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UMR 5224

Brigitte BidégarayFesquet — Research themes and main results
Subjects
Below the list of all the themes I have studied or I am currently studying.
Subjects:
 Optics
 Non Uniform Signal Processing
 Micromagnetism
 Discrete Lattices
 Molecular Dynamics
 Finite Volumes for Maxwell Equations
 Plasma Physics
 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 (CEACESTA), Pierre Degond (MIP, Toulouse), and Richard W. Ziolkowski (University of Arizona).
Students:
PhD: Didier Reignier, coadviser 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:
JeanClaude Saut (Orsay University).
Publications:
[A.14],
[P.6].
 Subwavelength 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 (GipsaLab, Grenoble).
Project:
UJF MSTIC projects: TATIE, OASIS,
Persyvallab exploratory project CEE.
Publications:
[A.16],
[A.18],
[A.22],
[A.24],
[P.7],
[P.9],
[P.10],
[P.11].
3. Micromagnetism (2008–)
 Micromagnetism

Themes:
Derivation of a mesoscopic model. Identification of the damping term.
Collaborators:
Stéphane Labbé (LJK).
Project:
RTRA Nanosciences project: HMMAG.
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 NANOD).
Student:
Maël Bosson.
6. Finite volumes for Maxwell equations (1995–2001)
 Genuine multidimensional methods

Themes:
Genuine multidimensional corrections to cellcentered schemes for Maxwell equations.
Collaborators:
JeanMichel 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)
