897 research outputs found
Von Neumann Stability Analysis of Finite Difference Schemes for Maxwell--Debye and Maxwell--Lorentz Equations
This technical report yields detailed calculations of the paper [1] (B.
Bid\'egaray-Fesquet, "Stability of FD-TD schemes for Maxwell-Debye and
Maxwell-Lorentz equations", Technical report, LMC-IMAG, 2005) which have been
however automated since (see
http://ljk.imag.fr/membres/Brigitte.Bidegaray/NAUtil/). It deals with the
stability analysis of various finite difference schemes for Maxwell--Debye and
Maxwell--Lorentz equations. This work gives a systematic and rigorous
continuation to Petropoulos previous work [5] (P.G. Petropoulos.,"Stability and
phase error analysis of FD-TD in dispersive dielectrics", IEEE Transactions on
Antennas and Propagation, 42(1):62--69, 1994).Comment: English translation of version
Stability of FD-TD schemes for Maxwell-Debye and Maxwell-Lorentz equations
The stability of five finite difference-time domain (FD-TD) schemes coupling
Maxwell equations to Debye or Lorentz models have been analyzed in [1] (P.G.
Petropoulos, "Stability and phase error analysis of FD-TD in dispersive
dielectrics", IEEE Transactions on Antennas and Propagation, vol. 42, no. 1,
pp. 62--69, 1994), where numerical evidence for specific media have been used.
We use von Neumann analysis to give necessary and sufficient stability
conditions for these schemes for any medium, in accordance with the partial
results of [1]
Data driven sampling of oscillating signals
The reduction of the number of samples is a key issue in signal processing
for mobile applications. We investigate the link between the smoothness
properties of a signal and the number of samples that can be obtained through a
level crossing sampling procedure. The algorithm is analyzed and an upper bound
of the number of samples is obtained in the worst case. The theoretical results
are illustrated with applications to fractional Brownian motions and the
Weierstrass function
From Newton's cradle to the discrete p-Schr\"odinger equation
We investigate the dynamics of a chain of oscillators coupled by
fully-nonlinear interaction potentials. This class of models includes Newton's
cradle with Hertzian contact interactions between neighbors. By means of
multiple-scale analysis, we give a rigorous asymptotic description of small
amplitude solutions over large times. The envelope equation leading to
approximate solutions is a discrete p-Schr\"odinger equation. Our results
include the existence of long-lived breather solutions to the original model.
For a large class of localized initial conditions, we also estimate the maximal
decay of small amplitude solutions over long times
A nonlinear Bloch model for Coulomb interaction in quantum dots
In this paper we first derive a Coulomb Hamiltonian for electron--electron
interaction in quantum dots in the Heisenberg picture. Then we use this
Hamiltonian to enhance a Bloch model, which happens to be nonlinear in the
density matrix. The coupling with Maxwell equations when interaction with an
electromagnetic field is also considered from the Cauchy problem point of view.
The study is completed by numerical results and a discussion about the
advisability of neglecting intra-band coherences, as is done in part of the
literature.Comment: 17 pages. Journal of Mathematical Physics (2014) \`a para\^itr
Positiveness and Pauli exception principle in raw Bloch equations for quantum boxes
The aim of this paper is to derive a raw Bloch model for the interaction of
light with quantum boxes in the framework of a two-electron-species (conduction
and valence) description. This requires a good understanding of the one-species
case and of the treatment of level degeneracy. In contrast with some existing
literature we obtain a Liouville equation which induces the positiveness and
the boundedness of solutions, that are necessary for future mathematical
studies involving higher order phenomena
Restructuration et mise à jour du registre de métadonnées de The European Library
Rapport de stage en Master GISTE 2006-2007 portant sur les bibliothèques numériques et, "The European library" en particulier (architecture, services, métadonnées)
On the propagation of an optical wave in a photorefractive medium
The aim of this paper is first to review the derivation of a model describing
the propagation of an optical wave in a photorefractive medium and to present
various mathematical results on this model: Cauchy problem, solitary waves
Impact of Metallic Interface Description on Sub-wavelength Cavity Mode Computations
17 pagesWe present a numerical study of electromagnetic reflection and cavity modes of 1D-sub-wavelength rectangular metallic gratings exposed to TM-polarized light. Computations are made using the modal development. In particular we study the influence of the choice of boundary conditions on the metallic surfaces on the determination of modes, on specular reflectance and cavity mode amplitudes. Our full real-metal approach shows some advantages when compared to former results since it is in better accordance with experimental results
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