Neutron noise and random trees -: Links between past and present

After reviewing personal reminiscences about the history of reactor noise research, the generalized notion of neutron importance is discussed and advantages of the backward generating. function equation are shown by calculating the space-time fluctuations of the neutron density in a simple virtual (one-dimensional) reactor. Similarities between chain reactions and randomly evolving trees are used to study the special properties of branching processes. It is assumed that at t = 0 the tree consists of a single living node called root which, after a certain time tau greater than or equal to 0, may produce nu greater than or equal to 0 new living nodes and then becomes dead. tau and nu are random variables with known distribution functions. Each new living node evolves further independently of the others as does the toot. The time dependence of the expectation value of the living nodes number is determined by the average number q(1) of the new nodes produced by one dying node. Depending on whether q(1) < 1 or q(1) = 1 or q(1) > 1 the randomly evolving tree is called subcritical, critical, and supercritical, respectively. The probability distributions of the tree lifetime and the tree size are determined in two exactly solvable models, and it is proven that a supercritical tree may be finite even at t = infinity with non-zero probability. (C) 2003 Elsevier Science Ltd. All rights reserved.