Finite element approach to trap-insect model

The trap-insect model considered in this presentation comprises a system of two advection-diffusion-reaction equations. We develop finite element approximation of the solution of the model in order to produce accurate numerical simulations using a non-uniform triangulation. The algorithm is used for computing estimates of the parameters of the insect population. Particular attention is paid to estimating the population size, including the case of spatially heterogeneous population distributions. Using traps is the common practice to gain knowledge on the presence of a particular insect population and its density. This work aims to contribute to optimizing field protocols for accurate parameters estimation. (Texte intégral

The boundary element approach to Van der Waals interactions

We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response. We achieve this by rewriting the interaction energy expression exclusively in terms of surface integrals of surface operators. We validate this approach in the Lifshitz case and give numerical results for the interaction of two spheres as well as the van der Waals self-interaction of a uniaxial ellipsoid. Our method is simple to implement and is particularly suitable for a full, non-perturbative numerical evaluation of non-retarded van der Waals interactions between objects of a completely general shape.Comment: 4 pages, 4 figures, RevTe

Finite Element Formalism for Micromagnetism

The aim of this work is to present the details of the finite element approach we developed for solving the Landau-Lifschitz-Gilbert equations in order to be able to treat problems involving complex geometries. There are several possibilities to solve the complex Landau-Lifschitz-Gilbert equations numerically. Our method is based on a Galerkin-type finite element approach. We start with the dynamic Landau-Lifschitz-Gilbert equations, the associated boundary condition and the constraint on the magnetization norm. We derive the weak form required by the finite element method. This weak form is afterwards integrated on the domain of calculus. We compared the results obtained with our finite element approach with the ones obtained by a finite difference method. The results being in very good agreement, we can state that our approach is well adapted for 2D micromagnetic systems.Comment: Proceedings of conference EMF200

Dipole matrix element approach vs. Peierls approximation for optical conductivity

We develop a computational approach for calculating the optical conductivity in the augmented plane wave basis set of Wien2K and apply it for thoroughly comparing the full dipole matrix element calculation and the Peierls approximation. The results for SrVO3 and V2O3 show that the Peierls approximation, which is commonly used in model calculations, works well for optical transitions between the d orbitals. In a typical transition metal oxide, these transitions are solely responsible for the optical conductivity at low frequencies. The Peierls approximation does not work, on the other hand, for optical transitions between p- and d-orbitals which usually became important at frequencies of a few eVsComment: 11 pages, 4 figure