摘要:

In this paper we review analytic solution methods for the problem of a monoenergetic pencil beam of radiation impinging perpendicularly upon a thin source-free slab, infinite in the transverse directions. If the scattering is highly peaked in the forward direction, and if the slab is sufficiently thin, this beam will remain nearly collimated as it passes through the slab. Making the continuous slowing down and straightahead approximations, the energy variable can be analytically eliminated from the problem. If a simplified Fokker-Planck approximation in angle is introduced into the resulting monoenergetic transport equation, a very simple analytic solution is possible. This result for the scalar flux is known as the Fermi-Eyges solution, and is Gaussian in radius. For scattering phase functions which do not admit a Fokker-Planck representation in angle, a very recent formalism is discussed for addressing this monoenergetic problem. A classic example is the widely used Henyey-Greenstein scattering phase function, and in this case an analytic solution, algebraic in radius, is obtained for the scalar flux. For screened Rutherford scattering, this formalism leads to a quadrature result for the scalar flux. An asymptotic numerical evaluation of this result shows good agreement with benchmark Monte Carlo calculations.

ISSN:0041-1450    

DOI:10.1080/00411450008205859

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

The solution to the age-old infinite medium Green's function is revisited using the hindsight of the past coupled with the wisdom of the present. A new solution is found based on a blend of the theories developed by F. Vanmassenhove and C. Grosjean, E. Inonu, K. Case and J. Mika. The solution is obtained from well-known recurrence relations and is shown to reduce to the singular eigenfunction representation of Case. Closure is shown to be a consequence of the infinite medium Green's function.

ISSN:0041-1450    

DOI:10.1080/00411450008205860

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

A self consistent gauge theory of Classical Lagrangian Mechanics, based on the introduction of the bundle ofaffine scalarsover the configuration manifold is proposed. In the resulting set-up, the “Lagrangian”Lis replaced by a section of a suitable principal fiber bundle over the velocity space, called the lagrangian bundle, while the associated Poincaré-Cartan 2-form is recognized as the curvature 2-form of a connection induced byLon a second “co-lagrangian” principal bundle. A parallel construction leads to the identification of a hamiltonian and a co-hamiltonian bundle over the phase space. An analysis of the properties of these spaces provides an intrinsic geometrical characterization of the Legendre transformation, thus allowing a systematic translation of the hamiltonian formalism into the newer scheme.

ISSN:0041-1450    

DOI:10.1080/00411450008205861

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In the paper we give a survey on the transition from kinetic theory to macroscopic fluid equations, where the macroscopic equations are defined as asymptotic limits of a kinetic equation. This relation can be used to derive computationally efficient domain decomposition schemes for the simulation of rarefied gas flows close to the continuum limit. Moreover, we present some basic ideas for the derivation of kinetic induced numerical schemes for macroscopic equations, namely kinetic schemes for general conservation laws as well as Lattice—Boltzmann methods for the incompressible Navier—Stokes equations.

ISSN:0041-1450    

DOI:10.1080/00411450008205862

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In this expository paper we discuss the role of probability in statistical physics: it should be that of a general tool guiding induction andmust not be restricted only to the empirical interpretationcoming from itsevaluationby an observed frequency. It is true that in many cases thevalueof a probability can be sensibly expressed by a suitable frequency, but this does not entails that the latter can be taken asdefinitionof probability. Moreover, in each situation in which one thinks that probabilities are physically real things and believes that something which is only “very probable” can be regarded as being “practically certain”, some “small” probabilities are actually ignored: this attitude of mind may render illegitimate also the probabilistic interpretation of the relevant physical laws. A “law” which is based on a probabilistic interpretation cannot aim at explainingwhy a fact that we forecast will occur, but rather at explainingwhy we forecast that this fact will occur. Finally, we emphasize the role ofconditionalprobability, and we show that looking at it from the right perspective allows to avoids also classic paradoxical aspects of quantum mechanics, without the need to resort to the interpretation based on the dualism “particle-wave”.

ISSN:0041-1450    

DOI:10.1080/00411450008205863

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

This paper deals with the analysis of a class of models of population dynamics with competition and kinetic interactions. Several models are proposed to describe the dynamics of large populations of individuals undergoing kinetic (stochastic) interactions which modify the states of the interacting pair. Models are characterized by time and space structure, and are motivated by recent research activity in mathematical immunology. The evolution equations are stated in terms of nonlinear integrodifferential equations which are similar to the Boltzmann equation. This paper deals with modelling and qualitative analysis of the related Cauchy problem.

ISSN:0041-1450    

DOI:10.1080/00411450008205864

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Extended discrete kinetic theory including sources, sinks, creation and absorption of test particles, inelastic scattering,… added to the elastic collisions, was introduced by Boffi and Spiga. For the mass conservation law (or momentum, energy), polynomials of the mass (or densities) are added, leading to a lack of conservation equations. We consider models with linear nonconservative terms, LNC (Spiga- Platkowski) and quadratic, QNC (Piechor-Platkowski). For quasi-linear systems of PDE (linear differential terms and quadratic nonlinearities), we present a general formalism for the determination of stationary, similarity, periodic and (1 + 1) dimensional exact solutions in one space variable. We present results for the two-velocity, the two and three dimensional Broadwell, the hexagonal 6viand the two-squares 8viDVMs (Discrete Velocity Models). The similarity solutions are obtained from the compatibility between different scalar nonlinear Riccati equations (NLODE), Firstly, we apply this method to the similarity solutions of the QNC models, while for (1 + 1) solutions only one density is not constant.

ISSN:0041-1450    

DOI:10.1080/00411450008205865

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Over the last two decades anomalous relaxation and diffusion processes have been studied from both the experimental and theoretical point of view. Anomalous transport processes occur usually in so-called complex, i.e. in disordered systems. Here, we review some recent developments in modeling non-standard relaxation and diffusion equations based on Riemann-Liouville fractional calculus techniques. Closed analytical expressions of the solutions of such fractional differential equations are given in terms of Fox's H-functions. The analytical calculations carried out are fully supported by ourMathematicapackageFractional Calculus.

ISSN:0041-1450    

DOI:10.1080/00411450008205866

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

An estimate for the thickness and temperature of a vertical sheet of cold ice1, given data on only two points of the upper boundary, is performed. The temperature continuous dependence with respect to the data in a suitable weightedL2—norm is studied.

ISSN:0041-1450    

DOI:10.1080/00411450008205867

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

We present some recent models describing the flow of mineral oils with a high content of paraffin at temperature below thecloud point(i.e. the crystallization temperature of paraffin) and more specifically below thepour pointat which the crystals aggregate and the oil takes a jel-like structure. From the rheological point of view such a system can be modelled as a Bingham fluid whose parameters evolve according to the volume fraction of crystallized paraffin and the aggregation degree of crystals. The problem is not studied in its full generality since a number of different situations can arise presenting various degrees of complexity. Therefore many questions remain open for further research.

ISSN:0041-1450    

DOI:10.1080/00411450008205868

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor