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

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

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

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

A new synthesis approach for non-uniform filters in the log-scale: proof of concept

International audienceWe theoretically describe and give the proof of a new way to synthesize filters that are affine in the log–log scale in the frequency domain and are especially appropriate to filter non-uniformly sampled data, and take advantage of a very low number of signal samples and filter coefficients. This approach leads to a summation formula which plays the same role as the discrete convolution for the usual finite impulse response filters

Level crossing sampling of strongly monoHölder functions

http://www.eurasip.org/Proceedings/Ext/SampTA2013/papers/p193-bidegaray-fesquet.pdfInternational audienceWe address the problem of quantifying the number of samples that can be obtained through a level crossing sampling procedure for applications to mobile systems. We specially investigate the link between the smoothness properties of the signal and the number of samples, both from a theoretical and a numerical point of view