Periodic Solutions for Completely Resonant Nonlinear Wave Equations with Dirichlet Boundary Conditions

We consider the nonlinear string equation with Dirichlet boundary conditions u_tt–u_xx=(u), with (u)=u³+O(u⁵) odd and analytic, 0, and we construct small amplitude periodic solutions with frequency for a large Lebesgue measure set of close to 1. This extends previous results where only a zero-measure set of frequencies could be treated (the ones for which no small divisors appear). The proof is based on combining the Lyapunov-Schmidt decomposition, which leads to two separate sets of equations dealing with the resonant and non-resonant Fourier components, respectively the Q and the P equations, with resummation techniques of divergent powers series, allowing us to control the small divisors problem. The main difficulty with respect to the nonlinear wave equations u_tt–u_xx+Mu=(u), M0, is that not only the P equation but also the Q equation is infinite-dimensional.     

Sensitivity of a tucuxi (Sotalia fluviatilis guianensis) to airborne sound

Auditory systems of cetaceans are considered highly specialized for underwater sound processing, whereas the extent of their hearing capacity in air is still a point of issue. In this study, the sensitivity to airborne sound in a male tucuxi (Sotalia fluviatilis guianensis) was tested by means of a go/no go response paradigm. Auditory thresholds were obtained from 2 to 31.5 kHz. Compared to the hearing thresholds of other dolphins as well as of amphibian mammals, the sensitivity to airborne sound of the test subject is low from 2 to 8 kHz, with the highest threshold at 4 kHz. Thresholds at 16 and 31.5 kHz reveal a sharp increase in hearing sensitivity. Thus, although not obtained in this study, the upper aerial hearing limit is in the ultrasonic range. A comparison of the present data with the underwater audiogram of the same test subject referred to sound intensity indicates that the sensitivity of Sotalia to underwater sound is generally better than to airborne sound.     

Raman phonon spectra and lattice dynamics of 9,10-dinitroanthracene under pressure

Abstract

Raman phonon spectra of 9, 10-dinitroanthracene have been recorded in the pressure range 0-6GPa. No phase transition is detected up to the maximum pressure studied. Quasi Harmonic Lattice Dynamics calculations, based on an atom-atom potential previously modeled on homologous 9,10-disubstituted anthracenes, have been performed. The optimized potential was used to calculate the equilibrium geometry and the lattice phonon frequencies as a function of pressure. The calculated structure at ambient conditions closely resembles the experimental one. The calculated phonon frequencies show a good agreement with the experimental values at all pressures measured.     

Unusual nucleation and growth of γ′ iron nitride upon nitriding Fe–4.75 at.% Al alloy

The influence of substitutionally dissolved Al in ferritic Fe–4.75 at.% Al alloy on the nucleation and growth of γ′ iron nitride (Fe₄N_{1? x} ) was investigated upon nitriding in NH₃/H₂ gas mixtures. The nitrided specimens were characterised employing optical microscopy, scanning electron microscopy, transmission electron microscopy, electron probe microanalysis and X-ray diffraction. As compared to the nitriding of pure ferrite (α-Fe), where a layer of γ′ develops at the surface, upon nitriding ferritic Fe–4.75 at.% Al an unusual morphology of γ′ plates develops at the surface, which plates deeply penetrate the substrate. In the diffusion zone, nano-sized precipitates of γ′ and of metastable, cubic (NaCl-type) AlN occur, having, with the ferrite matrix, a Nishiyama–Wassermann orientation relationship and a Bain orientation relationship, respectively. The γ′ plates contain a high density of stacking faults and fine ε iron nitride (Fe₂N_{1? z} ) precipitates, although the formation of ε iron nitride is not expected for the employed nitriding parameters. On the basis of dedicated nitriding experiments it is shown that the unusual microstructural development is a consequence of the negligible solubility of Al in γ′ and the obstructed precipitation of the thermodynamically stable, hexagonal (wurtzite-type) AlN in ferrite.     

From holes to sponge at irradiated Ge surfaces with increasing ion energy—an effect of defect kinetics?

We show that hole patterns and sponge-like layers at irradiated Ge surfaces originate from the same driving force, namely the kinetics of ion beam induced defects in the amorphous Ge surface layer. Ge hole patterns reported earlier for irradiation with low energy (5 keV) Ga⁺ ions were reproduced for low energy Bi⁺ but also for Ge⁺ self-irradiation, which proves that the dominating driving force for morphology evolution cannot originate from the implanted impurities. At higher ion energies the well-known formation of sponge-like Ge surface layers after heavy ion irradiation was found for Bi⁺ irradiation and Ge⁺ self-irradiation, also. The transition from smooth surfaces via hole patterns to sponge-like morphologies with increasing ion energies was studied in detail. A model based on the kinetics of ion beam induced defects was developed and implemented in 3D kinetic Monte Carlo simulations, which reproduce the transition from hole patterns to sponge-like layers with increasing ion energy.     

Breather Solutions in Periodic Media

For nonlinear wave equations existence proofs for breathers are very rare. In the spatially homogeneous case up to rescaling the sine-Gordon equation \({\partial^2_t u = \partial^2_x u - \sin (u)}\) is the only nonlinear wave equation which is known to possess breather solutions. For nonlinear wave equations in periodic media no examples of breather solutions have been known so far. Using spatial dynamics, center manifold theory and bifurcation theory for periodic systems we construct for the first time such time periodic solutions of finite energy for a nonlinear wave equation

$ s(x) \partial^2_t u(x,t) = \partial^2_x u(x,t) - q(x) u(x,t)+ r(x)u(x,t)^3, $

with spatially periodic coefficients s, q, and r on the real axis. Such breather solutions play an important role in theoretical scenarios where photonic crystals are used as optical storage.

     

Diverse population-bursting modes of adapting spiking neurons

We study the dynamics of a noisy network of spiking neurons with spike-frequency adaptation (SFA), using a mean-field approach, in terms of a two-dimensional Fokker-Planck equation for the membrane potential of the neurons and the calcium concentration gating SFA. The long time scales of SFA allow us to use an adiabatic approximation and to describe the network as an effective nonlinear two-dimensional system. The phase diagram is computed for varying levels of SFA and synaptic coupling. Two different population-bursting regimes emerge, depending on the level of SFA in networks with noisy emission rate, due to the finite number of neurons.     

Nonadiabatic two-parameter charge and spin pumping in a quantum dot

We study dc charge and spin transport through a weakly coupled quantum dot, driven by a nonadiabatic periodic change of system parameters. We generalize the model of Tien and Gordon to simultaneously oscillating voltages and tunnel couplings. When applying our general result to the two-parameter charge pumping in quantum dots, we find interference effects between the oscillations of the voltage and tunnel couplings. We show that these interference effects may explain recent measurements in metallic islands. Furthermore, we discuss the possibility to electrically pump a spin current in presence of a static magnetic field.     

Shear banding in biphasic liquid-liquid systems

In this Letter, we present the first systematic report of shear-induced banding in microconfined biphasic liquid-liquid systems, i.e., formation of alternating regions of high and low volume fraction of dispersed-phase droplets in a parallel plate flow cell. Such a flow-driven, gap-dependent phenomenon is only observed at low values of the viscosity ratio between the dispersed and the continuous phase, and in a given range of the applied shear rate. Based on rheological measurements, band formation is found to be associated with a viscosity decrease as compared to the homogeneous, structureless case, thus showing that system microstructure is somehow evolving towards reduced viscous dissipation under shear flow.