The Maxwell equation in a periodic medium : homogenization of the energy density
The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation.
The polarization in a ferroelectric thin film: local and nonlocal limit problems
In this paper, starting from classical non-convex and nonlocal 3D-variational model of the electric polarization in a ferroelectric material, via an asymptotic process we obtain a rigorous 2D-variational model for a thin film. Depending on the initial boundary conditions, the limit problem can be either nonlocal or local.
The potential distribution due to a dipole source in the fetal heart: A numerical model of the maternal abdomen.
The problem of scattering by a mixture of cracks and obstacles.
The RCWA method - A case study with open questions and perspectives of algebraic computations.
The solution of a singular integral equation with some applications in potential theory.
The transistor model of neuron and neuron net
The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle
Théorie nouvelle des ondes lumineuses.
Theta function identities from optical neural network transformations.
Time domain decomposition in final value optimal control of the Maxwell system
We consider a boundary optimal control problem for the Maxwell system with a final value cost criterion. We introduce a time domain decomposition procedure for the corresponding optimality system which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. In the limit full recovery of the coupling conditions is achieved, and, hence, the local solutions and controls converge to the global ones. The process is inherently parallel and is suitable for real-time...
Time Domain Decomposition in Final Value Optimal Control of the Maxwell System
We consider a boundary optimal control problem for the Maxwell system with a final value cost criterion. We introduce a time domain decomposition procedure for the corresponding optimality system which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. In the limit full recovery of the coupling conditions is achieved, and, hence, the local solutions and controls converge to the global ones. The process is inherently parallel and is suitable for real-time...
Time-dependent electromagnetic waves in a cavity
The electromagnetic initial-boundary value problem for a cavity enclosed by perfectly conducting walls is considered. The cavity medium is defined by its permittivity and permeability which vary continuously in space. The electromagnetic field comes from a source in the cavity. The field is described by a magnetic vector potential satisfying a wave equation with initial-boundary conditions. This description through is rigorously shown to give a unique solution of the problem and is the starting...
Time-discrete finite element schemes for Maxwell's equations
Topology and geometry of caustics in relation with experiments
Caustics of geometrical optics are understood as special types of Lagrangian singularities. In the compact case, they have remarkable topological properties, expressed in particular by the Chekanov relation. We show how this relation may be experimentally checked on an example of biperiodic caustics produced by the deflection of the light by a nematic liquid crystal layer. Moreover the physical laws may impose a geometrical constraint, when the system is invariant by some group of symmetries. We...
Total ponderomotive force on an extended test body.
Towards a two-scale calculus
We define and characterize weak and strong two-scale convergence in Lp, C0 and other spaces via a transformation of variable, extending Nguetseng's definition. We derive several properties, including weak and strong two-scale compactness; in particular we prove two-scale versions of theorems of Ascoli-Arzelà, Chacon, Riesz, and Vitali. We then approximate two-scale derivatives, and define two-scale convergence in spaces of either weakly or strongly differentiable functions. We also derive...
Trajectoires bornées d'une particule soumise à un champ magnétique symétrique linéaire
Trajectoires bornées d'une particule soumise à un champ magnétique symétrique linéaire