Fractional Calculus with Applications for Nuclear Reactor Dynamics

Introduces Novel Applications for Solving Neutron Transport Equations

While deemed nonessential in the past, fractional calculus is now gaining momentum in the science and engineering community. Various disciplines have discovered that realistic models of physical phenomenon can be achieved with fractional calculus and are using them in numerous ways. Since fractional calculus represents a reactor more closely than classical integer order calculus, Fractional Calculus with Applications for Nuclear Reactor Dynamics focuses on the application of fractional calculus to describe the physical behavior of nuclear reactors. It applies fractional calculus to incorporate the mathematical methods used to analyze the diffusion theory model of neutron transport and explains the role of neutron transport in reactor theory.

The author discusses fractional calculus and the numerical solution for fractional neutron point kinetic equation (FNPKE), introduces the technique for efficient and accurate numerical computation for FNPKE with different values of reactivity, and analyzes the fractional neutron point kinetic (FNPK) model for the dynamic behavior of neutron motion. The book begins with an overview of nuclear reactors, explains how nuclear energy is extracted from reactors, and explores the behavior of neutron density using reactivity functions. It also demonstrates the applicability of the Haar wavelet method and introduces the neutron diffusion concept to aid readers in understanding the complex behavior of average neutron motion.

This text:

• Applies the effective analytical and numerical methods to obtain the solution for the NDE
• Determines the numerical solution for one-group delayed neutron FNPKE by the explicit finite difference method
• Provides the numerical solution for classical as well as fractional neutron point kinetic equations
• Proposes the Haar wavelet operational method (HWOM) to obtain the numerical approximate solution of the neutron point kinetic equation, and more

Fractional Calculus with Applications for Nuclear Reactor Dynamics

Mathematical Methods in Nuclear Reactor Physics. Neutron Diffusion Equation Model in Dynamical Systems. Fractional Order Neutron Point Kinetic Model. Numerical Solution for Deterministic Classical and Fractional Order Neutron Point Kinetic Model. Classical and Fractional Order Stochastic Neutron Point Kinetic Model. Solution for Nonlinear Classical and Fractional Order Neutron Point Kinetic Model with Newtonian Temperature Feedback Reactivity. Numerical Simulation Using Haar Wavelet Method for Neutron Point Kinetic Equation Involving Imposed Reactivity Function. Numerical Solution Using Two- Dimensional Haar Wavelet Method for Stationary Neutron Transport Equation in Homogeneous Isotropic Medium. References.

Dr. Santanu Saha Ray is an associate professor at the National Institute of Technology, Rourkela, India. He earned a Ph. D. in applied mathematics at Jadavpur University. He is a member of SIAM, the AMS, and the Indian Science Congress Association, and serves as the editor-in-chief for the International Journal of Applied and Computational Mathematics. Dr. Saha Ray has done extensive work in the area of fractional calculus and its role in nuclear science and engineering.