INVARIANT IMBEDDING AND NEUTRON TRANSPORT THEORY. V: DIFFUSION AS A LIMITING CASE

Abstract

Diffusion theory classically has been regarded as an approximation to the more rigorous (but, of course, not completely rigorous) transport theory under the assumption of high velocity and small mean free path. Furthermore, passage to the limit in the 'telegrapher's equation,' a linear partial differential equation of hyperbolic type, has been carried out. The limits are studied of the non-linear functional equations obtained from the transport processes with finite velocity as the velocity increases without bound. Corresponding results are obtained for heat or diffusion processes, where the physical picture is not as clear. The equations can be interpreted in such a way as to be derived by invariant imbedding techniques. In all cases, the equations are of the generalized Riccati type which are characteristic of these processes of mathematical physics.

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Document Details

Document Type
Technical Report
Publication Date
Nov 09, 1959
Accession Number
AD0616403

Entities

People

  • G. M. Wing
  • Richard E. Bellman
  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Collisions
  • Corporations
  • Differential Equations
  • Diffusion
  • Diffusion Theory
  • Equations
  • Formulas (Mathematics)
  • Mathematics
  • Mean Free Path
  • New Mexico
  • Partial Differential Equations
  • Probability
  • Random Walk
  • Transport Ships

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Plasma Physics / Magnetohydrodynamics