Absorbing boundary conditions for reaction-diffusion equations

We treat here of the question of absorbing boundary conditionsfor nonlinear diffusion equations. We use the conditions designedfor the linear equation, we prove them to be well posed forthe nonlinear problem, and through numerical experiments thatthey are well suited for reaction–diffusion equations.     

Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

This paper is devoted to the proof of almost global existence results for Klein‐Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc.     

Nuclear spin lattice relaxation in the amorphous state: Towards an understanding

Full reports concerning the nuclear relaxation of ¹¹B, ²³Na, ²⁹Si and ⁷⁷Se in the following glasses: B₂O₃, Na₂B₄O₇, (Na₂O)_0.3(SiO₂)_0.7, Se are presented. Extended measurements confirm the existence of an efficient quadrupolar mechanism typical of glasses and show that the two-phonon process, responsible for the quadropolar relaxation in insulating crystals, is always negligible in our whole range of investigation. The relaxation rate T₁^?1, field independent in almost all cases, varies like T^(1+γ) with 0 < γ < 1 between 1.2 K and 100 K but exhibits different behaviour at higher T depending upon the analysed material. Whereas T₁ goes through a minimum at 300 K in B₂O₃, its T-dependence for ²³Na in Na₂B₄O₇ and (Na₂O)_0.3(SiO₂)_0.7 becomes faster than in the low-T regime. Several attempts made to interpret the data within the framework of the tunneling model, commonly invoked to explain the anomalous thermal properties of glasses, are reviewed in detail. It is concluded that the T₁ results are best accounted for by a process consisting of the modulation of the electric field gradient (EFG) at the nuclear site by its nearest neighbour tunneling defect. This EFG fluctuation is shown to be dominated by interactions between defects and an average correlation time of about 10^?9 sec is assigned to it. A complete T₁ calculation requires the previous knowledge of the physical nature of the defects, so far not available. Each defect is then tentatively identified with a bridging oxygen atom tunneling between two potential wells, which gives the correct energy dependence for the EEG matrix element. A defect number of 10²⁷ m^?3 is shown to be consistent with the results.     

Electron energy loss spectroscopy measurement of surface vibration dispersion on clean and oxygen-covered Ni(100)

Inelastic electron scattering has been carried out at 300 K on Ni(100) and at 150 K on p(2 × 2) and c(2 × 2) oxygen overlayers adsorbed on Ni(100). Impact energies ranged from 4 to 300 eV in order to measure the dispersion curves of surface vibrations throughout the two-dimensional Brillouin zone in the [110] direction. The Rayleigh mode has been observed in all cases. On O-coved surfaces a surface resonance and two vibrations of different polarizations associated with oxygen motion have been detected. The polarizations of the detected modes and the origin of the resonances, arising from the folding of the Brillouin zone due to the adsorbate, have been analysed with the help of symmetry considerations and the EELS selection rules. The O-coverage dependence of the Rayleigh mode frequency suggests a continuous outwards expansion of the first Ni plane starting from a contracted clean surface. The O-dispersion data are consistent with an O layer distant from the first Ni plane by ～ 0.9 Å in both investigated overlayers.     

Fluorescence versus laser effect: Towards a unified theory

A single evolution equation is established to treat the mechanisms of fluorescence and the laser effect, using a mixed representation, classical for the electromagnetic field and quantum for the dipoles. The model approach takes advantage of the principle of conservation of energy for the system of electromagnetic field and dynamic dipole. A resulting nonlinear differential equation is derived and is shown to sustain two fixed points associated with fluorescence and laser emission. The existence of a pumping threshold is confirmed for the laser effect. In particular the pumping rate determines whether light will be emitted by fluorescence or by the laser effect, and there is no pumping that engenders fluorescence and laser emission simultaneously. The initial physical conditions, chosen to integrate the evolution equation in time, assume a nonvanishing electric polarization of the emitting dipole rather than a nonvanishing electromagnetic field. The distribution function accounting for the thermal fluctuations of the random initial polarization is also calculated.     

Absorbing Boundary Conditions for One-dimensional Nonlinear Schrödinger Equations

We construct two families of absorbing boundary conditions for the nonlinear Schrödinger equation. The first one relies on the pseudodifferential calculus and the second one relies on the paradifferential calculus. We show that some of the corresponding initial boundary value problems are well-posed. We finally present numerical experiments illustrating the efficiency of these methods.     

A nonlinear approach to absorbing boundary conditions for the semilinear wave equation

We construct a family of absorbing boundary conditions for the semilinear wave equation. Our principal tool is the paradifferential calculus which enables us to deal with nonlinear terms. We show that the corresponding initial boundary value problems are well posed. We finally present numerical experiments illustrating the efficiency of the method.

     

Light-driven directed motion of azobenzene-coated polymer nanoparticles in an aqueous medium

Azobenzene-coated polymer nanoparticles in the 16-nm-diameter range act as phototriggered nanomotors combining photo to kinetic energy conversion with optical control through light intensity gradients. The grafted dyes act as molecular propellers: their photoisomerization supplies sufficient mechanical work to propel the particles in an aqueous medium toward the intensity minima with velocities of up to 15 μm/s. It is shown that nanoparticles can be driven over tens of micrometers by translating the intensity gradients in the plane. The analysis of the particles motion demonstrates the decisive role of photoisomerization in the transport with a measured driving force that is 3 to 4 orders of magnitude higher than optical forces.