A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects

The time-dependent equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear parabolic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions and initial conditions are prescribed.The existence of weak solutions is proven. The key of the proof is (i) a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrizes the equations, and (ii) a priori estimates obtained by using the entropy function. Finally, the entropy inequality is employed to show the convergence of the solutions to the thermal equilibrium state as the time tends to infinity.     

Quantization of complex Lagrangian submanifolds

Let Λ be a smooth Lagrangian submanifold of a complex symplectic manifold X. We construct twisted simple holonomic modules along Λ in the stack of deformation-quantization modules on X.     

Surface and interfacial properties of PVDF/acrylic copolymer blends before and after UV exposure

Morphological and chemical properties of both the surface and interface of poly(vinylidene fluoride)/poly(methyl methacrylate)-co-poly(ethyl acrylate) (PVDF/PMMA-co-PEA) blend films have been investigated before and after the samples were exposed to ultraviolet (UV) irradiation using a xenon arc lamp at 50 °C and 9% relative humidity (RH) for 7 months. Surface and interfacial morphologies were studied by atomic force microscopy (AFM). Chemical composition information was obtained by confocal Raman microscopy, attenuated total reflection-FTIR spectroscopy (ATR-FTIR), X-ray photoelectron spectroscopy (XPS), and contact angle measurements. Results show an enrichment of the PVDF material at the air surface, while the acrylic copolymer enriches the interface. Blends having greater than 50% mass fraction of PVDF show little change in the surface morphology after UV exposure for 7 months. However, for a lower PVDF content, blends exhibit significant degradation of PMMA-co-PEA copolymer and a much rougher surface after UV exposure. Microstructural changes in the PVDF spherulites are also observed after UV degradation. It is found that the surface and interfacial morphologies are correlated with the chemical properties.     

Almost sure estimates for the concentration neighborhood of Sinai’s walk

We consider Sinai’s random walk in random environment. We prove that infinitely often (i.o.) the size of the concentration neighborhood of this random walk is bounded almost surely. We also get that i.o. the maximal distance between two favorite sites is bounded almost surely.     

Convenient preparation of 5-ethynyl-octaethylporphyrin free base and zinc complex

A method leading to the preparation of the free base or zinc meso-ethynyl functionalized octaethylporphyrin has been developed, which will open the access to various meso-ethynyl metalloporphyrins.     

A new, fast and efficient synthesis of 3-aryl indenones: intramolecular cyclization of 1,3-diarylpropynones in superacids

1,3-Diarylpropynones were cleanly converted to the corresponding 3-arylindenones in various superacidic media. This new, simple, one-pot reaction proved to be efficient (yields up to 95%) and very fast (reaction time less than 30 min).     

Trois formulations d'un modèle de plasma quasi-neutre avec courant non nul

In this Note, we propose three formulations of a model describing a quasi-neutral plasma with non-vanishing current. In order to study and compare the numerical efficiency of each formulation, two test-problems are implemented in one dimension. The first is a periodic perturbation of a uniform stationary plasma. The second is a case of plasma expansion in vacuum between two electrodes. To cite this article: P. Crispel et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Markovian Solutions of Inviscid Burgers Equation

For solutions of (inviscid, forceless, one dimensional) Burgers equation with random initial condition, it is heuristically shown that a stationary Feller–Markov property (with respect to the space variable) at some time is conserved at later times, and an evolution equation is derived for the infinitesimal generator. Previously known explicit solutions such as Frachebourg–Martin's (white noise initial velocity) and Carraro–Duchon's Lévy process intrinsic-statistical solutions (including Brownian initial velocity) are recovered as special cases.