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Perturbation Theory in the Nuclear Power


Preparation of the Scientific Monograph "Perturbation Theory and Adjoint Function Method in the Problems of Nuclear Power"

Tech Area / Field

  • FIR-MOD/Modelling/Fission Reactors
  • FIR-REA/Reactor Concept/Fission Reactors

3 Approved without Funding

Registration date

Leading Institute
FEI (IPPE), Russia, Kaluga reg., Obninsk


  • University of Tennessee, USA, TN, Knoxville\nTokyo Institute of Technology / Research Laboratory for Nuclear Reactors, Japan, Tokyo

Project summary

The objective of the Project is to prepare scientific monograph “Perturbation theory and adjoint function method in the problems of nuclear power” for publication in English. The monograph is dedicated to the subjects of using the perturbation theory and the adjoint equations apparatus in engineering-physical problems of nuclear power.
Along with basic differential equations of mathematical physics describing certain processes, it is possible to consider formally the equations adjoint to the principal ones in the interpretation of Lagrange. The solutions for adjoint equations are the functions that have a certain physical meaning. This circumstance is the basis for the viability and competitiveness of the adjoint function method, which paves new ways for the investigators in practical solution of various problems.
The conjugate function method has found a wide application in quantum mechanics, in neutronics research of nuclear reactors and protection against radiations in the activities involving calculations, designing, optimizations, and experimental research of characteristics of reactors and protection for nuclear power facilities (NPF). However, the analogous approach is not widely used in research in the area of engineering, technical, and economic problems of NPF (heat exchange, strength of structural elements, hydrodynamics, electrophysics, kinetics and control of reactors, etc.). This is to a certain extent owing to the fact that no monograph to systematically present the conjugate function method and perturbation theory based thereon has been available. There being no monograph in English, foreign scientists do not have a possibility to know the related results obtained in Russia, which also aggravates the situation.
The book proposed is to refill the vacuum. It will consistently formulate the perturbation theory and apparatus of adjoint equations for solving the problems of engineering physics as applicable to the nuclear reactor and facility as a whole; the issues of mathematical modeling for the nuclear industry economics will be also addressed.
Perturbation theory, which expresses the variation of some functional from a function of some practical interest (temperature, deformation, potential, current, flow rate of coolant, etc.), gives a possibility to define the variations of this functional as influenced by the variation of physical properties of the environment and intensity of the external sources operating therein. This offers the possibility to use the perturbation theory for the following objectives.
1) An upgraded accuracy of calculation of the difference-related effects (as compared with two independent direct calculations).
2) Direct accounting for the effect of tolerance and dispersion of the parameters determining the effect of external factors on the values of functionals studied in the environment.
3) The most generalized statement of the variation problems for finding an optimum distribution of different physical values and conditions for the external factors’ effect.
4) Solving the problems of identification and engineering diagnostics for the NPF components, development of adequate mathematical models on the experimental characteristics of NPF.
5) Solving the inverse problems of mathematical physics of steady-state and non-stationary types using the experimental information for defining the related physical parameters of fundamental nature in the environment under study.
The monograph will present a consistent exposition of the conjugate function method and perturbation theory and its popularization for the Russian and foreign investigators of the method as applicable to the engineering aspects of the development and studies on NPF with machine-supported and direct conversion of thermal energy into electrical and laser one.
The basis for the book is constituted by theoretical developments published by the authors since 1966 in different editions. These results will be summarized and systematized in the monograph.
The monograph is intended primarily for research workers and experts in the area of engineering-physical and economic issues of nuclear power, as well as in applied mathematics dealing with these problems. The project participants have gained a long-term experience in the information and computation technologies.
The project fully corresponds to the ISTC goals in terms of supporting fundamental and applied research oriented to the use of non-traditional methods for modeling of physical processes in nuclear power facilities, substantiation of their physical engineering characteristics.
Close cooperation with the foreign collaborators is suggested in the course of the project implementation for sharing information on the works fulfilled, and their prospects, including resolving the problems related to the future publication of the monograph abroad.