Commutability of homogenization and linearization at identity in finite elasticity and applications

We prove under some general assumptions on elastic energy densities (namely, frame indifference, minimality at identity, non-degeneracy and existence of a quadratic expansion at identity) that homogenization and linearization commute at identity. This generalizes a recent result by S. Müller and the second author by dropping their assumption of periodicity. As a first application, we extend their Γ-convergence commutation diagram for linearization and homogenization to the stochastic setting under standard growth conditions. As a second application, we prove that the Γ-closure is local at identity for this class of energy densities.     

Synthesis and reactivity of a phosphine-stabilized monogermanium analogue of alkynes

The synthesis of the first isolable C-phosphino-Ge-aminogermyne, stabilized by a phosphine ligand, has been achieved. X-ray diffraction analysis indicates a quite long Ge-C bond whose length is between that of a single and a double bond but consistent with the theoretically predicted values for a germyne bearing π-donating substituents. The isomerization of this germyne derivative affords a new stable N-heterocyclic germylene through migration of the original phosphine ligand from germanium to the carbon center.     

Description of the response of a fiber optic velocity sensor applied to capillary gas chromatography

This paper explores the response of a novel fiber optics sensor allowing real-time determination of the migration rate of vapor zones in capillary gas chromatography. The sensitivity is related to the gradient of the vapor zone distribution in the capillary and it is highest when vapor zones show steep variations in concentration. The expected linearity between the height of the velocity peaks and the response of a thermal conductivity detector is demonstrated experimentally. The sensor can be used to infer an approximate value of the analyte diffusion coefficient from the time response. Finally, the time evolution of the envelope of the optical signal is explained with experimental evidences.     

Three-dimensional imaging of sulfides in silicate rocks at submicron resolution with multiphoton microscopy

We report the first application of multiphoton microscopy (MPM) to generate three-dimensional (3D) images of natural minerals (micron-sized sulfides) in thick (～120 μm) rock sections. First, reflection mode (RM) using confocal laser scanning microscopy (CLSM), combined with differential interference contrast (DIC), was tested on polished sections. Second, two-photon fluorescence (TPF) and second harmonic signal (SHG) images were generated using a femtosecond-laser on the same rock section without impregnation by a fluorescent dye. CSLM results show that the silicate matrix is revealed with DIC and RM, while sulfides can be imaged in 3D at low resolution by RM. Sulfides yield strong autofluorescence from 392 to 715 nm with TPF, while SHG is only produced by the embedding medium. Simultaneous recording of TPF and SHG images enables efficient discrimination between different components of silicate rocks. Image stacks obtained with MPM enable complete reconstruction of the 3D structure of a rock slice and of sulfide morphology at submicron resolution, which has not been previously reported for 3D imaging of minerals. Our work suggests that MPM is a highly efficient tool for 3D studies of microstructures and morphologies of minerals in silicate rocks, which may find other applications in geosciences.     

Integral Representation Results for Energies Defined on Stochastic Lattices and Application to Nonlinear Elasticity

This article is devoted to the study of the asymptotic behavior of a class of energies defined on stochastic lattices. Under polynomial growth assumptions, we prove that the energy functionals F_e{F_\varepsilon} stored in the deformation of an e{{\varepsilon}}-scaling of a stochastic lattice Γ-converge to a continuous energy functional when e{{\varepsilon}} goes to zero. In particular, the limiting energy functional is of integral type, and deterministic if the lattice is ergodic. We also generalize, to systems and nonlinear settings, well-known results on stochastic homogenization of discrete elliptic equations. As an application of the main result, we prove the convergence of a discrete model for rubber towards the nonlinear theory of continuum mechanics. We finally address some mechanical properties of the limiting models, such as frame-invariance, isotropy and natural states.     

Quinone transfer radical polymerization (QTRP) of styrene: Catalysis by different metal complexes

Styrene has been polymerized by a Quinone Transfer Radical Polymerization (QTRP) based on the redox reaction of an ortho‐quinone and a metal catalyst. Several metal acetylacetonates have been tested in this work. The radical polymerization of styrene is largely controlled when phenanthrenequinone (PhQ) is used with catalytic amounts of Co(acac)₂, Ni(acac)₂, Mn(acac)_{2 or 3}, and Al(acac)₃. As a rule, in the presence of all these metallic complexes, the polystyrene molar mass increases with the monomer conversion, and polydispersity (M_w/M_n) is in the 1.3–1.6 range (at least until 40% monomer conversion). Styrene polymerization has also been resumed by polystyrene chains prepared by QTRP. In the specific case of manganese acetylacetonates, an amine or phosphine ligand has to be added for the control to be effective. Finally, two mechanistic hypotheses have been proposed, depending on whether the oxidation state of the metal can be easily changed or not. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2723‐2733, 2005     

Classical Yang-Mills-Dirac equations: Qualitative analysis of some solutions with a noncompact symmetry group

We consider classical Yang-Mills and Yang-Mills-Dirac equations on Minkowski space, with gauge group SU(2), and look for solutions invariant (up to a gauge transformation) under SO(3)×SO₀(1, 1) and SO₀(2, 1)×SO(2), respectively. In each case, we analyze the qualitative features of the solutions, in particular the asymptotic behavior as the solution approaches its singularities. The method is based on standard theorems from the theory of nonlinear ordinary differential equations.