摘要:

Calculations of various integral parameters of branching transport processes (neutron counts, ionisation yield, number of defects, sputtering yield) show widely varying relative variances, such that both deeply sub-Poisson and highly over-Poisson types (even diverging ones) can occur. To understand and explain the reasons for such varied behaviour in apparently similar transport processes, the correlation structure, i.e. two-point density functions, were calculated for sputtering and defect creation, both in infinite media and half-spaces whenever applicable. The calculations were made by constant cross sections and hard-sphere scattering, employing the Khinchin-Pease damage model. It was shown that in addition to the sputtering yield, also the vacancy and interstitial yields have a highly over-Poisson variance in a half-space. The energy and spatial structure of the two-point correlations was investigated by Monte-Carlo calculations. Large positive correlations exist in the energy and depth of origin of sputtered particles. Defect correlation functions have a more complicated structure. Correlations in semi-infinite and infinite media show that the two parts of the cascade in infinite medium, separated by the injection point of the initial particle, develop nearly exclusive and independent of each other. The correlation functions presented illuminate the intrinsic laws governing the yield variances, and give some further interesting insight into the cascade dynamics.

ISSN:0041-1450    

DOI:10.1080/00411459708221772

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

In this paper we study the mathematical properties of a scaled nonlinear model for interaction of algae with light. The growth dynamics is modeled by a couple of nonlinear equations for the evolution of the concentration of algae and the light intensity, in a column of water. A diffusion model is derived applying formally the modified Chapman-Enskog expansion to the Boltzmann-like evolution system for a small parameter ϵ, proportional to the average time between successive photon-water collisions. Existence and uniqueness of a positive solution are proved, using semigroup perturbation theory.

ISSN:0041-1450    

DOI:10.1080/00411459708221773

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

It has been shown recently that the equation of diffusion in a porous medium can be obtained in a suitable scaling limit by a two velocity model of the Boltzmann equation. Here, the macroscopic equations induced by this model are investigated numerically for small values of the scaling parameter. This leads to an approximation of the solution to the porous media equation which is completely different from the usual ones. Comparison with previous numerical experiments is included.

ISSN:0041-1450    

DOI:10.1080/00411459708221774

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

In this paper two modern numerical methods for computational physics are introduced. One of them is the nonlinear Galerkin method for nonlinear partial differential equations; the approximation properties are discussed and the errors are estimated. For the other one the Schwarz algorithm for the neutron transport equation is constructed, and the convergence properties are proved.

ISSN:0041-1450    

DOI:10.1080/00411459708221775

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

In this paper, the spectral properties of the one-velocity transport operator and the streaming operator with integral boundary condition of Maxwell type in a sphere are considered. It is proved that the streaming operator and the transport operator are the infinitesimal generators of positive Co semigroups.

ISSN:0041-1450    

DOI:10.1080/00411459708221776

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

This paper was presented at the 14th International Conference on Transport Theory in Beijing. Its aim is to compare various approaches to the asymptotic analysis of linear Boltzmann equation with and without an external field discussing their availability, advantages and limitations.

ISSN:0041-1450    

DOI:10.1080/00411459708221777

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The expansion method in the kinetic theory of gases is often used for the calculation of entropy production in rarefied gas flows, usually in terms of Her-mite polynomials. In this paper, the method of Sonine polynomials expansion is used and the calculation of entropy production is carried out. First, the formal evaluation of the entropy production in rarefied gas flows is introduced. Then the calculation of the entropy production for arbitrary molecules with spherically symmetric intermolecular forces by Sonine polynomials expansion is presented and the formula for entropy production in the thirteen-moment approximation is obtained. It is shown that the entropy production can be expressed as a linear combination of square terms in the thirteen-moment approximation. This formula can be applied to slightly rarefied gas flows.

ISSN:0041-1450    

DOI:10.1080/00411459708221778

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The Boltzmann equation, which is central to the description of many linear and nonlinear transport processes, is the equation of an ideal gas of point molecules. The Enskog equation was proposed to model the finite diameter of molecules of real gases, but does not include the effects of intermolecular potentials. We describe some models which include a finite range approximation of such intermolecular potentials. In particular, we outline the existence of weak global-in-time solutions for a kinetic equation with piecewise constant intermolecular potential.

ISSN:0041-1450    

DOI:10.1080/00411459708221779

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

In this paper, we consider the nonlinear transport equation with delayed neutrons. By means of the tneory of nonlinear perturbations ofCo-semigroups, the existence and uniqueness of the mild solution, strong solution and local solution inLp(1 ≤p< +00) are proved. It is showed that the mild solution of this equation can be constructed by iterative method. The convergence speed of the iterative solution is also estimated.

ISSN:0041-1450    

DOI:10.1080/00411459708221780

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The control system of a nuclear reactor is an important distributed parameter system governed by the neutron transport equation. This paper summarizes part of the authors and their colleagues' recent work on this subject, including the spectral analysis of the neutron transport operator, the asymptotic stability theory of the solution of the time dependent transport equation, the convergence of the discrete-ordinate method for the time dependent neutron transport equation, the optimal control and identification problems arising from the nuclear reactor, etc.

ISSN:0041-1450    

DOI:10.1080/00411459708221781

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor