摘要:

Previously reported elementary solutions of the linear transport equation for an exponential scattering ratio c(z) = coe−z/sare shown to be complete on the range [−s/(s+1),1] provided coand s satisfy a certain inequality; thus these eigenfunctions areincompleteon the full range [−1,1]. A new set of elementary solutions with a larger spectrum is constructed and completeness is proved for the larger interval [−l,l]–but from which two certain subintervals of arbitrarily small width have been deleted, again provided coand s satisfy a certain inequality. Other half-range completeness questions are also addressed.

ISSN:0041-1450    

DOI:10.1080/00411458208230838

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

A singular integral equation has been derived (and solved numerically, by the FNmethod), which the unknown fluxes exiting a finite slab must satisfy. Here we prove analytically that this equation has a unique solution, and thus, that it uniquely determines the exiting fluxes.

ISSN:0041-1450    

DOI:10.1080/00411458208230839

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The purpose of this note is to establish an existence and uniqueness theorem for the spherically and azimuthally symmetric steady-state linear transport equation. The methods used are similar to those of Olhoeft1for bounded three-dimensional geometry and of Nelson2for linear transport in a slab. Our basic result contains the corollary that, for very general scattering laws, nonmultiplying transport of linear particles in a spherically and azimuthally symmetric situation necessarily is subcritical. This should be contrasted with the example due to Nelson2of critical nonmultiplying linear transport in a slab. Our result also, when combined with that of Olhoeft1(see also 3 Theorem 12 of Case and Zweifel3) establishes rigorously that the linear transport equation subject to spherically and azimuthally symmetric data has a solution that also enjoys these symmetries. Finally, we note that our basic technique should have application to the extension to spherical geometry of convergence results known for the discrete-ordinates method in other settings.4–10We have in mind here both the classical SNapproach in which the differential angular redistribution operator is angularly discretized along with the scattering integral, and the more recent workl3–15employing angular discretization along with the method of characteristics.

ISSN:0041-1450    

DOI:10.1080/00411458208230840

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The mathematical formulation of the Porous Media System, (PMS) describing two-phase, immiscible, compressible, fluid flow in linear, homogeneous porous media is reviewed and expanded. It is shown that families of common vertex, coaxial parabolas and families of parallel lines are the only families of curves on which solutions of the PMS may be constant. A coordinate transformation is used to change the partial differential equations of the PMS to a system of ordinary differential equations, referred to as a Similarity Porous Media System (SPMS), in which the independent variable denotes movement from curve to curve in a selected family of curves. Properties of solutions of the first boundary value problem are developed for the SPMS.

ISSN:0041-1450    

DOI:10.1080/00411458208230841

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

We discuss the difficulties of using quasiclassical methods to describe two time correlation functions for spin systems. We show that there is an inherent difficulty in deriving quasiclassical equations of motion. In particular, we show that for the two spin case the equivalents of the Heisenberg operators S∼j(t) satisfy equations which deviate dramatically from what one would expect for classical equations.

ISSN:0041-1450    

DOI:10.1080/00411458208230842

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The seventh in the continuing series of Sitges Conferences in Statistical Physics convened during the second week of September at that outstanding Spanish seaside resort. The unusual late summer date was due, of course, to an equally important event: the World Cup soccer matches held in Barcelona and Madrid. It is envisioned that the next Sitges Conference will again be in early summer.

ISSN:0041-1450    

DOI:10.1080/00411458208230843

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411458208230844

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor