No production of entropy in the Euler fluid
We derive the Euler equations as the hydrodynamic limit of a stochastic model of a hard-sphere gas. We show that the system does not produce entropy.
Nouveaux algorithmes performants en théorie du transport
Numerical study of the systematic error in Monte Carlo schemes for semiconductors
The paper studies the convergence behavior of Monte Carlo schemes for semiconductors. A detailed analysis of the systematic error with respect to numerical parameters is performed. Different sources of systematic error are pointed out and illustrated in a spatially one-dimensional test case. The error with respect to the number of simulation particles occurs during the calculation of the internal electric field. The time step error, which is related to the splitting of transport and electric field...
On a class of nonlinear integral equations arising in neutron transport.
On numerical solution to the problem of reactor kinetics with delayed neutrons by Monte Carlo method
In this paper, the linear problem of reactor kinetics with delayed neutrons is studied whose formulation is based on the integral transport equation. Besides the proof of existence and uniqueness of the solution, a special random process and random variables for numerical elaboration of the problem by Monte Carlo method are presented. It is proved that these variables give an unbiased estimate of the solution and that their expectations and variances are finite.
On steady-state carrier distributions in semiconductor devices
The author proves the existence of solution of Van Roosbroeck's system of partial differential equations from the theory of semiconductors. His results generalize those of Mock, Gajewski and Seidman.
On the approximate solution of the multi-group time-dependent transport equation by -method
This paper concerns -velocity model of the general linear time-dependent transport equation. The assumed probability of the collision (scattering, fission) depends only on the angle of the directions of the moving neutron before and after the collision. The weak formulation of the problem is given and a priori estimates are obtained. The construction of an approximate problem by -method is given. In the symmetric hyperbolic system obtained by -method dissipativity and -orthogonality of the relevant...
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann type, yet...
On the Lax-Phillips scattering theory for transport equation
On the number of solutions of some integral equations arising in radiative transfer.
On the Transport-Diffusion Algorithm and Its Applications to the NavierStokes Equations.
On three problems of neutron transport theory
In this paper, the initial-value problem, the problem of asymptotic time behaviour of its solution and the problem of criticality are studied in the case of linear Boltzmann equation for both finite and infinite media. Space of functions where these problems are solved is chosen in such a vay that the range of physical situations considered may be so wide as possible. As mathematical apparatus the theory of positive bounded operators and of semigroups are applied. Main results are summarized in...
On two-dimensional hamiltonian transport equations with Llocp coefficients
Periodicity and transport from round-off errors.
Point Approximation of a Space-Homogeneous Transport Equation.
Product Integration for the Linear Transport Equation in Slab Geometry.
Properties of operators related to the Boltzmann collision term
Quantum Dynamics and generalized fractal dimensions: an introduction
We review some recent results on quantum motion analysis, and in particular lower bounds for moments in quantum dynamics. The goal of the present exposition is to stress the role played by quantities we shall call Transport Integrals and by the so called generalized dimensions of the spectral measure in the analysis of quantum motion. We start with very simple derivations that illustrate how these quantities naturally enter the game. Then, gradually, we present successive improvements, up to most...
Quelques applications de la positivité en théorie du transport