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Homogenization And Diffusion Asymptotics Of The Linear Boltzmann Equation
, 2003
"... We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coecients may depend on both slow and fast variables. Passing to the limit, we are led to an ef ..."
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We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coecients may depend on both slow and fast variables. Passing to the limit, we are led to an effective driftdiffusion equation. We also describe the diffusive behaviour when the equilibrium function has a nonvanishing flux.
An optimality condition for the assembly distribution in a nuclear reactor Laurent Thevenot
, 2003
"... We give here an optimality condition for the optimization problem of the assembly distribution in a nuclear reactor, by using the homogenization method. In this paper the reactivity of the reactor core is measured by the critical eigenvalue for both continuous and multigroup neutron transport modeli ..."
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Cited by 4 (0 self)
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We give here an optimality condition for the optimization problem of the assembly distribution in a nuclear reactor, by using the homogenization method. In this paper the reactivity of the reactor core is measured by the critical eigenvalue for both continuous and multigroup neutron transport modelings. In particular, we extend the spectral theory of the critical eigenvalue and prove the dierentiability of this latter with respect to the design parameter, the con guration of the fuels. MS Classi cation: 49K20, 49J50, 35P05, 35F15. Key words: Neutron Transport, Nuclear Reactor, Optimization, Optimality Condition, Homogenization, Critical Eigenvalue, Eigenvalue Derivative.
Anisotropic Diffusion of Neutral Particles in Stochastic Media
, 2009
"... ii ACKNOWLEDGEMENTS I must first thank Marco Túllio Vilhena, for showing me the way to the fascinating subject of transport theory. I am fortunate to have had him as a teacher; I am proud to have him as a mentor; and I am delighted to have him as a friend. I am immensely grateful to Ed Larsen, with ..."
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Cited by 2 (2 self)
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ii ACKNOWLEDGEMENTS I must first thank Marco Túllio Vilhena, for showing me the way to the fascinating subject of transport theory. I am fortunate to have had him as a teacher; I am proud to have him as a mentor; and I am delighted to have him as a friend. I am immensely grateful to Ed Larsen, without whom I would probably have stayed in Brazil. As my “transcontinental ” coadvisor during my Masters, he encouraged me to focus on the subject of transport in stochastic media, which has been a fabulous journey. He is the reason I came to work in the United States, and in every step of the way he has shown me what a monumentally wise decision that was. His patience, kindness, and dedication were always beyond the call of duty; I will be forever indebted to him for the confidence he has put in me. I should also mention that, thanks to him, Michigan Ice Hockey has gained another fervent fan. I am deeply thankful to Charlie Doering, who has most kindly accepted me as a student and guided me through the tortuous ways of an interdisciplinary program. I have profited
IOS Press Homogenization of a neutronic multigroup evolution model
"... Abstract. In this paper is studied the homogenization of an evolution problem for a cooperative system of weakly coupled elliptic partial differential equations, called neutronic multigroup diffusion model, in a periodic heterogenous domain. Such a model is used for studying the evolution of the neu ..."
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Abstract. In this paper is studied the homogenization of an evolution problem for a cooperative system of weakly coupled elliptic partial differential equations, called neutronic multigroup diffusion model, in a periodic heterogenous domain. Such a model is used for studying the evolution of the neutron flux in nuclear reactor core. In this paper, we show that under a symmetry assumption, the oscillatory behavior of the solutions is controled by the first eigenvector of a multigroup eigenvalue problem posed in the periodicity cell, whereas the global trend is asymptotically given by a homogenized evolution problem. We then turn to cases when the symmetry condition is not fulfilled. In domains without boundaries, the limit equation for the global trend is then a homogenized transport equation. Alternatively, we show that in bounded domains and with well prepared initial data, the microscopic scale does not only control the oscillatory behavior of the solutions, but also induces an exponential drift. 1.
Homogenization of a nonlinear transport equation
"... In this paper, we investigate the homogenization of a nonlinear kinetic equation modeling electron transport in semiconductors. We compute effective scattering coefficients for medium with periodic inhomogeneities. Keywords: ..."
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In this paper, we investigate the homogenization of a nonlinear kinetic equation modeling electron transport in semiconductors. We compute effective scattering coefficients for medium with periodic inhomogeneities. Keywords:
Adjusted LevermorePomraning equations for diffusive random systems
"... in slab geometry ..."
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GUIDING CENTER DRIFT INDUCED BY HOMOGENIZATION
, 2011
"... The guiding center drift induced by the homogenization of the Lorentz forces is studied. It generates memory effects. The memory (or nonlocal) kernel is described by the Volterra integral equation. The memory kernel can be characterized explicitly in terms of a Radon measure. It describes the extra ..."
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The guiding center drift induced by the homogenization of the Lorentz forces is studied. It generates memory effects. The memory (or nonlocal) kernel is described by the Volterra integral equation. The memory kernel can be characterized explicitly in terms of a Radon measure. It describes the extra velocity drift. By way of velocity drift, we view the Gauss’s law with polarization charges.