A Review of Nonlinear Reactor Dynamics Problems
Author | : Jack Chernick |
Publisher | : |
Total Pages | : 16 |
Release | : 1962 |
Genre | : Nuclear reactor kinetics |
ISBN | : |
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Author | : Jack Chernick |
Publisher | : |
Total Pages | : 16 |
Release | : 1962 |
Genre | : Nuclear reactor kinetics |
ISBN | : |
Author | : Mahmoud Ahmad Salehi |
Publisher | : |
Total Pages | : 624 |
Release | : 1983 |
Genre | : |
ISBN | : |
Author | : Jack Chernick |
Publisher | : |
Total Pages | : 210 |
Release | : 1973 |
Genre | : Nuclear reactors |
ISBN | : |
Author | : Ziya Akcasuh |
Publisher | : Elsevier |
Total Pages | : 473 |
Release | : 2012-12-02 |
Genre | : Science |
ISBN | : 0323149081 |
Mathematical Methods in Nuclear Reactor Dynamics covers the practical and theoretical aspects of point-reactor kinetics and linear and nonlinear reactor dynamics. The book, which is a result of the lectures given at the University of Michigan, is composed of seven chapters. The opening chapter of the book describes various physical phenomena influencing the temporal behavior of neutrons to provide insights into the physics of reactor dynamics and the interrelationships between various diverse phenomena. The text then presents a set of equations, called point kinetic equation, which describes the time behavior of the total power generated in the medium. The book also provides a short discussion on Gyftopoulos modification and Becker’s formulation. The next chapters explore the exact methods for solving the feedback-free point kinetic equations for a number of reactivity insertions and the validity of the various approximate methods of solution. The book also examines the derivation of models for a certain reactor type and briefly discusses the validity of these models in certain cases against experimental data. A chapter focuses on a concise presentation of the stability theory of linear systems with feedback. Lastly, the concepts of stability in nonlinear reactor systems and the criteria for asymptotic stability in the large as well as in a finite domain of initial disturbances are covered in the concluding chapter. The text is an ideal source for nuclear engineers and for those who have adequate background in reactor physics and operational and applied mathematics.
Author | : Richard Allen Olsen |
Publisher | : |
Total Pages | : 122 |
Release | : 1975 |
Genre | : Mechanical engineering |
ISBN | : |
The solution of the nonlinear two-dimensional reactor dynamics equation subjected to prompt feedback conditions using the finite element technique leads to a matrix formulation. The task of this thesis is the development of computational techniques which allow the problem to be solved for large systems. Specifically, these techniques are: (1) the treatment of the nonlinearity on the element level, (2) the compacting of the sparce matrices to include only non-zero terms, and (3) the construction of a new computer code based on the Crank-Nicolson formulation for the solution of differential equations. To support the theory presented, test problems were solved by the original method, the linearized technique, and the Crank-Nicolson treatment. The results were analyzed and compared graphically. All three of the innovations developed in this thesis appear to be useful tools for solving nonlinear time dependent differential equations.
Author | : |
Publisher | : |
Total Pages | : 0 |
Release | : 1976 |
Genre | : |
ISBN | : |
This work examines the three-dimensional dynamic response of a nonlinear fast reactor with temperature-dependent feedback and delayed neutrons when subjected to uniform and local disturbances. The finite element method was employed to reduce the partial differential reactor equation to a system of ordinary differential equations which can be numerically integrated. A program for the numerical solution of large sparse systems of stiff differential equations developed by Franke and based on Gear's method solved the reduced neutron dynamics equation. Although a study of convergence by refining element mesh sizes was not carried out, the crude finite element mesh utilized yielded the correct trend of neutron dynamic behavior. (Author).
Author | : |
Publisher | : |
Total Pages | : 1124 |
Release | : 1987 |
Genre | : Aeronautics |
ISBN | : |
Author | : Eulogio Conception Bermudes |
Publisher | : |
Total Pages | : 160 |
Release | : 1976 |
Genre | : Mechanical engineering |
ISBN | : |
This work examines the three-dimensional dynamic response of a nonlinear fast reactor with temperature-dependent feedback and delayed neutrons when subjected to uniform and local disturbances. The finite element method was employed to reduce the partial differential reactor equation to a system of ordinary differential equations which can be numerically integrated. A program for the numerical solution of large sparse systems of stiff differential equations developed by Franke and based on Gear's method solved the reduced neutron dynamics equation. Although a study of convergence by refining element mesh sizes was not carried out, the crude finite element mesh utilized yielded the correct trend of neutron dynamic behavior. (Author).
Author | : |
Publisher | : |
Total Pages | : 616 |
Release | : |
Genre | : Nuclear engineering |
ISBN | : |
Author | : Yousry Azmy |
Publisher | : Springer Science & Business Media |
Total Pages | : 476 |
Release | : 2010-04-15 |
Genre | : Technology & Engineering |
ISBN | : 9048134110 |
Nuclear engineering has undergone extensive progress over the years. In the past century, colossal developments have been made and with specific reference to the mathematical theory and computational science underlying this discipline, advances in areas such as high-order discretization methods, Krylov Methods and Iteration Acceleration have steadily grown. Nuclear Computational Science: A Century in Review addresses these topics and many more; topics which hold special ties to the first half of the century, and topics focused around the unique combination of nuclear engineering, computational science and mathematical theory. Comprising eight chapters, Nuclear Computational Science: A Century in Review incorporates a number of carefully selected issues representing a variety of problems, providing the reader with a wealth of information in both a clear and concise manner. The comprehensive nature of the coverage and the stature of the contributing authors combine to make this a unique landmark publication. Targeting the medium to advanced level academic, this book will appeal to researchers and students with an interest in the progression of mathematical theory and its application to nuclear computational science.