Neutron Diffusion : Concepts and Uncertainty Analysis for Engineers and Scientists book cover
1st Edition

Neutron Diffusion
Concepts and Uncertainty Analysis for Engineers and Scientists

ISBN 9780367889807
Published December 10, 2019 by CRC Press
196 Pages

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Book Description

This book is designed for a systematic understanding of nuclear diffusion theory along with fuzzy/interval/stochastic uncertainty. This will serve to be a benchmark book for graduate & postgraduate students, teachers, engineers and researchers throughout the globe.

In view of the recent developments in nuclear engineering, it is important to study the basic concepts of this field along with the diffusion processes for nuclear reactor design. Also, it is known that uncertainty is a must in every field of engineering and science and, in particular, with regards to nuclear-related problems. As such, one may need to understand the nuclear diffusion principles/theories corresponding with reliable and efficient techniques for the solution of such uncertain problems. Accordingly this book aims to provide a new direction for readers with basic concepts of reactor physics as well as neutron diffusion theory. On the other hand, it also includes uncertainty (in terms of fuzzy, interval, stochastic) and their applications in nuclear diffusion problems in a systematic manner, along with recent developments. The underlying concepts of the presented methods in this book may very well be used/extended to various other engineering disciplines viz. electronics, marine, chemical, mining engineering and other sciences such as physics, chemistry, biotechnology etc. This book then can be widely applied wherever one wants to model their physical problems in terms of non-probabilistic methods viz. fuzzy/stochastic for the true essence of the real problems.

Table of Contents

Basic Reactor Principles

Atomic Structure

Binding energy

Nuclear fusion

Nuclear fission


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


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


Point Kinetic Diffusion

Theory of point kinetic neutron diffusion equation

Case study


Stochastic Point Kinetic Diffusion

Stochastic point kinetic model


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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.