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### A new method for numerical solution of checkerboard fields.

Journal of Applied Mathematics

### Correctors and error estimates in the homogenization of a Mullins–Sekerka problem

Annales de l'I.H.P. Analyse non linéaire

### Homogenization and diffusion asymptotics of the linear Boltzmann equation

ESAIM: Control, Optimisation and Calculus of Variations

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 coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.

### Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation

ESAIM: Control, Optimisation and Calculus of Variations

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 coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.

### Homogenization of micromagnetics large bodies

ESAIM: Control, Optimisation and Calculus of Variations

A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies$\phantom{\rule{-17.07164pt}{0ex}}{ℰ}_{\epsilon }\left(m\right)={\int }_{\Omega }\phi \left(x,\frac{x}{\epsilon },m\left(x\right)\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x-{\int }_{\Omega }{h}_{e}\left(x\right)·m\left(x\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x+\frac{1}{2}{\int }_{{ℝ}^{3}}{|\nabla u\left(x\right)|}^{2}\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x$of a large ferromagnetic body is obtained.

### Homogenization of micromagnetics large bodies

ESAIM: Control, Optimisation and Calculus of Variations

A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies ${ℰ}_{\epsilon }\left(m\right)={\int }_{\Omega }\phi \left(x,\frac{x}{\epsilon },m\left(x\right)\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x-{\int }_{\Omega }{h}_{e}\left(x\right)·m\left(x\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x+\frac{1}{2}{\int }_{{ℝ}^{3}}{|\nabla u\left(x\right)|}^{2}\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x$ of a large ferromagnetic body is obtained.

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