Structural Stability of Discontinuous Galerkin Schemes

The goal of this work is to determine classes of traveling solitary wave solutions for a differential approximation of a discontinuous Galerkin finite difference scheme by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solutions of the original continuous equations. This paper extends our previous work about classical schemes to discontinuous Galerkin schemes (David and Sagaut in Chaos Solitons Fractals 41(4):2193?C2199, 2009; Chaos Solitons Fractals 41(2):655?C660, 2009).     

A finite‐volume scheme for the multidimensional quantum drift‐diffusion model for semiconductors

A finite‐volume scheme for the stationary unipolar quantum drift‐diffusion equations for semiconductors in several space dimensions is analyzed. The model consists of a fourth‐order elliptic equation for the electron density, coupled to the Poisson equation for the electrostatic potential, with mixed Dirichlet‐Neumann boundary conditions. The numerical scheme is based on a Scharfetter‐Gummel type reformulation of the equations. The existence of a sequence of solutions to the discrete problem and its numerical convergence to a solution to the continuous model are shown. Moreover, some numerical examples in two space dimensions are presented. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1483–1510, 2011     

Photochemical reactivity of α,β-unsaturated δ-lactams: Synthesis of seco-steroids. Photochemical reactions. XIII [1]

The UV. irradiation of 17 β-hydroxy-2-aza-4-androsten-3-one (1) , N-methyl-17 β-hydroxy-2-aza-4-androsten-3-one (3) , 17 β-hydroxy-4-aza-5 β-androst-1-en-3-one (2) and N-methyl-17 β-hydroxy-4-aza-5 β-androst-1-en-3-one (4) , gives rise to 1,10-seco (from 1 and 3 ) and 5, 10-seco (from 2 and 4 ) steroids.     

Rheology of lyotropic and thermotropic lamellar phases

We investigate the steady-state rheological behaviour of the lamellar phase of a lyotropic system (CpCl, hexanol, brine) and of a thermotropic system (8CB). Power laws characterize the behaviour of the imposed stress as a function of the measured shear rate and similarities are observed for both systems; the same regime γ˙∼σ ^m with m≈1.7 is obtained at low shear stresses corresponding to a texture of oily streaks oriented in the direction of the flow, as shown by microscopic observations. The “onion state” only exists in the case of dilute samples of the lyotropic lamellar phase; the stress then varies as γ˙∼σ ^m with m≈4.8, as already observed by other groups with different systems. Rheological measurements at different temperatures allow determination of different activation energies relating to the still badly understood processes involved in the different rheological regimes. We propose a model which reproduces the experimental power laws and which is based on an analogy with the theory of high-temperature creep in metals and alloys. Received: 19 October 1999/Accepted: 1 November 1999     

Adaptive instant record signals applied to detection with time reversal operator decomposition

Time reversal arrays are becoming common tools whether for detection or tomography. These applications require the measurement of the response from the array to one or several receivers. The most natural way to record the impulse responses for several sources is to generate pulses successively from each emitting point and record simultaneously the signals from the receivers. However, this method is very time consuming or inefficient in terms of signal-to-noise ratio. To overcome this limitation quasi-orthogonal pseudonoise signals like Kasami sequences can be used. For guided wave propagation, a very high degree of orthogonality between the signal is necessary to allow an accurate measure of the whole multipath structure of the transfer function. Hence, in this work, we propose a new family of pseudo-orthogonal signals that is adapted to the environment and more specifically, to highly dispersive media. These adaptive instant records signals are used experimentally to detect targets using the time reversal operator decomposition method. The accuracy of the 15 x 15 transfer functions acquired simultaneously, and therefore the detection capability, are demonstrated in an experimental ultrasonic waveguide as a small-scale model of shallow water propagation including bottom absorption and reverberation.     

Reliability of Speaking and Maximum Voice Range Measures in Screening for Dysphonia

Speech range profile (SRP) is a graphical display of frequency-intensity occurring interactions during functional speech activity. Few studies have suggested the potential clinical applications of SRP. However, these studies are limited to qualitative case comparisons and vocally healthy participants. The present study aimed to examine the effects of voice disorders on speaking and maximum voice ranges in a group of vocally untrained women. It also aimed to examine whether voice limit measures derived from SRP were as sensitive as those derived from voice range profile (VRP) in distinguishing dysphonic from healthy voices. Ninety dysphonic women with laryngeal pathologies and 35 women with normal voices, who served as controls, participated in this study. Each subject recorded a VRP for her physiological vocal limits. In addition, each subject read aloud the "North Wind and the Sun" passage to record SRP. All the recordings were captured and analyzed by Soundswell's computerized real-time phonetogram Phog 1.0 (Hitech Development AB, T?by, Sweden). The SRPs and the VRPs were compared between the two groups of subjects. Univariate analysis results demonstrated that individual SRP measures were less sensitive than the corresponding VRP measures in discriminating dysphonic from normal voices. However, stepwise logistic regression analyses revealed that the combination of only two SRP measures was almost as effective as a combination of three VRP measures in predicting the presence of dysphonia (overall prediction accuracy: 93.6% for SRP vs 96.0% for VRP). These results suggest that in a busy clinic where quick voice screening results are desirable, SRP can be an acceptable alternate procedure to VRP.     

Exploring the origins of the power-law properties of energy landscapes: An egg-box model

Multidimensional potential energy landscapes (PELs) have a Gaussian distribution for the energies of the minima, but at the same time the distribution of the hyperareas for the basins of attraction surrounding the minima follows a power-law. To explore how both these features can simultaneously be true, we introduce an “egg-box” model. In these model landscapes, the Gaussian energy distribution is used as a starting point and we examine whether a power-law basin area distribution can arise as a natural consequence through the swallowing up of higher-energy minima by larger low-energy basins when the variance of this Gaussian is increased sufficiently. Although the basin area distribution is substantially broadened by this process, it is insufficient to generate power-laws, highlighting the role played by the inhomogeneous distribution of basins in configuration space for actual PELs.     

2-μm high-power multiple-frequency single-mode Q-switched Ho:YLF laser for DIAL application

We report on the development and the demonstration of a two-wavelength single-frequency laser oscillator based on Ho:YLF crystal. This laser is especially suitable for application as a transmitter in differential absorption lidar (DIAL)/integrated path differential absorption (IPDA) measurements of atmospheric carbon dioxide (CO₂) using the R30 CO₂ absorption line at 2,050.967 nm. The oscillator consists in a fiber-coupled and free-space solid-state hybrid system and can be used in high-energy middle-rate or moderate-energy high-rate configurations. The latter produced On and Off sequentially single-frequency laser pulses with 13 mJ of energy at a repetition rate of 2 kHz and pulse duration of 42 ns. The pulse energy and frequency stabilities are specially documented in free-running, single-frequency and two-frequency seeding single-mode operations. Standard deviation is 7.7 % for pulse energy and 2 MHz for frequency stability for the two-wavelength seeding operation. Allan variance plot shows that frequency fluctuations are reduced below 70 kHz for 10 s of averaging which is suitable for accurate CO₂ DIAL or IPDA measurements.