On the Amplitude Equations for Weakly Nonlinear Surface Waves

Nonlocal generalizations of Burgers’ equation were derived in earlier work by Hunter (Contemp Math, vol 100, pp 185–202. AMS, 1989), and more recently by Benzoni-Gavage and Rosini (Comput Math Appl 57(3–4):1463–1484, 2009), as weakly nonlinear amplitude equations for hyperbolic boundary value problems admitting linear surface waves. The local-in-time well-posedness of such equations in Sobolev spaces was proved by Benzoni-Gavage (Differ Integr Equ 22(3–4):303–320, 2009) under an appropriate stability condition originally pointed out by Hunter. The same stability condition has also been shown to be necessary for well-posedness in Sobolev spaces in a previous work of the authors in collaboration with Tzvetkov (Benzoni-Gavage et al. in Adv Math 227(6):2220–2240, 2011). In this article, we show how the verification of Hunter’s stability condition follows from natural stability assumptions on the original hyperbolic boundary value problem, thus avoiding lengthy computations in each particular situation. We also show that the resulting amplitude equation has a Hamiltonian structure when the original boundary value problem has a variational origin. Our analysis encompasses previous equations derived for nonlinear Rayleigh waves in elasticity.     

Search for EPR markers of the history and origin of the insoluble organic matter in extraterrestrial and terrestrial rocks

The insoluble organic matter (IOM) of three carbonaceous meteorites (Orgueil, Murchison and Tagish Lake meteorites) and three samples of cherts (microcrystalline SiO2 rock) containing microfossils with age ranging between 45 million years and 3.5 billion years is studied by electron paramagnetic resonance (EPR). The age of the meteorites is that of the solar system (4.6 billion years). The purpose of this work was to determine the EPR parameters, which allow us to discriminate between biogenic and extra terrestrial origin for the organic matter. Such indicators should be relevant for the controversy regarding the biogenicity of the organic matter in the oldest cheroot (3.5 billion years) and in Martian meteorites containing microbe-like microstructures. The organic matter of meteorites contains a high concentration of diradicaloid moieties characterised by a diamagnetic ground state S = 0 and a thermally accessible triplet state S = 1. The three meteorites exhibit the same singlet-triplet gap (ST gap) DeltaE approximately 0.1 eV. To the best of our knowledge, such diradicaloids are unknown in insoluble organic matter of terrestrial origin. We have also shown that the EPR linewidth of insoluble organic matter in cherts and coals decrease logarithmically with the age of the organic matter. We conclude from this result that the organic matter in the oldest cherts (3.5 billion years) has the same age as their SiO2 matrix, and is not due to a latter contamination by bacteria, as was recently found in meteoritic samples.     

Heterogeneous reactivity of chlorine atoms with ammonium sulfate and ammonium nitrate particles

In this laboratory study, model particles of ammonium sulfate (AS) and ammonium nitrate (AN) were exposed to chlorine atoms and uptake experiments were performed in a coated wall flow tube reactor coupled to a molecular beam mass spectrometer. The reactive surfaces were prepared by coating the inner surface of the reactor using two different methods: either by depositing size-selected particles on the halocarbon wax or by spray depositing thin films using a constant output atomizer. The observed uptake coefficients vary for (NH(4))(2)SO(4), ranging from γ(Cl)(AS)≈ 1 × 10(-3) for size-selected particles to γ(Cl)(AS)≈ 6 × 10(-2) for thin films prepared by spray. An uptake coefficient of γ(Cl)(AN)≈ 2.5 × 10(-3) of Cl˙ on size-selected NH(4)NO(3) particles was measured. A heterogeneous recombination of Cl atoms to from Cl(2) molecules was observed for the two surfaces. Furthermore, an ageing process was observed for AS particles, this phenomenon leading to the formation of new chlorine species on the solid substrate.     

Mapping of muscle deformation during heating: in situ dynamic MRI and nonlinear registration

We present developments in dynamic magnetic resonance imaging that allow internal structural muscle markers to be followed during heating. This monitoring is based on quantitative characterization of the experimental conditions and their temperature time course. A nonlinear image registration technique was optimized and applied to consecutively acquired images to measure the deformation fields in the muscle. A model coupling local deformation and temperature was obtained, which for the first time takes into account the variations of deformation and temperature in the sample. This modeling opens the way to a better understanding of the mechanisms responsible for mass loss and degradation of the textural properties of muscle during heating.     

Strain-induced yielding in bubble clusters

We study how shearing clusters of two or four bubbles induces bubble separation or topological rearrangement. The critical deformation at which this yielding occurs is measured as a function of shear rate, liquid composition, and liquid content in the cluster. We establish a geometrical yield criterion in the quasistatic case on the basis of these experimental data as well as simulations. In the dynamic regime, the deformation where the cluster yields increases with the strain rate, and we derive a scaling law describing this phenomenon based on the dynamical inertial rupture of the liquid meniscus linking the two bubbles. Our experiments show that the same scaling law applies to two- and four-bubble clusters.     

Spin-polarized surface states on Fe-deposited Au(111) surface: A theoretical study

We have studied electronic structure of Fe-deposited Au(111) by performing ab initio density functional theory calculations. We find that the magnetic moment on the deposited Fe layer is enhanced as compared to that in bulk iron. We observe a large number of new states on the Fe-deposited surface — one of which is in the majority spin channel having similar dispersion to that on the clean surface, and others in the minority spin channel. The effective mass of electrons in surface states near the Fermi level increases on Fe deposition. The electronic properties are found to be insensitive to the stacking of near-surface layers. We need to use very thick slabs in our calculations to avoid splitting of surface states due to spurious interactions between the two surfaces of the slab. Using the local density of states profiles for different surface states, we conclude that in scanning tunneling microscope experiments one can detect two of the surface states — one in the majority channel below the Fermi level, and another in the minority channel appearing just above the Fermi energy. We compare our results to those from scanning tunneling spectroscopy experiments.     

Towards dual photodynamic and antiangiogenic agents: design and synthesis of a phthalocyanine-chalcone conjugate

A phthalocyanine-chalcone conjugate has been designed to combine the vascular disrupting effect of chalcones with the photodynamic effect of phthalocyanines. This potential dual photodynamic and antiangiogenic agent was obtained by the condensation of a tetrahydroxylated non-peripherally substituted Zn(ii) phthalocyanine with an amino chalcone converted into the corresponding activated isocyanate. The conjugate was fully characterized.     

Giant core-shell nanospherical clusters composed of 32 Co or 32 Ni atoms held by 6 p-tert-butylthiacalix[4]arene units

Using combinations of p-tert-butylthiacalix[4]arene (TCA) and [M(DMSO)(6)(BF(4))(2)] salts (M = Co(II) or Ni(II)), two almost isostructural core-shell-type thermally stable giant nanoclusters, composed of 32 metal centers, 6 deprotonated calix units binding the metal centers by both their O and S atoms, 24 μ-oxo or μ-hydroxo bridging groups, and 6 MeOH molecules, have been prepared under mild and reproducible conditions. For both giant clusters, the oxidation state II [M(II)(32)O(16)(OH)(8)(CH(3)OH)(6)TCA(6) (M = Co or Ni)] for the metal center was demonstrated by X-ray photoelectron and electronic absorption spectroscopies.     

Prestress effects on the eigenfrequencies of the soundboards: experimental results on a simplified string instrument

This paper presents an experimental study of the effects of prestresses on the vibration behavior of string instruments. These prestresses are created by gluing ribs (crowning) and tensioning string (downbearing). The effects of these prestresses were previously studied numerically for a piano soundboard by Mamou-Mani et al. [J. Acoust. Soc. Am. 123, 2401-2406 (2008)] and analytically for simplified models by Mamou-Mani et al. [Acta Acust. Unit. Acust. 95, 915-926 (2009)]. In the present study, a specified test bench is designed, including a simplified soundboard (a rectangular plate), a bridge, and a single string. The plate is subjected to in-plane and transverse loads. Vibrational eigenmodes are identified using nearfield acoustical holography (NAH) measurement. The evolution of eigenfrequencies with these specific prestresses is studied. The results show the effectiveness of NAH for this purpose and a very good qualitative concordance with previous numerical and analytical calculus.