The probability distribution of transmutation events and its application for solving burnup problems

Probabilistic approach of solving burnup problems

“…( 1) mathematically. This endeavour is underpinned by the utilization of the probability distribution given by [7],…”

“…where y (0)≡ y 0 is the initial nuclides concentration at t=0. Here, the smaller the value of ∆ t, the larger the number of sub-steps, thus the better the accuracy [7]. However, such a computation with small ∆ t requires arbitrary precision arithmetic to avoid the floating-point error.…”

“…The Chebyshev Rational Approximation Method (CRAM) [2] and Transmutation Trajectory Analysis (TTA) [3] are two methods that earlier academics used to address challenging situations [4], and both are computationally efficient but are mathematically abstract. On the other hand, [5] recently found an unconventional way of solving burnup problems by deriving a probability distribution that predicts whether a nucleus will transform into another species. This paper presents a new non-deterministic approach to solve burnup problems, and the method is implemented in a C++ program named CNUCTRAN to verify the method.…”