
The polynomial chaos functions of Wiener are used to solve a stochastic differential equation. It is shown that a variety of polynomials are available according to the probability distribution of the underlying random element. Using the Legendre chaos polynomials, we have solved the problem of radiation transmission through a slab of random material properties in the P1 approximation. For a special case, it is possible to obtain an exact solution to this problem, and hence the rate of convergence of the chaos expansion can be examined. Results are shown in tabular form and graphically, which compare the stochastic average with the deterministic average and significant differences are found. In addition we calculate the variance in the flux and current across the slab, thereby giving a measure of the uncertainty associated with the average. The method of polynomial chaos offers an alternative procedure to the normally used closure, or special statistics, methods for the study of spatial randomness and has the potential to deal with very complex systems, although the full computational implications have yet to be determined. In the Appendix, we show how the Boltzmann equation, with spatially random cross sections, can be reduced to a coupled set of deterministic equations.