Elliptic equations with critical exponent on S3: new non-minimising solutions

Consider the problem:

$\{\begin{array}{cc}?{\Delta }_{S^3}U=\lambda U+U^5\text{,}U>0\hfill & \text{on?}{B}^{\prime }\text{,}\hfill \\ U=0\hfill & \text{on?}?B^{\prime }\text{,}\hfill \end{array}$

where $B^{\prime }$ is a ball on ${\mathbf{S}}^3$ with geodesic radius ${\theta }_1$, and ${\Delta }_{S^3}$ is the Laplace–Beltrami operator on ${\mathbf{S}}^3$. We prove that for any ${\theta }_1\in (\pi /2\text{,}\pi )$ and any $k>1$, there exist at least 2k solutions of this problem for λ sufficiently large negative. To cite this article: H. Brezis, L.A. Peletier, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Storage possibilities for radioactive krypton (85Kr)

A review of the different storage possibilities for radioactive krypton (⁸⁵Kr) is given. Various strategies can be applied to store⁸⁵Kr safely over many decades: storage in pressure containers and encapsulation in various solid matrices.     

Tryptophan-to-dye fluorescence energy transfer applied to oxygen sensing by using type-3 copper proteins

A fluorescence-based system to sense oxygen in solution is described. The method exploits the sensitivity of the endogenous fluorescence of type-3 copper proteins towards the presence of oxygen by translating the near-UV emission of the protein to label fluorescence in the visible range through a FRET mechanism. The main protein in this study, a recombinant tyrosinase from the soil bacterium Streptomyces antibioticus, has been covalently labeled with a variety of fluorescent dye molecules with emission maxima spanning the whole visible wavelength range. In all cases, the emission of the label varied considerably between O2-bound and O2-free protein with a contrast exceeding that of the Trp emission for some labels. It is shown that different constructs may be simultaneously observed using a single excitation wavelength. Next to the described application in oxygen sensing, the method may be applicable to any protein showing variations in tryptophan fluorescence, for example as a function of ligand binding or catalysis.     

Anionic rare-earth thiocyanate complexes as building blocks for low-melting metal-containing ionic liquids

The first examples of ionic liquids with rare-earth-containing anions are presented. These ionic liquids based on rare-earth thiocyanate complexes are liquid at room temperature, despite the multivalent character of the anionic building blocks.     

Sheared force networks: anisotropies, yielding, and geometry

A scenario for the yielding of granular matter is presented by considering the ensemble of force networks for a given contact network and applied shear stress tau. As tau is increased, the probability distribution of contact forces becomes highly anisotropic, the difference between average contact forces along minor and major axes grows, and the allowed networks span a shrinking subspace of all force networks. Eventually, contacts start to break, and at the maximal shear stress the packing becomes effectively isostatic. The size of the allowed subspace exhibits simple scaling properties, which lead to a prediction for the yield stress for packings of an arbitrary contact number.     

LPE growth of DH laser structures with the double source method

For the reproducible processing of double heterojunction injection laser structures to stripe geometry laser diodes, e.g. by proton bombardment, the thickness of the p-Ga_0.7Al_0.3As confining layer and of the p-GaAs top layer are of great importance. It is shown that the thickness control of these layers grown by liquid phase epitaxy can be improved considerably by introducing two source crystals into the growth system. Both source crystals are brought into contact with the solutions consecutively and prior to the seed. If this method is combined with the use of relatively thin melts (about 2 mm), a growth scheme may be chosen such that the growth rates of the p-GaAlAs and of the p-GaAs layers have reached a practically constant value on the seed crystal, independent of the initial degree of supersaturation. This behaviour is found to be in accordance with the diffusion-limited growth model applied for thin solutions, including a temperature dependence for both the diffusion constant and the slope of the liquidus curve. The results indicate that a second solid phase may appear in the p-GaAlAs solutions at a supersaturation as small as 4°C, which reduces the growth rate on the substrates by a factor of about 2. This situation is different from that of GaAs solutions, where a second phase appears only at a much higher degree of supersaturation. For the p-GaAlAs and the p-GaAs layers a thickness control of ⁺_-0.2 μm is thus achieved with this growth method, without the necessity of very precise temperature control and weighing so as to keep the total supersaturation less than 0.2°C.     

Laser ablation of silicon in water with nanosecond and femtosecond pulses

We describe laser ablation of Si under water by 5 ns, 355 nm and 100 fs, 800 nm pulses. Compared to that in air, an approximately twofold improvement in the ablation rate is found in water for femtosecond and nanosecond pulses. For higher laser irradiances, the plasma that forms at the water-air interface hampers further improvement of the ablation rate. We investigated the enhanced ablation process in water and found that the cavity-confinement geometry that increases the laser energy coupling to the target and allows more energy to be transferred to the cavity sidewalls plays an important role in the escalated material removal process. In addition, we show that the water layer that effectively reduces the oxidation and redeposition of the ablated debris is also responsible for improvements in the ablation process.     

High-intensity bowtie-shaped nano-aperture vertical-cavity surface-emitting laser for near-field optics

We report a high-intensity nano-aperture vertical-cavity surface-emitting laser (VCSEL) utilizing a bowtie-shaped aperture. A maximum power of 188 microW is achieved from a 180 nm bowtie aperture at a wavelength of 970 nm. The near-field full width at half-maximum intensity spot size 20 nm away from the bowtie aperture is 64 nm x 66 nm from simulation, and the peak near-field intensity is estimated to be as high as 47 mW/microm(2). This intensity is high enough to realize near-field optical recording, and the small spot size corresponds to storage densities up to 150 Gbits/in(2). The bowtie-aperture VCSEL also enables other applications, such as compact high-intensity probes for ultrahigh-resolution near-field imaging and single molecule fluorescence and spectroscopy.     

Adsorption of nonionic surfactants on cellulose surfaces: adsorbed amounts and kinetics

Kinetic and equilibrium aspects of three different poly(ethylene oxide) alkylethers (C12E5, C12E7, C14E7) near a flat cellulose surface are studied. The equilibrium adsorption isotherms look very similar for these surfactants, each showing three different regions with increasing surfactant concentration. At low surfactant content both the headgroup and the tail contribute to the adsorption. At higher surface concentrations, lateral attraction becomes prominent and leads to the formation of aggregates on the surface. The general shape of the isotherms and the magnitude of the adsorption resemble mostly those for hydrophilic surfaces, but both the ethylene oxide and the aliphatic segments determine affinity for the surface. The adsorption and desorption kinetics are strongly dependent on surfactant composition. At bulk concentrations below the CMC, the initial adsorption rate is attachment-controlled. Above the CMC, the micellar diffusion coefficient and the micellar dissociation rate play a crucial role. For the most hydrophilic surfactant, C12E7, both parameters are relatively large. In this case, the initial adsorption rate increases with increasing surfactant concentration, also above the CMC. For C12E5 and C14E7 there is no micellar contribution to the initial adsorption rate. The initial desorption kinetics are governed by monomer detachment from the surface aggregates. The desorption rate constants scale with the CMC, indicating an analogy between the surface aggregates and those formed in solution.     

Bi‐Enzyme Sensor for Phenolic Compounds with Fluorescent Read‐Out

In this paper, the use of tyrosinase (Ty) from Streptomyces antibioticus, labeled with a fluorescent tag, in combination with soluble quinoprotein (PQQ‐containing) glucose dehydrogenase (s‐GDH) to measure trace amounts of phenols is explored. Proof of concept is provided by a series of experiments, which show a clear quantitative dependence of the response on the phenol concentration. One of the advantages of the detection system is that apart from a standard fluorimeter no further instrumentation is required.