Neutron Diffusion

Dr. S. Chakraverty has over 25 years of experience as a researcher and teacher. Currently he is working at the National Institute of Technology, Rourkela, Odisha as a full Professor and Head of the Department of Mathematics. Prior to this he was with CSIR Central Building Research Institute, Roorkee, India. After graduating from St. Columba’s College (Ranchi University), he obtained his M. Sc in Mathematics and M. Phil in Computer Applications from the University of Roorkee (now the Indian Institute of Technology Roorkee), earning First Position in the University honors. Dr. Chakraverty received his Ph. D. from IIT Roorkee in 1992. Thereafter he did his post-doctoral research at Institute of Sound and Vibration Research (ISVR), University of Southampton, U.K. and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He was also a visiting professor at Concordia and McGill Universities, Canada, during 1997-1999 and visiting professor of University of Johannesburg, South Africa during 2011-2014. Sukanta Nayak received his B.Sc. (Mathematics) from Government Autonomous College, Rourkela in 2008 and M.Sc. (Mathematics) from National Institute of Technology, Rourkela in 2010. He has done his Ph. D. (Mathematics) from National Institute of Technology, Rourkela in 2016. He is the awardee of P. G. level scholarship, Government of Odisha in 2008 and qualified GATE, Government of India, in 2012. Currently he is doing his post-doctoral research at the University of Johannesburg, South Africa. He has published 9 research papers in international peer-reviewed journals, and 2 book chapters.

Basic Reactor Principles


Atomic Structure


Binding energy


Nuclear fusion


Nuclear fission


Radioactivity


Principles, Production, and interaction of neutrons with matter


Production of neutrons


Neutron reactions and radiation


Inelastic and elastic scattering of neutrons


Maxwell-Boltzmann distribution


Neutron diffusion theory


Cross section of neutron reactions


Rates of neutron reactions


Fission neutrons


Prompt neutrons


Delayed neutrons


Neutron transport and diffusion equation


Fundamentals of Uncertainty


Probabilistic uncertainty


Non-probabilistic uncertainty


Interval uncertainty


Fuzzy uncertainty


Uncertain Neutron diffusion


Uncertain factors involved in neutron diffusion theory


Modeling of uncertain neutron diffusion equations


One group model


Analytical methods


Numerical methods


Finite difference method


Finite element method


Conclusion


Uncertain One Group Model


Interval arithmetic and Fuzzy Finite Element Method (FFEM)


Formulation of the uncertain stiffness matrices and force vectors


Bare square homogeneous reactor


Multi group model


Uncertain factors involved in multi group neutron diffusion theory


Formulation of uncertain multi group neutron diffusion equations


Uncertain Multi Group Model


Fuzzy finite element for coupled differential equations


Fuzzy multi group neutron diffusion equation


Case study


Results and discussion


Conclusion


Point Kinetic Diffusion


Theory of point kinetic neutron diffusion equation


Case study


Conclusion


Stochastic Point Kinetic Diffusion


Stochastic point kinetic model


Euler-Maruyama method


Example


Hybridised uncertainty in point kinetic diffusion


Development of stochastic point kinetic model with fuzzy parameters


Fuzzy Euler-Maruyama method


Case Study


Conclusion


Index