Displaying similar documents to “Homogenization of a spectral equation with drift in linear transport”

Homogenization of a spectral equation with drift in linear transport

Guillaume Bal (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper deals with the homogenization of a spectral equation posed in a periodic domain in linear transport theory. The particle density at equilibrium is given by the unique normalized positive eigenvector of this spectral equation. The corresponding eigenvalue indicates the amount of particle creation necessary to reach this equilibrium. When the physical parameters satisfy some symmetry conditions, it is known that the eigenvectors of this equation can be approximated...

Homogenization of the criticality spectral equation in neutron transport

Grégoire Allaire, Guillaume Bal (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. One term is the first eigenvector of the transport equation in the periodicity cell. The other...

Fourier approach to homogenization problems

Carlos Conca, M. Vanninathan (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems...