1,616 research outputs found
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
Backward lasing yields a perfect absorber
Backward lasing yields a perfect absorbe
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
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
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
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
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)
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 symmetry of the QHE on
sphere leads to algebra in the equator . We explain this result by a
contraction of . 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 algebra .Comment: 8 pages,latex,no figur
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