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Full 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.
Contents
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
