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
Written in English
|The Physical Object|
|Pagination||v, 63 leaves,|
|Number of Pages||63|
This is a scalar function, which depends on the next variables: the position vector of the neutron in a datum coordinate system, the neutron speed and the time. The density is the solution of an integral-differential equation named the neutron transport equation. Many authors paid attention to this problem and its applications , , , . Quasi-Elastic Neutron Scattering • Neutron exchangggyes small amount of energy with atoms in the sample • Harmonic motions look like flat background • Vibrations are often treated as Inelastic Debye-Waller Factor • Maximum of intensity is always at = 0 • Sl h f i l QSamples the component of motion along Q • Low-Q – typically less than 5 Å-1File Size: 3MB. The transport approximation has been widely used in neutron transport and radiative transfer calculations for many years. The quality of this approach has been analyzed in earlier studies by Pomraning (), Bell et al. (), Potter (), and Crosbie and Davidson (). Journal of Chemical Physics Vol Number 1, José Canosa and H. R. Penafiel Parallel shooting solution of the neutron transport equation in spherical Jr. and G. Milton Wing An invariant imbedding algorithm for the solution of inhomogeneous linear.
The neutron has a dipole moment n is times smaller than the electron moment 1. n e e m m A dipole in a magnetic field has potential energy r B r & Correspondingly the field exerts a torque and a force V B & & F B & driving the neutron parallel to high field regionsFile Size: 4MB.
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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 Applications of invariant imbedding to problems of neutron transport in a slab. book 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 Applications of invariant imbedding to problems of neutron transport in a slab.
book S. Karanjai, G. Biswas. imbedding approach is applied to a more realistic problem - that of transport through a slab, Further generalizations are Applications of invariant imbedding to problems of neutron transport in a slab.
book. 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.
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. (1) successfully used the invariant technique for the solution of problems in radiative transfer in slabs of finite thickness T'rith inotropic scattering. Ka^ivrada and Kalaba (3) ha;/e numerically solved the scalar equation of transfer for an atmosphere vrith a scatter in,a-uhaseCited by: This thesis is a study of the solutions of the equations of radiative transfer by an invariant imbedding approach.
Physical Description vi, 37,  leaves: by: 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. 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  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. You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read.
Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. The time-dependent transport. equation is also examined and it is shown that the application of the finite element method in conjunction.
with the Crank-Nicholson time discretization method results in a system of algebraic equations which is readily solved. The Chebyshev polynomial approximation (UN method) is used to solve the critical slab problem in one‐speed neutron transport theory using Marshak boundary condition.
The isotropic scattering kernel with the combination of forward and backward scattering is chosen for the neutrons in a uniform finite slab. Numerical results obtained by the UN method are presented in the tables together Author: Hakan Öztürk, Süleyman Güngör.
Get this from a library. Terrestrial radiative transfer: modeling, computation and data analysis. [Harriet H Natsuyama; Sueo Ueno; Alan P Wang] -- The remote sensing of earth from space is a nonlinear problem of estimating physical parameters from measurements.
From an analytical point of view, it is a case of radiative transfer in. Computational Methods of Neutron Transport. by E. Lewis (Author) › Visit Amazon's E. Lewis Page. Find all the books, read about the author, and more. See search results for this author. Are you an author. Learn about Author Central.
Lewis (Author Cited by: Neutron Transport - Introduction • References: G.J. Habetler & B.J. Matkowsky, Uniform asymptotic expansions in tranport theory with small mean free paths and the diffustion approximation, J.
Math. Phys. 16 () K.M. Case and P.F. Zweifel, Linear Transport Theory, Addison-Wesley, () • Neutron Motion - Boltzmann Transport Equation.
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Computational methods of neutron transport by E. Lewis,American Nuclear Society edition, in English. THE NEUTRON TRANSPORT EQUATION boundary: ~¡¡ = fx 2 ¡:~ ^n(x). Invariant Imbedding and Noncoherent Scattering in a Finite, Inhomogeneous Atmosphere.
Part of a broader investigation concerned with the diffuse reflection in an inhomogeneous layer of atmosphere. Such problems are of current interest in the fields of meteorology and astrophysics, and the detection of nuclear blasts. The homogenization of neutron pdf source problems in a finite domain with periodic structure is considered.
It is known that the solution of such problems can be factored asymptotically as the product of two terms. The first one gives the localCited by: 6.arising in neutron transport theory.
The smallest positive real eigenvalue of the problem contains valuable information about the status of the ﬁssion chain reaction in the nuclear reactor (i.e. the criticality of the reactor), and thus plays an important role in the design and safety of nuclear power stations.THE INVERSE POWER METHOD FOR Ebook FACTORS IN THE NEUTRON TRANSPORT EQUATION by ROBB M.
BERRY, Ebook. A THESIS IN MATHEMATICS Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE Approved Chairperson of the Committee Accepted May,