Exterior complex scaling as a perfect absorber in time-dependent problems

It is shown that exterior complex scaling provides for complete absorption of outgoing flux in numerical solutions of the time-dependent Schr\"odinger equation with strong infrared fields. This is demonstrated by computing high harmonic spectra and wave-function overlaps with the exact solution for a one-dimensional model system and by three-dimensional calculations for the H atom and a Ne atom model. We lay out the key ingredients for correct implementation and identify criteria for efficient discretization

La fiche "AGEVEN" : un outil pour la collecte des données rétrospectives

La fiche "AGEVEN" permet, grâce à sa simplicité d'emploi, une meilleure datation des événements et d'opérer un classement respectif des événements démographiques (naissances et décés), des changements matrimoniaux et des changements de lieux de résidence. Les données obtenues servent à reconstituer avec précision les conditions socio-économiques au moment où se produisent les événements démographiques étudiés. (Résumé d'auteur

The "AGEVEN" record : a tool for the collection of retrospective data

La fiche "AGEVEN" permet, grâce à sa simplicité d'emploi, une meilleure datation des événements et un classement respectif des événements démographiques (naissances et décés), des changements matrimoniaux et des changements de lieux de résidence. Les données obtenues servent à reconstituer avec précision les conditions socio-économiques au moment où se produisent les événements démographiques étudiés. (Résumé d'auteur

Asymptotic behavior of age-structured and delayed Lotka-Volterra models

In this work we investigate some asymptotic properties of an age-structured Lotka-Volterra model, where a specific choice of the functional parameters allows us to formulate it as a delayed problem, for which we prove the existence of a unique coexistence equilibrium and characterize the existence of a periodic solution. We also exhibit a Lyapunov functional that enables us to reduce the attractive set to either the nontrivial equilibrium or to a periodic solution. We then prove the asymptotic stability of the nontrivial equilibrium where, depending on the existence of the periodic trajectory, we make explicit the basin of attraction of the equilibrium. Finally, we prove that these results can be extended to the initial PDE problem.Comment: 29 page

A nonstationary form of the range refraction parabolic equation and its application as an artificial boundary condition for the wave equation in a waveguide

The time-dependent form of Tappert's range refraction parabolic equation is derived using Daletskiy-Krein formula form noncommutative analysis and proposed as an artificial boundary condition for the wave equation in a waveguide. The numerical comparison with Higdon's absorbing boundary conditions shows sufficiently good quality of the new boundary condition at low computational cost.Comment: 12 pages, 9 figure

Transparent Boundary Conditions for Time-Dependent Problems

A new approach to derive transparent boundary conditions (TBCs) for dispersive wave, Schrödinger, heat, and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physically reasonable and unreasonable solutions by the location of the singularities of the Laplace transform of the exterior solution. Here the Laplace transform is taken with respect to a generalized radial variable. To obtain a numerical algorithm, a Möbius transform is applied to map the Laplace transform onto the unit disc. In the transformed coordinate the solution is expanded into a power series. Finally, equations for the coefficients of the power series are derived. These are coupled to the equation in the interior and yield transparent boundary conditions. Numerical results are presented in the last section, showing that the error introduced by the new approximate TBCs decays exponentially in the number of coefficients

Quantum group symmetry of the Quantum Hall effect on the non-flat surfaces

After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a first example we show that the $su(2)$ symmetry of the QHE on sphere leads to $su_q(2)$ algebra in the equator . We explain this result by a contraction of $su(2)$ . Secondly , with the help of the symmetry operators of QHE on the Pioncare upper half plane , we will show that the ground state wave functions form a representation of the $su_q(2)$ algebra .Comment: 8 pages,latex,no figur

A Static Analyzer for Large Safety-Critical Software

We show that abstract interpretation-based static program analysis can be made efficient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement of a general purpose static analyzer and later adaptation to particular programs of the family by the end-user through parametrization. This is applied to the proof of soundness of data manipulation operations at the machine level for periodic synchronous safety critical embedded software. The main novelties are the design principle of static analyzers by refinement and adaptation through parametrization, the symbolic manipulation of expressions to improve the precision of abstract transfer functions, the octagon, ellipsoid, and decision tree abstract domains, all with sound handling of rounding errors in floating point computations, widening strategies (with thresholds, delayed) and the automatic determination of the parameters (parametrized packing)

Multilevel preconditioning techniques for Schwarz waveform relaxation domain decomposition methods for real-and imaginary-time nonlinear Schrödinger equations

International audienceThis paper is dedicated to the derivation of a multilevel Schwarz Waveform Relaxation (SWR) Domain Decomposition Method (DDM) in real-and imaginary-time for the NonLinear Schrödinger Equation (NLSE). In imaginary-time, it is shown that the use of the multilevel SWR-DDM accelerates the convergence compared to the one-level SWR-DDM, resulting in an important reduction of the computational time and memory storage. In real-time, the method requires in addition the storage of the solution in overlapping zones at any time, but on coarser discretization levels. The method is numerically validated on the Classical SWR and Robin-based SWR methods but can however be applied to any SWR approach