Physical, mathematical and numerical models in nonlinear electromagnetism

Below the list of all the themes I have studied or I am currently studying. Subjects:

1. Optics
2. Micromagnetism
3. Molecular dynamics
4. Asynchronous signal processing
5. Finite Volumes for Maxwell equations
6. Plasma Physics
7. Invariant Measures

1. Optics (1993–)

Quantum optics

Themes: Study of the Maxwell–Bloch system. Introduction of physical relaxation terms. Conception and implementation of time numerical schemes that preserve physical properties.
Collaborators: Antoine Bourgeade (CEA-CESTA), Pierre Degond (MIP, Toulouse), and Richard W. Ziolkowski (University of Arizona).
Students: PhD: Didier Reignier, co-adviser of Olivier Saut.
Publications: [A.6], [A.10], [A.11], [L.3], [P.3], [P.4].

Quantum dots

Themes: Models for quantum dots. Caracterization.
Collaborators: Éric Bonnetier (LJK).
IMAG project Physique des Interactions Fines
Students: PhD: Chokri Ogabi.
Publications: [A.17].

Asymptotics for quantum models

Themes: Schrödinger–Bloch model. Local Cauchy problem, and global in the adiabatic case. Convergence to rate equations.
Collaborations: François Castella (IRMAR, Rennes), Pierre Degond (MIP, Toulouse), Éric Dumas (Institut Fourier, Grenoble), and Marguerite Gisclon (LAMA, Chambéry).
Publications: [A.12], [A.13].

Classical models

Themes: Maxwell–Debye model. Maxwell–Lorentz model. Stability of FDTD schemes.
Publications: [A.15], [P.5], [R.2].

Classical models in the paraxial approximation

Themes: Schrödinger–Debye model. Local Cauchy problem. Numerical methods, relaxation and splitting methods. Order for splitting methods.
Collaborators: Christophe Besse (MIP, Toulouse) and Stéphane Descombes (UMPA, ENS de Lyon).
Publications: [A.0], [A.4], [A.5], [A.7], [A.8].

Models for photorefractive materials

Themes: Dimensionless physical models. Cauchy problem. Stability of bright and dark solitons.
Collaborators: Jean-Claude Saut (Orsay University).
Publications: [A.14], [P.6].

Sub-wavelength gratings

Themes: Impact of metal boundary condition on cavity modes. Case of Kerr material filled cavities.
Collaborators: Aude Barbara and Pascal Quémerais (Institut Néel, Grenoble), and Éric Dumas (Institut Fourier, Grenoble).
Project: UJF MSTIC project: MADISON.
Publications: [A.18], [P.8].

2. Micromagnetism (2008–)

Micromagnetism

Themes: Derivation of a mesoscopic model. Identification of the damping term.
Collaborators: Stéphane Labbé (LJK).
Project: RTRA Nanosciences project: HM-MAG.

3. Molecular dynamics (2009–)

Quantum models in molecular dynamics

Themes: Adaptive sampling. Quantum models.
Collaborators: Stéphane Redon (LJK, INRIA project NANO-D).
Student: Maël Bosson.

4. Asynchronous Signal Processing (2002–)

Filtering and spectral analysis

Themes: Interpolation of asynchronous signals. IIR Filters. Fourier Analysis.
Collaborators: Fabien Aeschlimann, Laurent Fesquet, and Saeed Mian Qaisar (TIMA, Grenoble), and Nicolas Marchand and Carlos Canudas de Wit (Gipsa-Lab, Grenoble).
Project: UJF MSTIC project: TATIE.
Publications: [A.16], [P.7], [P.9].

5. Finite volumes for Maxwell equations (1995–2001)

Genuine multidimensional methods

Themes: Genuine multidimensional corrections to cell-centered schemes for Maxwell equations.
Collaborators: Jean-Michel Ghidaglia (ENS de Cachan) and Maria Lukacova (Universities of Magdeburg and Brno).
Publications: [A.9], [P.2], [R.1].

6. Plasma physics (1991–1995)

Nonlocal Zakharov system

Themes: Study of the local Cauchy problem. Limit to the nonlocal nonlinear Schrödinger equation. Study of the envelope approximation.
Collaborators: Thierry Colin (University of Bordeaux I) and Luc Bergé (CEA).
Publications: [A.1], [A.3], [P.1].

7. Invariant measures (1992–1993)

Invariant measures for Hamiltonian systems

Themes: Poincaré recurrence for Hamiltonian systems. Construction of Gaussian measures on phase spaces. Application to Schrödinger, wave and Zakharov equations and to numerical schemes.
Publications: [A.2].