Studies in branching, population genetics, probability bounds, and prediction in nuclear safety analysis

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This proposal describes scientific problems whose behaviour is stochastic in nature and which require probabilistic and statistical tools for their analysis. One important class is concerned with modeling and nuclear safety in CANDU reactors. As these reactors age, safety margins decrease and it becomes necessary to adopt statistical methods to determine whether they meet operating licenses under current conditions of whether they need to be de-rated. De-rating a reactor means it must operated at reduced power with an enormous loss of revenue. Previously, it was adequate to carry out deterministic safety analyses or limit of envelope computations that took into account extreme operating conditions. Such methods are unduly unrealistic and need to be replaced with statistical methods. This proposal continues collaboration with scientists and engineers at Ontario Power Generation. One of the most significant previous contributions by the applicant in which a rigorous statistical approach benefited the industry involved the feeder pipes at Pickering Nuclear Generating Station A where he showed that additional large sampling was unnecessary, thus shortening the time and lost revenue while the reactor units were down, for submission of restart letters to the Canadian Nuclear Safety Commission. Potential future directions of research include best estimate and uncertainty analysis to neutron overpower protection and channel/bundle power compliance. A statistical approach provides benefits in providing better margins to the license limits while adhering to safety standards. Another class of problems concerns partition distributions in population genetics and ecology. These distributions describe the observed variation in present day population. Understanding these distributions sheds light on the underlying evolutionary process. The applicant has developed a framework in which many of these partitions can be derived from one unifying principle and hopes to use this approach to develop tools for making inferences about the evolutionary forces which have led to the observed diversity of species and genetic variation.