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Developed mathematical technique for fractional stochastic point kinetics model in nuclear reactor dynamics
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作者 Ahmed E.Aboanber Abdallah A.Nahla Adel M.Edress 《Nuclear Science and Techniques》 SCIE CAS CSCD 2018年第9期197-213,共17页
Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic m... Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic model for the point kinetics system with multi-group of precursors,including the effect of temperature feedback, has been developed and analyzed. A major mathematical and inflexible scheme to the point kinetics model is obtained by merging the fractional and stochastic technique. A novel split-step method including mathematical tools of the Laplace transforms, Mittage–Leffler function, eigenvalues of the coefficient matrix, and its corresponding eigenvectors have been used for the fractional stochastic matrix differential equation. The validity of the proposed technique has been demonstrated via calculations of the mean and standard deviation of neutrons and precursor populations for various reactivities: step, ramp, sinusoidal, and temperature reactivity feedback. The results of the proposed method agree well with the conventional one of the deterministic point kinetics equations. 展开更多
关键词 Ito stochastic point kinetics equations Temperature feedback effects Wiener process Fractional calculus Mittage–Leffler function
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