A hierarchy of hydrodynamic models for plasmas. Zero-electron-mass limits in the drift-diffusion equations
A Lie connection between Hamiltonian and Lagrangian optics.
A Matrix Approach to the Energy-Norm Bisection in Wave Motion
A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals : an application to KDP
This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell’s equations for the wave field coupled with a version of Bloch’s equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material....
A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP
This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell's equations for the wave field coupled with a version of Bloch's equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material. ...
A mixed–FEM and BEM coupling for a three-dimensional eddy current problem
We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.
A mixed–FEM and BEM coupling for a three-dimensional eddy current problem
We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.
A model of evolution of temperature and density of ions in an electrolyte
We study existence and nonexistence of solutions (both stationary and evolution) for a parabolic-elliptic system describing the electrodiffusion of ions. In this model the evolution of temperature is also taken into account. For stationary states the existence of an external potential is also assumed.
A multi-D model for Raman amplification
In this paper, we continue the study of the Raman amplification in plasmas that we initiated in [Colin and Colin, Diff. Int. Eqs. 17 (2004) 297–330; Colin and Colin, J. Comput. Appl. Math. 193 (2006) 535–562]. We point out that the Raman instability gives rise to three components. The first one is collinear to the incident laser pulse and counter propagates. In 2-D, the two other ones make a non-zero angle with the initial pulse and propagate forward. Furthermore they are symmetric with respect...
A multi-D model for Raman amplification
In this paper, we continue the study of the Raman amplification in plasmas that we initiated in [Colin and Colin, Diff. Int. Eqs.17 (2004) 297–330; Colin and Colin, J. Comput. Appl. Math.193 (2006) 535–562]. We point out that the Raman instability gives rise to three components. The first one is collinear to the incident laser pulse and counter propagates. In 2-D, the two other ones make a non-zero angle with the initial pulse and propagate forward. Furthermore they are symmetric with respect to...
A Nekhoroshev-type theorem for the Pauli-Fierz model of classical electrodynamics
A new approach to nonsinusoidal steady-state power system analysis.
A new constrained formulation of the Maxwell system
A new H(div)-conforming p-interpolation operator in two dimensions
In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) -1/2(div, K)-regularity (r > 0) on the reference element (either triangle or square) K. We show that this operator is stable...
A new H(div)-conforming p-interpolation operator in two dimensions
In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) -1/2(div, K)-regularity (r > 0) on the reference element (either triangle or square) K. We show that this operator is stable with...
A non elliptic spectral problem related to the analysis of superconducting micro-strip lines
This paper is devoted to the spectral analysis of a non elliptic operator , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator has been derived, we determine its continuous spectrum. Then, we show that is unbounded from below and that it has a sequence of negative eigenvalues tending to . Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions...
A non elliptic spectral problem related to the analysis of superconducting micro-strip lines
This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some...
A note on point source diffraction by a wedge.
A note to Friedrichs' inequality
A numerical minimization scheme for the complex Helmholtz equation
We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate...