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




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