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
Latest Magazine Issues
Mar 2026
Jan 2026
Latest Journal Issues
Nuclear Science and Engineering
April 2026
Nuclear Technology
February 2026
Fusion Science and Technology
Latest News
ANS hosts webinar on criticality safety standards
A diagram depicting the NRC’s regulatory structure for nuclear criticality safety. (Image: Oak Ridge National Laboratory)
The American Nuclear Society’s Risk-informed, Performance-based Principles and Policy Committee (RP3C) held another presentation in its monthly Community of Practice (CoP) series last month. RP3C chair Steven Krahn opened the meeting with brief introductory remarks about the importance of risk-informed, performance based (RIPB) decision-making and the need for new approaches to nuclear design that go beyond conventional and deterministic methods.
V. Deniz
Nuclear Science and Engineering | Volume 28 | Number 3 | June 1967 | Pages 397-403
Technical Paper | doi.org/10.13182/NSE67-A28954
Articles are hosted by Taylor and Francis Online.
A general transport-theory formulation of lattice kinetics is obtained by studying an infinite lattice with a macroscopic spatial-flux variation of the form exp(i B · r). A study is first made of the variation of the asymptotic inverse period and of the flux distribution as a function of the buckling vector, these being, respectively, the eigenvalue and the eigenfunction of the balance equation for the nonstationary system. This allows one to define the parameters which characterize the anisotropic migration of neutrons in the lattice. One also sees in the process that the introduction of a macroscopic curvature not only introduces net leakage,. but also modifies the mean disappearance probability from the net effect of production and absorption. The finite-medium kinetic parameters which follow are defined in terms of the corresponding zero-buckling parameters and of the buckling-dependent part of the inverse period. All the parameters are expressed in terms of integrals of periodic functions only over a unit cell instead of over the whole pile. In particular, for homogeneous systems, the volume integral drops out. In the context of the formulation of this paper, the following known facts are restressed. First, there exists a choice in defining multiplication factors, which depends on whether the production operator employed is characteristic of instantaneous production rates or of production rates in stationary systems. Second, and added to this, there is a further arbitrariness in the definition of parameters such as mean lifetimes and multiplication factors, which stems from the freedom one has in the choice of weight functions. This arbitrariness is characteristic of all parameters that are not eigenvalues. However, with a proper choice of weight functions, the multiplication factors can be made identical to the eigenvalues of static-theory balance equations. These eigenvalues have the unambiguous meaning of being the reciprocals of the factors by which v is uniformly changed in order to stabilize nonstationary systems. Apart from its application to nonstationary systems around the critical point, the study is also applicable to pulsed systems which may be multiplying or non-multiplying. An extension to exponential experiments on nondiverging infinite lattices can be very easily obtained.