|Statement||by R.E. Bellman (et al.).|
|Series||Modern analytic and computational methods in science and mathematics|
|Contributions||Bellman, Richard, 1920-1984.|
Proceedings of the Summer Workshop on Invariant Imbedding held at the University of Southern California, June – August Usually dispatched within 3 to 5 business days. Imbedding is a powerful and versatile tool for problem solving. Rather than treat a question in isolation, we view it as a member of a family of related problems. Bellman, R., R. Kalaba, and G.M. Wing: (a) ‘On the Principle of Invariant Imbedding and Neutron Transport Theory–I’, Journal of Mathematics and Mechanics 7 (), (b) ‘On the Principle of Invariant Imbedding and Neutron Transport Theory–II’, Journal of Mathematics and Mechanics 7 ()3 Google Scholar. All rights of reproduction in any form reserved. INVARIANT IMBEDDING 2. A SCATTERING PROCESS Our base process is an idealized transport process which may be described briefly in the following terms. N different types of particles move in either direction along a line of finte length, by: 7. In a recent series of papers, based on the principle of invariant imbedding, which stems from the invariance principles of Ambarzumian and Chandrasekhar, various kinds of time-dependent neutron-transport problems in a fixed rod of finite length made of fissionable material were exactly treated by Bellman and Kalaba [l] and Wing .
In this chapter we will deal with time dependent transport of particles in a medium with given parametric values describing the interaction of the particles with the medium. Imbedding methods to study the emergent beams are dealt with in detail. Laplace transform techniques are also applied to arrive at the solutions both internal and by: 9. The boundary effects on time-dependent transport equations are discussed. The general results are applicable to problems of transmission-line theory, radiative transfer, and neutron transfer in slab geometry. A specific example of the time-dependent problem for particles moving in a rod is by: 2. Abstract. The principle of invariance, more widely known as invariant imbedding, is a powerful method of analyzing linear systems. The principle of invariance was first used by Ambarzumian , and Chandrasekhar  who later extended the work of by: 8. A~~endix A. The method of invariant imbedding The initial conditions can depend on the problem, but are normally taken to bc T(0) = 1, and R(0) = 0. Another physically appealing method to derive the above equations is the follow- ing graphical method. Consider File Size: KB.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 9, () Invariant Imbedding and Time-Dependent Scattering of Light in a One-Dimensional Medium RICHARD BELLMAN, ROBERT KALABA, AND SUEO NO The Rand Corporation, Santa Monica, California I. INTRODUCTION In a recent series of papers, based on the principle of invariant imbedding, which Cited by: 4. Invariant Imbedding T-matrix Method for Light Scattering by Nonspherical and Inhomogeneous Particles propels atmospheric research forward as a resource and a tool for understanding the T-Matrix method in relation to light scattering. The text explores concepts ranging from electromagnetic waves and scattering dyads to the fundamentals of the T-Matrix method. Invariant Imbedding and Time-Dependent Transport Processes-Diffuse Reflection with Delta-Function Input by Richard Ernest Bellman, H. H. Natsuyama, Robert E. Kalaba CitationAuthor: Richard Ernest Bellman, H. H. Natsuyama, Robert E. Kalaba. The concept of invariant imbedding constitutes an expansion of the original problem, while the quasilinearization technique represents an iterative approach. Quasilinearization is purely numerical, while invariant imbedding constitutes a completely different formulation of the original problem.