2 edition of **Applications of invariant imbedding to problems of neutron transport in a slab.** found in the catalog.

Applications of invariant imbedding to problems of neutron transport in a slab.

Glenn R. Ingram

- 145 Want to read
- 32 Currently reading

Published
**1962**
.

Written in English

- Neutrons.

The Physical Object | |
---|---|

Pagination | v, 63 leaves, |

Number of Pages | 63 |

ID Numbers | |

Open Library | OL16882459M |

neutron population in a reactor core is based on two main approaches: (a) deterministic approach where the Boltzmann transport equation is solved explicitly, and (b) stochastic approach or the Monte Carlo method where neutron transport and interactions are modeled explicitly. o The Monte Carlo method is an accurate mimic of the neutron histories. Numerical Methods in the Theory of Neutron Transport Revised, Subsequent Edition by G. I. Marchuk (Author)Cited by:

A simple model of time-independent neutron transport on a line as a stochastic process, using the method of invariant imbedding, is considered. Non- linear equations for the expected values (flux) are also obtained and solved, the results are compared with the ordinary linear theory, and possible advantages of the new formulation are cited. We introduce a modification to the standard spherical harmonic closure used with linear kinetic equations of particle transport. While the standard closure is known to produce negative particle concentrations, the modification corrects this defect by requiring that the ansatz used to close the equations itself be a nonnegative function. We impose this requirement via explicit constraints in a Cited by:

mandatory in problems where the quantities of interest depend on the microscopic properties and on the geometry of the moderating material, as will be shown in the following for the simple problem of neutron beams crossing a moderating slab. Recently, Peralta [10] has proposed an educational Monte Carlo simulation of neutron. The neutron transport equation is of fundamental importance in nuclear reactor theory and shielding design [9, 12, 17, 22]. The stochastic nature of the neutron transport process has been of interest for many years. Classic studies of the stochastic theory of neutron transport are given in [7, 8].Author: Edward J. Allen.

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INVARIANT IMBEDDING; THE EQUATIONS OF BELLMAN, KALABA, AND WING The usual approach to problems of neutron transport is to define a density function N(x, E, p., t) such that N(x, E, p., t)dxdEdp, represents the number of neutrons at time t in a square centimeter of the slab from x to x + dx, with energies between E and E + dE and whose direction Cited by: 3.

Ridihalgh, John Lou, "Application of invariant imbedding to radiation transport theory " ().Retrospective Theses and Dissertations. The first applications of invariant imbedding to nuclear methods used for the gamma problem also apply to neutron transport problems.

The problems of radiation transportAuthor: John Lou Ridihalgh. Mathematical Modeling of Neutron Transport Milan Hanu s Department of Mathematics University of West Bohemia, Pilsen Thesis submitted in partial ful llment of the requirements for the degree of Doctor of Philosophy (Applied Mathematics) Supervisor: Doc.

Ing. File Size: 7MB. Here is a book that provides the classical foundations of invariant imbedding, a concept that provided the first indication of the connection between transport theory and the Riccati Equation.

The reprinting of this classic volume was prompted by a revival of interest in the subject area because of. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATI () Invariant Imbedding and Scattering Processes ALAN PING-I WANG Aerospace Group, Scientific Computing Services Hughes Aircraft Company, Culver City, California Submitted by Richard Bellman by: Abstract.

Expressions for time-dependentX- andY-functions for a one-speed neutron transport problem in a finite slab have been derived using a technique combining invariant imbedding method and eigenfunction expansion atmosphere has been considered to scatter : S. Karanjai, G.

Biswas. imbedding approach is applied to a more realistic problem - that of transport through a slab, Further generalizations are dis-cussed. The last two sections deal with the application of invariant imbedding to shielding problems and certain approxima-tions suggested by the imbeddIng approach.

The discussion of the theory, given in Section II, is. Applications of the Invariant Imbedding Method to Monoenergetic Neutron Transport Theory in Slab Geometry J.

Mingle 1x Biorthogonal Angular Polynomial Expansions of the Boltzmann Trans- port Equation K. Lathrop and N. Demuth - October 1, BOOK. Don't show me this again. Welcome. This is one of over 2, courses on OCW.

Find materials for this course in the pages linked along the left. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum.

No enrollment or registration. With the use of invariance principles in a systematic fashion, we shall derive not only new analytic formulations of the classical particle processes, those of transport theory, radiative transfer, random walk, multiple scattering, and diffusion theory, but, in addition, new computational algorithms which seem well fitted to the capabilities of digital by: The invariant imbedding technique is applied to the problems of radiation transfer in a plane-parallel inhomogeneous atmosphere.

All the parameters which describe the elementary event of scattering and the distribution of the energy sources are allowed to vary with depth. Mathematically, the considered standard problems of the theory are reduced to initial-value problems which are better Author: Arthur G.

Nikoghossian. Applications of finite groups to iterative problems in reactor physics Article in Applied Numerical Mathematics 59(6) June with 36 Reads How we measure 'reads'. Neutron shielding design is also indispensable in the packaging and storage of isotopic neutron sources.

Most efforts in the development of neutron shielding design have been concentrated on nuclear reactor shielding because of its huge mass and strict requirement of accuracy.

withw(a)=c andw(T)= initial-value problem for the optimizing function is derived directly from the variational problem. It is shown that the solution of the initial-value problem satisfies the usual Euler by: 8.

passage through the slab. In the limit, these cumulative functions tend to these Chandrasekhar’s functions for the standard transfer problem.

Furthermore, the invariant imbedding is applied for the initial value solutions of the two-components radiation field, i.e., the Cauchy system governing.

Neutron Transport Theory. Neutron transport theory is concerned with the transport of neutrons through various media. As was discussed neutrons are neutral particles, therefore they travel in straight lines, deviating from their path only when they actually collide with a nucleus to be scattered into a new direction or absorbed.

Transport theory is relatively simple in principle and an exact. A numerical method is presented for calculating neutron transport problems in three-dimensional (x,y,z) geometry on the basis of a method of direct integration of the integral transport equation.

CHAPTER 4 Reactor Statics Prepared by Dr. Benjamin Rouben, 12 & 1 Consulting, Adjunct Professor, McMaster University & University of Ontario Institute of Technology (UOIT) and Dr. Eleodor Nichita, Associate Professor, UOIT Summary: This chapter is devoted to the calculation of the neutron flux in a nuclear reactor under specialFile Size: 1MB.

Abstract: This paper examines the theoretical and practical application of the finite element method to the neutron transport equation. The theoretical examination which is applicable to the general transport equation in arbitrary geometry includes a derivation of the equivalent integral law (or weak form) of the first order neutron transport equation, to which the finite element method Cited by: 4.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATI () The Initial-Value Transport Problem for Monoenergetic Neutrons in an Infinite Slab with Delayed Neutron Production HANS G. KAPER* Nuclear Engineering Division, Mechanical Engineering Department, Stanford University, Stanford, California.

Invariant Imbedding and Neutron Transport Theory. IV. Generalized Trans- port Theory Richard Bellman, Robert Kalaba, and G. Milton Wing - September EIR-BERTCHT m Neutron Flux Measurements in Bent Air Ducts through Water Jean-Marie Paratte and Akbar Etemad - March AEEW-M- File Size: KB.Triangular Mesh Method for the Neutron Transport Equation,” Los Alamos Report, () We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems.

It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three.The source matrices of this problem satisfy Fredholm integral equations of the second kind. The invariant imbedding technique developed by R.

Bellman and co-workers is used to replace these integral equations with the equivalent Cauchy initial-value problems which can be solved using an appropriate quadrature formula and integration : A M. Khounsary, A C. Coaley, W J. Minkowycz.