New a priori estimates of solutions to anisotropic elliptic equations

Under consideration is the Dirichlet problem for singular anisotropic elliptic equations with a nonlinear source. Some new a priori estimates are obtained, implying that the solvability of the Dirichlet problem in the class of bounded solutions essentially depends on the dimension of the domain of the problem.     

Fundamental structure of Fresnel diffraction: longitudinal uniformity with respect to fractional Fourier order

Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. Transverse samples can be taken on these surfaces with separation that increases with propagation distance. Here, we are concerned with the separation of the spherical reference surfaces along the longitudinal direction. We show that these surfaces should be equally spaced with respect to the fractional Fourier transform order, rather than being equally spaced with respect to the distance of propagation along the optical axis. The spacing should be of the order of the reciprocal of the space-bandwidth product of the signals. The space-dependent longitudinal and transverse spacings define a grid that reflects the structure of Fresnel diffraction.     

Influence of synthesis method on structural and magnetic properties of cobalt ferrite nanoparticles

The Co–ferrite nanoparticles having a relatively uniform size distribution around 8 nm were synthesized by three different methods. A simple co-precipitation from aqueous solutions and a co-precipitation in an environment of microemulsions are low temperature methods (50 °C), whereas a thermal decomposition of organo-metallic complexes was performed at elevated temperature of 290 °C. The X-ray diffractometry (XRD) showed spinel structure, and the high-resolution transmission electron microscopy (HRTEM) a good crystallinity of all the nanoparticles. Energy-dispersive X-ray spectroscopy (EDS) showed the composition close to stoichiometric (~CoFe₂O₄) for both co-precipitated nanoparticles, whereas the nanoparticles prepared by the thermal decomposition were Co-deficient (~Co_0.6Fe_2.4O₄). The X-ray absorption near-edge structure (XANES) analysis showed Co valence of 2+ in all the samples, Fe valence 3+ in both co-precipitated samples, but average Fe valence of 2.7+ in the sample synthesized by thermal decomposition. The variations in cation distribution within the spinel lattice were observed by structural refinement of X-ray absorption fine structure (EXAFS). Like the bulk CoFe₂O₄, the nanoparticles synthesized at elevated temperature using thermal decomposition displayed inverse spinel structure with the Co ions occupying predominantly octahedral lattice sites, whereas co-precipitated samples showed considerable proportion of cobalt ions occupying tetrahedral sites (nearly 1/3 for the nanoparticles synthesized by co-precipitation from aqueous solutions and almost 1/4 for the nanoparticles synthesized in microemulsions). Magnetic measurements performed at room temperature and at 10 K were in good agreement with the nanoparticles’ composition and the cation distribution in their structure. The presented study clearly shows that the distribution of the cations within the spinel lattice of the ferrite nanoparticles, and consequently their magnetic properties are strongly affected by the synthesis method used.     

Structure of manganese zinc ferrite spinel nanoparticles prepared with co-precipitation in reversed microemulsions

The structure of Mn_0.5Zn_0.5Fe₂O₄ spinel ferrite nanoparticles is studied as a function of their size and the experimental conditions of their synthesis using X-ray absorption spectroscopy. The nanoparticles of different sizes down to approximately 2 nm and with a narrow size distribution were synthesized using co-precipitation in reverse microemulsions. Simultaneous refinement of the X-ray absorption fine structure (EXAFS) of three constituting metals shows a migration of Mn and Zn ions to the octahedral site of the spinel lattice compensated by the corresponding migration of the Fe ions. To a smaller extent, Mn ions switch the occupation site already in bulk and in larger nanoparticles, while a sporadic migration of Zn is detected only in the nanoparticles with sizes below approximately 5 nm. X-ray absorption near edge structure (XANES) reveals considerable variations in the position of the Mn K edge, suggesting the average Mn valence in the nanoparticles to be higher than 3+. Annealing at 500 °C relaxes the structure of as-synthesized nanoparticles toward the structure of the ceramic bulk standard. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Measurement of strong photon recycling in ultra‐thin GaAs n/p junctions monolithically integrated in high‐photovoltage vertical epitaxial heterostructure architectures with conversion efficiencies exceeding 60%

Photon‐recycling effects are studied experimentally in photovoltaic power converting III–V semiconductor devices designed with the vertical epitaxial heterostructure architecture (VEHSA). The responsivity of VEHSA structures with multiple thin GaAs n/p junctions is measured for various optical input powers and for different wavelength detuning values with respect to the peak of the spectral response. While the detuning of the optical excitation decreases the external quantum efficiency and the responsivity at low input powers, this study demonstrates that at high optical intensities, a large fraction of the performance can be recovered despite significant detuning values. The photon coupling effects therefore broaden the spectral range for which the VEHSA devices convert high‐power optical inputs with high efficiencies into an electrical output having a preset voltage. The devices exhibit a near optimum responsivity of up to 0.645 A/W for tuned excitation conditions or at high optical intensities for spectral detuning values of up to ～25 nm and corresponding to an external quantum efficiency of ～94%. Efficiencies of 62.0% and 61.8% have been obtained for current‐matched excitations and for a detuning of >10 nm, respectively. An output power of 5.87 W is reported and an open circuit voltage enhancement of 92 meV per n/p junction is measured compared to a device with a side by side planar architecture. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

High-field electron paramagnetic resonance study of the polymerization in Na2Rb1−x Cs x C60

We report on the study of the magnetic properties of the low-temperature polymer phases in N₂Rb_1?xCs_xC₆₀ at 110 GHz microwave frequency withx varying between 0 and 1. The magnetic and structural properties of the polymer phase strongly depend on the Cs content and its electronic structure progressively becomes quasi-one-dimensional asx is increased. While the electronic properties of the polymeric Na₂RbC₆₀ appear to be close to three-dimensional metal, Na₂Rb_0.3Cs_0.7C₆₀ shows characteristics of quasi-one-dimensional metal where instability in the electronic structure was found as detected by the sudden disappearance of the ESR intensity due to the opening of the gap at the Fermi surface. The observation of an additional resonance line below 15 K, which could be attributed to antiferromagnetic resonance, suggests that the low-temperature polymeric phase in Na₂Rb_0.3Cs_0.7C₆₀ has a well-defined magnetic ground state.     

Elucidating the Reaction Kinetics of Hydrophobic Porphyrin Nanoaggregates Dispersed in PVA Films Exposed to HCl Vapors

The behavior of the absorbance profiles of free‐base 5,10,15,20–tetraphenylporphyrin (TPPH₂) and zinc 5,10,15,20‐tetraphenylporphyrinate (ZnTPP) under exposure to HCl vapors was investigated to establish in detail the mechanism of protonation of these porphyrinic compounds and their potential for use as HCl sensors. We show that the intensities of diprotonated tetraphenylporphyrin absorption bands that arise at 444–446 and 662–666 nm increase as a function of the HCl exposure time. Reactions of free‐base meso‐tetraphenylporphyrin protonating and of zinc meso‐tetraphenylporphyrinate demetalation and subsequent protonating are discussed, and the solutions of the corresponding kinetic equations and respective reaction rates are also obtained. Finally, from a theoretical analysis we deduce the presence of intermediated monoprotonated porphyrin that helps us to explain why the isosbestic point in the TPPH₂ reaction with HCl is not well defined.     

Simulations and experiments of mode-locking of semiconductor lasers: pulse evolution,frequency detuning,and bias dependence

Simulations of a mode-locked diode laser based on a travelling-wave rate-equation model have been compared with experiments. The pulse measurement technique involved a conventional intensity autocorrelator together with an internally generated second-harmonic emission measurement set-up. The latter is ideal for systematic relative measurements. For the first time, pulse evolution as a function of the number of round-trips was measured. Short optical pulses were obtained after approximately 40 round-trips. The experimental and simulated detuning range was about 1 MHz and the d.c. bias dependence was investigated.On leave from Physics Institute of the Lithuanian Academy of Sciences, 232 600 Vilnius, Lithuania.     

Kinetics of photoinitiated polymerization in viscous media with one-sided illumination of a planar layer

A qualitative and numerical analysis of the solution of a system of nonlinear partial differential equations describing the kinetics of photoinitiated polymerization with one-sided illumination of a planar layer of viscous photopolymerizing composition is given. An equation of the integral rate of the process, expressed in units of contraction of the layer, that can be compared with experimental data is proposed.Published as a discussion.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, Nos. 5–6, pp. 420–423, September–December, 1992.