V. C. Boffi

Anisotropy of scattering and fission in neutron transport theory

The problems of the anisotropy of both scattering and fission and of its effects on monoenergetic neutron flux distributions are discussed for both plane and spherical symmetries. After a statement of the problem for the case of a general anisotropy, the case of a finite-order anisotropy with azimuthal symmetry is considered, and various quantities of interest are studied as a function of a parameter that appropriately accounts for the different anisotropic behaviors of scattering and fission. Numerical results for the linearly anisotropic critical case in both plane and spherical symmetries are reported and are completed with the ones obtained by asymptotic method.

Radiative transfer in an absorbing-scattering slab bounded by emitting and reflecting surfaces☆

Abstract An exact integral theory of the planar radiative transfer with isotropic scattering and general boundary conditions is presented in the paper. The analytical solution to the problem is numerically processed for two different specializations of the emissivity and reflectivity properties of the bounding surfaces. Results are given for the total and angular radiation intensities as well as for the net radiative flux.

Integral transform method in radiative transfer

Abstract A method based on integral Fourier transform technique is proposed for obtaining the radiation intensity in a nonconservative, isotropically scattering, finite slab with a general internal isotropic source and with general transparent boundary conditions. The theory of the method is first presented and it is shown to provide an exact analytical solution for the problem. Numerical results for various physical situations are then reported and compared with previous other results wherever possible. The case of the universal functions Θ(τ) and Θ g (τ) is also considered.

Evaluation of the electrical conductivity via the time-dependent integral boltzmann equation

Abstract Following the integral method developed in neutron transport theory, the exact time-dependent density distribution and current density describing electron motion under the influence of a conservative force are obtained. From the expression for the current density, the validity of Ohms law for various scattering interaction models can be verified.

Evaluation of the neutron flux-depression factor via the integral transform method

The integral transform method is used to solve a two-region problem relevant to the evaluation of a neutron flux-depression factor. For the latter, numerical results are reported for different values of the physical parameters involved and compared with those obtained through other methods.

Rigorous constructive solutions in radiative heat transfer

Abstract A method based on integral Fourier transform technique is proposed for obtaining both the total and angular radiation intensity in a nonconservative, isotropically scattering, finite slab with an internal source and with general transparent boundary conditions. The theory of the method is first presented, and it is shown to provide rigorous constructive solutions for the problem. Numerical results for various physical situations are then reported and compared with previous other results wherever possible. The case of the universal functions Θ(τ) and Θ g (τ) is also considered.

Rigorous constructive solution to monodimensional poiseuille and thermal creep flows

SommarioNella nota viene discusso un rigoroso metodo costruttivo per risolvere le equazioni integrali lineari che regolano sia il moto di Poiseuille che il moto di scorrimento termico di un gas rarefatto fra due piastre piane parallele. Per ambedue le situazioni fisiche vengono presentati vari risultati numerici connessi con la portata e con le velocità. Dove possibile, i risultati ottenuti sono confrontati con quelli disponibili nella letteratura.SummaryA rigorous constructive method is discussed for solving the linear integral equations which govern either the Poiseuille flow and the thermal creep flow of a rarefied gas between parallel plates. In both cases numerical results are presented for the nondimensionalized mass flow rate, and for certain quantities which are closely related to the mass and slip velocities. Critical comparison with previous results is made wherever possible.

Calculation of the number densities in an extended kinetic theory of gas mixtures

Abstract Analytical and numerical results for the number densities p. (t) (j=l,2,—,N) of a N-component gas mixture, including removal and self-generation effects, are presented, especially for N=2 and N=3. The dynamics of the mixture considered is also illustrated by curves describing the physical behaviour of the single p. versus t.

Methods of similarity analysis in the study of nonlinear dynamics of a gas mixture

Abstract On the basis of a Lie group analysis similarity variables are first derived, and, then, some exact invariant solutions are constructed for a semi-linear hyperbolic system governing the evolution of the number densities of a mixture of N = 2 gases of interacting particles.

Spatial effects in the study of nonlinear evolution problems of particle transport theory

Explicit analytical solutions to a nonlinear spatially inhomogeneous model Boltzmann equation are presented for a physical situation of reference, characterized by constant collision frequencies and scattering probability distributions depending only on the velocity after collision. The results obtained are approximately commented on physical grounds.