Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition

In this article, elastic wave propagation in a homogeneous isotropic elastic medium with a rigid boundary is considered. A method based on the decoupling of pressure and shear waves via the use of scalar potentials is proposed. This method is adapted to a finite element discretization, which is discussed. A stable, energy preserving numerical scheme is presented, as well as 2D numerical results.     

Adaptation of the Generic PDE’s Results to the Notion of Prevalence

Many generic results have been proved, especially concerning the qualitative behaviour of solutions of partial differential equations. Recently, a new notion of “almost always”, the prevalence, has been developed for vectorial spaces. This notion is interesting since, for example, prevalence sets are equivalent to the full Lebesgue measure sets in finite dimensional spaces. The purpose of this article is to adapt the generic PDE’s results to the notion of prevalence. In particular, we consider the cases where Sard–Smale theorems or arguments of analytic perturbations of the parameters are used. Dedicated to Professor Pavol Brunovsky in honor of his 70th birthday.     

Biodegradation study of plasticised corn flour/poly(butylene succinate-co-butylene adipate) blends

Plasticised corn flour/poly(butylene succinate-co-butylene adipate) (PBSA) materials were prepared by extrusion and injection in order to study the impact of PBSA ratio on their physicochemical properties and biodegradability. Scanning electron microscopy observations showed that corn flour and PBSA are incompatible. Three types of morphology have been observed: (i) starch dispersed in a PBSA matrix, (ii) a “co-continuous-like” morphology of starch and PBSA, and (iii) PBSA dispersed in a starch matrix. As expected, the extent of plasticised corn flour starch hydrolysis by amylolytic enzymes decreased when the amount of PBSA increased. Addition of a lipase to hydrolyse PBSA ester bonds enhanced enzymatic hydrolysis of starch by amylolytic enzymes in materials where PBSA formed a continuous phase. This suggests that PBSA formed a barrier restricting the access of amylolytic enzymes to starch. This was consistent with aerobic and anaerobic biodegradation assays, which also showed lower biodegradability of materials containing a majority of PBSA.     

Femtosecond nonlinear fiber optics in the ionization regime

By using a gas-filled kagome-style photonic crystal fiber, nonlinear fiber optics is studied in the regime of optically induced ionization. The fiber offers low anomalous dispersion over a broad bandwidth and low loss. Sequences of blueshifted pulses are emitted when 65 fs, few-microjoule pulses, corresponding to high-order solitons, are launched into the fiber and undergo self-compression. The experimental results are confirmed by numerical simulations which suggest that free-electron densities of ～10(17) cm(-3) are achieved at peak intensities of 10(14) W/cm(2) over length scales of several centimeters.     

Mechanism of inclusion chaining in SmC* free-standing films

The self-assembly of colloidal inclusions has recently been shown in smectic C* freely suspended films. In such 2D systems, the organization of the inclusions is qualitatively explained by elastic interactions induced by the disruption of the orientational order in the SmC* host phase. The interaction between resulting inclusion-defect pairs exhibits a dipolar character. We have developed a simplified model representing every inclusion and its companion hyperbolic defect by (+1)- and (-1)-wedge disclination lines, respectively. A finite anchoring energy has been introduced to explain the coalescence of the thinnest inclusions. Our model enables us to explain the chaining of the thickest inclusions and confirms the inclusion size dependence on the stability of the chains.     

Laboratory spectroscopic calibration of infrared tunable laser spectrometers for the in situ sensing of the Earth and Martian atmospheres

This paper reports the laboratory spectroscopic calibration of near- and mid- infrared tunable laser spectrometers used to determine in situ trace gases in the middle atmosphere of the Earth or in development for the investigation of the Martian atmosphere. The use of infrared absorption spectroscopy to measure gas concentrations requires a proper knowledge of the rotation–vibration spectra of the targeted molecules as well as a proper investigation of the tunable laser spectral emission properties. This last point is of particular importance for the use of new-generation lasers like quantum-cascade lasers or room-temperature multi-quantum wells laser diodes emitting between 2 and 3 μm. Purposely, we have developed various laboratory tunable laser set-ups to obtain accurate line strengths and pressure-broadening coefficients of atmospheric molecules and to test the performances of cutting-edge laser technology for trace gas sensing. In this paper, the spectroscopic calibration work is described. Several atmospheric applications of tunable laser are reported to stress the impact on concentration retrieval of a proper spectroscopic calibration work. PACS 07.57.T; 93.85; 07.87     

A principle of images for absorbing boundary conditions

When one uses high-order finite difference schemes for the wave equation, for instance fourth order schemes, the treatment of boundary conditions poses a real difficulty since one needs several additional equations (for the nodes close to the boundary), while one single scalar boundary condition is available. In the case of perfectly reflecting boundary conditions, namely the homogeneous Neumann or Dirichlet conditions, this difficulty can be overcomed by the use of the well-known image principle, which permits the extension of the equation outside of the domain of calculation by an appropriate symmetrization of the data. We propose in this article a generalization of this principle to the absorbing boundary conditions. Through a symmetrization process, we are led to introduce a damped wave equation with a damping term supported by the boundary. The treatment of the boundary condition is then replaced by the approximation of this new damped wave equation in the whole space. The theoretical justification of our approach is based on new energy estimates for the wave equation (when high-order absorbing boundary conditions are used), and constitutes an alternative to the use of the well-known Kreiss criterion to prove the stability of the associated initial boundary value problems. © 1994 John Wiley & Sons, Inc.     

Istope effects in aromatization of 1,4-dihydrobenzene and 1,4-dihydronaphthalene with quinones

Aromatization of 1,4-dihydronaphthalene with 2,3-dichloro-5,6-p-benzoquinone or chloranil is accompanied with kinetic isotope effects of 9.9 and 8.0 respectively.