# TRANSPORT THEORY AND SPECTRAL PROBLEMS

## Abstract

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. Generalizations to a large class of transport problems are discussed. The nonlinear timedependent operator for transport in one dimension is considered in detail. It has a pure point spectrum, and expansion theorems can be proved. These results contrast with those for isotropic one-velocity neutron transport in the infinite slab. Here there are only a finite number of points in the point spectrum, with a halfplane in the continuous spectrum. Approximations to the eigenvalues and eigenfunctions for the slab case, as well as extensions to the multivelocity problem, are mentioned. There is a brief discussion of recent spectral and expansion theorems for very general geometries. (auth)

- Authors:

- Publication Date:

- Research Org.:
- New Mexico. Univ., Albuquerque

- OSTI Identifier:
- 4259132

- Report Number(s):
- SCR-88

- NSA Number:
- NSA-13-018477

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Presented at American Mathematical Society Symposium on Reactor Theory, New York, April 1959. Orig. Receipt Date: 31-DEC-59

- Country of Publication:
- United States

- Language:
- English

- Subject:
- PHYSICS AND MATHEMATICS; CONFIGURATION; NEUTRON FLUX; NEUTRONS; NUMERICALS; SPECTRA; TRANSPORT THEORY; VARIATIONS; VELOCITY

### Citation Formats

```
Wing, g. M.
```*TRANSPORT THEORY AND SPECTRAL PROBLEMS*. United States: N. p., 1959.
Web. doi:10.2172/4259132.

```
Wing, g. M.
```*TRANSPORT THEORY AND SPECTRAL PROBLEMS*. United States. https://doi.org/10.2172/4259132

```
Wing, g. M. 1959.
"TRANSPORT THEORY AND SPECTRAL PROBLEMS". United States. https://doi.org/10.2172/4259132. https://www.osti.gov/servlets/purl/4259132.
```

```
@article{osti_4259132,
```

title = {TRANSPORT THEORY AND SPECTRAL PROBLEMS},

author = {Wing, g. M.},

abstractNote = {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. Generalizations to a large class of transport problems are discussed. The nonlinear timedependent operator for transport in one dimension is considered in detail. It has a pure point spectrum, and expansion theorems can be proved. These results contrast with those for isotropic one-velocity neutron transport in the infinite slab. Here there are only a finite number of points in the point spectrum, with a halfplane in the continuous spectrum. Approximations to the eigenvalues and eigenfunctions for the slab case, as well as extensions to the multivelocity problem, are mentioned. There is a brief discussion of recent spectral and expansion theorems for very general geometries. (auth)},

doi = {10.2172/4259132},

url = {https://www.osti.gov/biblio/4259132},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1959},

month = {5}

}