Homoclinic Solutions for Swift-Hohenberg and Suspension Bridge Type Equations

We establish the existence of homoclinic solutions for a class of fourth-order equations which includes the Swift-Hohenberg model and the suspension bridge equation. In the first case, the nonlinearity has three zeros, corresponding to a double-well potential, while in the second case the nonlinearity is asymptotically constant on one side. The Swift-Hohenberg model is a higher-order extension of the classical Fisher-Kolmogorov model. Its more complicated dynamics give rise to further possibilities of pattern formation. The suspension bridge equation was studied by Chen and McKenna (J. Differential Equations136 (1997), 325-355); we give a positive answer to an open question raised by the authors.     

Development and application of a novel immunoassay for measuring oxidative DNA damage in the environment

We developed a facile, cost-effective competitive binding assay for the analysis of 8-oxo-7,8-dihydro-2'-deoxyguanosine (8-oxodGuo) in DNA, using a polyclonal rabbit antiserum raised against an 8-oxodGuo hapten coupled to bovine serum albumin and radiolabeled synthetic ligand containing multiple 8-oxodGuo residues. This radioimmunoassay (RIA) displays a high affinity for 8-oxodGuo in DNA, with a detection limit of approximately 1 adduct in 10(5) bases of DNA. 8-oxodGuo standards for RIA were quantified by high-performance liquid chromatography and electrochemical detection in DNA diluted in methylene blue and exposed to visible light. As an initial application we quantified 8-oxodGuo in dosimeters deployed at increasing depths in the Southern Ocean during the austral spring of the 1998 field season or at the surface at Palmer Station, Antarctica, throughout the 1999 field season. Cyclobutane pyrimidine dimers (CPD) were quantified using an established RIA. We found that the frequency of both photoproducts decreased with depth. However, CPD induction was attenuated at a faster rate than 8-oxodGuo, correlating with the differential attenuation of solar ultraviolet wavelengths in the water column. CPD induction was closely related with ultraviolet-B radiation (UVB) attenuation, whereas the lower attenuation of 8-oxodGuo suggests that oxidative damage is more closely related to ultraviolet-A radiation (UVA) irradiance. The ratio of 8-oxodGuo: CPD was also found to covary with changes in stratospheric ozone concentrations at Palmer Station. These data demonstrate the usefulness of these assays for environmental photobiology and the potential for their use in studying the relative impacts of UVB versus UVA, including ozone depletion events.     

Oxidation of alcohols by transition metal complexes part V. Selective catalytic monoalkylation of arylacetonitriles by alcohols

Selective catalytic monoalkylation of arylacetonitriles by primary alcohols can be achieved at ≤ 100° using a catalyst prepared in situ from rhodium trichloride, triphenylphosphine and sodium carbonate. RuH₂(PPh₃)₄ is a more effective catalyst for this process.     

Theory of mesoscopic magnetism in photonic crystals

We provide a rigorous theoretical basis for the artificial magnetic activity of metamaterials near resonances. Our approach is a renormalization-based scheme that authorizes a completely general theory. The major result is an explicit expression of the effective permeability, in terms of resonant frequencies. The theoretical results are checked numerically, and we give applications of our theory to left-handed media and to the solution of the Pokrovski-Efros paradox.     

Roughness-Induced Effects on the Quasi-Geostrophic Model

We study in this paper the effect of small-scale irregularities on the quasi-geostrophic model. This study is motivated by some problems related to oceanography, as the Gulf Stream separation, or the impact of the topography on the global circulation. We first consider the role of coastal roughness in the phenomenon of western intensification of boundary currents. We show that the roughness is responsible for a nonlinear dynamics of the boundary layers, governed by a quasilinear elliptic equation. We thus extend substantially the classical derivation of Munk layers [15] and the results of convergence obtained in [10]. We then discuss the effect of a rough topography, by generalizing and justifying some formal computations of [17]. In particular, we derive rigorously a simplified model of oceanic circulation, with a nonlinear and nonlocal dissipative term due to the roughness.Acknowledgement This work has been partially supported by the GDR Amplitude Equations and Qualitative Properties (GDR CNRS 2103: EAQP) and by the IDOPT project in Grenoble.     

Spin-charge separation in two-dimensional frustrated quantum magnets

The dynamics of a mobile hole in two-dimensional frustrated quantum magnets is investigated by exact diagonalization techniques. Our results provide evidence for spin-charge separation upon doping the kagome lattice, a prototype of a spin liquid. In contrast, in the checkerboard lattice, a symmetry broken valence bond crystal, a small quasiparticle peak is seen for some crystal momenta, a finding interpreted as a restoration of weak holon-spinon confinement.