Crack path prediction in anisotropic brittle materials

A force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure and macroscopic linear elasticity. The path is uniquely determined by the directional anisotropy of the fracture energy, independent of details of the failure process. The derivation exploits the gradient dynamics and translation symmetry properties of this class of models to define a generalized energy-momentum tensor whose integral around an arbitrary closed path enclosing the crack tip yields all forces acting on this tip, including Eshelby's configurational forces, cohesive forces, and dissipative forces. Numerical simulations are in very good agreement with analytic predictions.     

Applications of Bruhat decompositions to complex hyperbolic geometry

The double coset space AΛ (n, ℂ) / U (n − 1, 1) is studied, where A consists of the diagonal matrices in GL (n, ℂ). This space naturally arises in the harmonic analysis on the hermitian symmetric space GL (n, ℂ) / U (n − 1, 1). It is shown here that these double cosets also represent a class of basic invariants related to complex hyperbolic geometry. An algebraic parametrization for the double cosets is given and it is shown how this may be used to conveniently compute the geometric invariants.     

Représentation des processus ponctuels multivariés à l'aide d'un processus de Poisson

Sans résumé     

Attachment of alkali cations on beta-D-glucopyranose: matrix-assisted laser desorption/ionization time-of-flight studies and ab initio calculations

In matrix-assisted laser desorption/ionization mass spectrometry, carbohydrates ionize by attachment of an alkali cation, and the ion yield varies with the nature of the cation. In an attempt to contribute to the understanding of the mechanisms involved, we have conducted matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) experiments on the simple glucose molecule with the alkali cations Li+, Na+ and K+, and have also performed ab initio calculations. The calculations show that, for the most stable carbohydrate-cation geometry, the carbohydrate ring is twisted and the cation is coordinated to four oxygen atoms. Calculations also show that in these complexes the positions of the three cations are very similar, and the smaller the cation, the closer it is to the oxygen atoms. Finally, the calculated formation enthalpies of the different complexes agree with the experimental results obtained for the order of stability of these complexes.     

White-Light-Emitting Self-Assembled NanoFibers and Their Evidence by Microspectroscopy of Individual Objects

The self-assembly of a blue-emitting light-harvesting organogelator and specifically designed highly fluorescent tetracenes yields nanofibers with tunable emissive properties. In particular, under near-UV excitation, white light emission is achieved in organogels and dry films of nanofibers. Confocal fluorescence microspectroscopy demonstrates that each individual nanofiber emits white light. A kinetic study shows that an energy transfer (ET) occurs between the blue-emitting anthracene derivative and the green- and red-emitting tetracenes, while inter-tetracene ETs also take place. Moreover, microscopy unravels that the nanofibers emit polarized emission in the blue spectral region, while at wavelengths higher than 500 nm the emission is not significantly polarized.     

Sustainable and green microextraction of organophosphorus flame retardants by a novel phosphonium‐based deep eutectic solvent

Based on the solidification of a hydrophobic deep eutectic solvent in air‐assisted liquid phase microextraction combined with gas chromatography and mass spectrometry, a green and sustainable microextraction technique was developed for extracting, separating, and detecting organophosphorus flame retardants in aqueous samples. In this study, some strategies were considered for overcoming or improving the challenges of conventional solvent microextraction procedures. In addition, a hydrophobic deep eutectic solvent with a freezing point near the ambient temperature was employed as an extraction phase, the dispersive solvent was substituted by the syringe pump process, and the centrifugation step was omitted by using salting‐out phenomenon. Further, the effect of the main independent variables was evaluated by using the chemometric methods in order to maximize the extraction efficiency of the procedure. Under optimal conditions, the calibration model was linear in the range of 0.01–25.0 µg/L. Limits of detection and quantitation were assessed at the concentration levels of 2–23 and 9–65 ng/L, respectively. The precision involving repeatability and reproducibility was evaluated by estimating the relative standard deviation, the levels of which were <6.6 and <8.7%, respectively. The applicability of the method was successfully evaluated by analyzing the target analytes in real aqueous samples, which illustrated satisfactory recoveries (95–104.61%).     

A reformulation of the nonsmooth approaches of M. Frémond and J.J. Moreau for rigid body dynamics

This paper deals with the nonsmooth dynamics of a rigid bodies system. The proposed theory is inspired by the formalism of J.J. Moreau and that of M. Frémond and relies on the notion of percussion which is the integral of the contact force during the duration of the collision. Contrary to classical discrete element models, it is here assumed that percussions can be expressed as a function of only the velocity before the impact. This assumption is checked for the usual mechanical constitutive laws for collisions derived from a pseudopotential of dissipation or the Coulomb friction law. Motion equations are then reformulated taking into account simultaneous collisions of solids. A mathematical study of the new model is presented: the existence and uniqueness of the solution are discussed according to the regularity of both the forces (Lebesgue‐density occurring during the regular evolution of the system) and the percussions (Dirac‐density describing the collision). In the light of the principles of thermodynamics, a condition on the internal percussion assuring that the collision is thermodynamically admissible, is established. Finally, an application of this new model to the motion of a system of rigid disks, including simultaneous collisions is presented.     

Covariant Wigner function approach to the relativistic quantum electron gas in a strong magnetic field

This paper is concerned with a unified approach to some equilibrium properties of the relativistic quantum electron plasma embedded in a strong external magnetic field. This unified approach rests on the systematic use of a covariant Wigner function. The equilibrium Wigner function of the noninteracting gas is derived and its main properties are studied. In particular, it satisfies equations that are the complete analog of the usual Liouville equation and thus can be termed “relativistic quantum Liouville equation” whose properties are considered. The equations of state are rederived in this formalism and the results obtained earlier by Canuto and Chiu are found anew. Also, the covariant Wigner funetion of the magnetized vacuum is derived: it is needed, in this formalism, in order to obtain, e.g., the vacuum polarization tensor. Since we are also interested in the plasma modes, the fluctuations of one-particle quantities—and their spectrum—(in particular, of the four current) are calculated in view of their use in the fluctuation-dissipation theorem. We also outline a microscopic proof of this theorem, on the basis of a BBGKY hierarchy for the covariant Wigner functions, and point out the existence of an effective plasma frequency.