UMR 5224

Brigitte Bidégaray-Fesquet — Research themes and main results


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

  1. Optics
  2. Non Uniform Signal Processing
  3. Micromagnetism
  4. Discrete Lattices
  5. Molecular Dynamics
  6. Finite Volumes for Maxwell Equations
  7. Plasma Physics
  8. 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, Kole Keita.
Publications: [A.17], [A.20].
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.23], [P.8].

2. Non Uniform Signal Processing (2002–)

Filtering and spectral analysis
Themes: Interpolation of asynchronous signals. IIR Filters. Fourier Analysis. Filter design.
Collaborators: Fabien Aeschlimann, Laurent Fesquet, and Saeed Mian Qaisar (TIMA, Grenoble), Nicolas Marchand and Christophe Prieur (Gipsa-Lab, Grenoble).
Project: UJF MSTIC projects: TATIE, OASIS, Persyval-lab exploratory project CEE.
Publications: [A.16], [A.18], [A.22], [A.24], [P.7], [P.9], [P.10], [P.11].

3. Micromagnetism (2008–)

Themes: Derivation of a mesoscopic model. Identification of the damping term.
Collaborators: Stéphane Labbé (LJK).
Project: RTRA Nanosciences project: HM-MAG.
Publications: [A.20].

4. Discrete Lattices (2011–)

Asymptotic models of Newton's cradle
Themes: Discrete lattice. Asymptotics.
Collaborators: Eric Dumas (Institut Fourier), Marguerite Gisclon (LAMA), and Guillaume James (LJK).
Publications: [A.19].

5. Molecular dynamics (2009–2012)

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

6. 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].

7. 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].

8. 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].
(Last updated December 2014)