摘要:

In the medical discipline of radiation oncology, collimated beams of high-energy radiation are directed toward malignant tumor sites. The objective is twofold: (i) to deliver a sufficiently strong dose to the tumor to ensure with high probability that it is “controlled,” and (ii) to deliver a sufficiently weak dose to the surrounding healthy tissue to ensure with high probability that complications will not occur. In solving this optimization problem, medical physicists use a sequence of computer-generated 3-D transport (dose) calculations that simulate the effects of radiation beams penetrating through human tissue. This paper briefly reviews the concepts that underlie radiation oncology, some current numerical algorithms for performing dose calculations, and open problems.

ISSN:0041-1450    

DOI:10.1080/00411459708224421

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

A systematic theory for the simultaneous homogenization of lattice cells and fuel assemblies and a self-consistent debomogenization theory for the reconstruction of the heterogeneous transport flux are developed simultaneously by introducing three spatial scales into the neutron transport equation for a three-dimensional heterogeneous medium, and carrying out an analysis based on an asymptotic expansion. The development provides both a theoretical basis and practical homogenization and dehomogenizaion procedures for use in coarse-mesh nodal diffusion calculations, and it yields: a lattice-cell homogenized diffusion equation for a fuel assembly with consistent definitions of the homogenized diffusion tensor, homogenized cross sections, and flux discontinuity factors at the lattice cell interfaces; an assembly-homogenized global diffusion equation with consistent definitions of the homogenized diffusion tensor, homogenized cross sections, and flux discontinuity factors at the fuel assembly interfaces; and a self-consistent de-homogenization procedure for the reconstruction of the local heterogeneous transport theory fluxes.

ISSN:0041-1450    

DOI:10.1080/00411459708224422

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

For a general class of collision operators, we show that the stationary boundary valve problem of the one dimensional linear Boltzmann equation on a finite intcrvall including an arbitrarily high constant external force can be solved analytically (apart form an inverse Laplace transform) at zero temperature of the host medium. As a byproduct we obtain existence, positivity and uniqueness of the solution. Our method also applies to coupled initial-boundary value problems, for which we demonstrate the decay to the solution of the stationary boundary value problem.

ISSN:0041-1450    

DOI:10.1080/00411459708224423

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The Mathematics Research Institute at Oberwolfach (Germany) hosted the third meeting of the aeries entitled “Nonlinear Equations in Many-Particle Systems”, which WPM organized by J. Batt (Munich) and C. Cercignani (Milano). The meeting wm attended by forty speakers from Germany, Canada, Italy, Sweden, fiance, Spain, Russia, India, Japan, and the United State. There were four main themes.

ISSN:0041-1450    

DOI:10.1080/00411459708224424

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor