A Global Existence Result for the Compressible Navier–Stokes Equations in the Critical L p Framework

The present paper is dedicated to the global well-posedness issue for the barotropic compressible Navier–Stokes system in the whole space \mathbbR^d{\mathbb{R}^d} with d ≧ 2. We aim at extending the work by Danchin (Inventiones Mathematicae 141(3):579–614, 2000) to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L ^p -type Besov norms, we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true. In passing, we obtain new estimates for the linearized and the paralinearized systems which may be of interest for future works on compressible flows.     

Effective temperature in driven vortex lattices with random pinning

We study numerically correlation and response functions in nonequilibrium driven vortex lattices with random pinning. From a generalized fluctuation-dissipation relation, we calculate an effective transverse temperature in the fluid moving phase. We find that the effective temperature decreases with increasing driving force and becomes equal to the equilibrium melting temperature when the dynamic transverse freezing occurs. We also discuss how the effective temperature can be measured experimentally from a generalized Kubo formula.     

Dewetting of thin polymer films near the glass transition

Dewetting of ultrathin polymer films near the glass transition exhibits unexpected front morphologies [G. Reiter, Phys. Rev. Lett. 87, 186101 (2001)]. Here, we present the first theoretical attempt to understand these features, focusing on the shear-thinning behavior of these films. We analyze the profile of the dewetting film, and characterize the time evolution of the dry region radius, R(d)(t), and of the rim height, h(m)(t). After a transient time, depending on the initial thickness, h(m)(t) grows like square root[t] while R(d)(t) increases like exp(square root[t]). Different regimes of growth are expected, depending on the initial film thickness and experimental time range.     

On the asymptotic completeness of the Volterra calculus

The Volterra calculus is a simple and powerful pseudodifferential tool for inverting parabolic equations which has found many applications in geometric analysis. An important property in the theory of pseudodifferential operators is asymptotic completeness, which allows the construction of parametrices modulo smoothing operators. In this paper, we present new and fairly elementary proofs of the asymptotic completeness of the Volterra calculus. The author was partially supported by the European RT NetworkGeometric Analysis HPCRN-CT-1999-00118.     

Dammarane Triterpenes from Gardenia aubryi Vieill.

Three new dammarane triterpenoids, gardaubryones A–C ( 1 – 3 ), were isolated from the gum collected on the aerial parts of Gardenia aubryi Vieill ., together with the known compounds hydroxydammarenone II ( 4 ), ocotillone ( 5 ), cabraleone, and hollongdione. The structures of the novel compounds were established on the basis of mass spectrometry, NMR experiments, and chemical‐correlation reactions.     

Comparative study of the effect of various electrode membranes on biofouling and electrochemical measurements

Stability of sensors in biosamples is a critical issue and can be mitigated by membranes. The effect of different membranes (Nafion, cellulose acetate, chitosan, fibronectin, PSS/PL) on the electrochemistry of an outer-sphere redox couple (ruthenium II/III hexaammine) and on the electrocatalytic reduction of dissolved oxygen are described. Biofouling has been induced by albumin solutions. Results demonstrate good performances of fibronectin in all situations investigated. Other membranes do not provide a satisfactory protection from biofouling and some of them, PSS/PL in particular, seriously disturb electrochemical mechanisms.     

Bismuth (III) coordination to cyclen and cyclam bearing four appended groups

The synthesis of new cyclam and cyclen derivatives (respectively L₁ and L₂), able to efficiently coordinate to Bi(III) are presented here. The two ligands bearing two different pendant arms (two-pycolyl and two (2-(2-hydroxyethoxy)ethyl)-2-aminoacetamide in trans position) were synthesized in the aim to obtain stable and water soluble complexes. The thermodynamic and kinetic of the formation of the corresponding complexes in aqueous solution were studied by means of NMR and potentiometric investigations. The fast kinetic of complexation and the high stability of the complexes are encouraging for further application with the alpha-emitting ²¹³Bi isotope.     

Theoretical and experimental investigation of the structural and spectroscopic properties of coumarin 343 fluoroionophores

A joint theoretical-experimental investigation has been carried out to unravel the details of the complexation of cations by fluoroionophores based on coumarin 343 and to interpret the modifications in the ligand and also in the coumarin structural, electronic, magnetic, and vibrational properties. It is confirmed that C343-dea (1) complexes the cations by both the lactone and the amide oxygen atoms whereas for C343-crown (2) and C343-dibenzocrown (3), the cations are complexed by the oxygen atoms of the lactone as well as those of the crown ligand. These complexations induce geometric modifications, which are delocalized over the coumarin backbone and are related to electronic reorganizations that modify the spectroscopic signatures. This paper analyzes these signatures and shows how they are related as well as how they can be used to monitor the complexation process. Upon complexation, the UV-visible absorption spectra display a bathochromic shift of the most intense electronic transition; this shift is generally larger for the most flexible compound 1 as well as when complexing divalent cations. NMR spectra bear many signatures of the complexation, of which the most remarkable ones are the large shielding of C(1) and the large deshieldings of C(9) and C(16). Additional makers of complexation are highlighted in the IR vibrational spectra, in particular the bands associated with the lactone and amide CO vibrations, which are downshifted when the corresponding CO is involved in the complexation mode and, otherwise, upshifted. A high degree of consistency characterizes the different geometrical, electronic, magnetic, and vibrational signatures, which substantiates the assignment of the modes of complexation in 1-3. In addition, the agreement between the experimental data and the theoretical values is rather satisfactory, in that it at least enables us to interpret the spectral signatures.