Backlund Transformation and Exact Solutions for a New Generalized Zakharov-Kuzentsov Equation with Nonlinear Terms of Any Order

In this paper, with the help of symbolic computation, a new Backlund transformation (BT) for a newgeneralized Zakharov-Kuznetsov equation with nonlinear term of any order, ut+aupux +bu2pux +γuxy +δuxxx +ρuxyy=0, is obtained by using the homogeneous balance method. Based on the BT, some exact solutions are presented.     

Cooperative luminescence quenching on many-particle acceptors in disordered media

Many-body cooperative energy transfer is an important process in biology, medicine, photosynthesis, rare-earth-doped laser materials, responsible for up- and down-conversion of energy, optical excitation sensitization and relaxation. We present an analytical solution for long-time asymptotic of static luminescence quenching kinetics due to cooperative energy transfer to ensembles of acceptors comprised of two-, three-, and more particles. For cooperative energy transfer and cooperative luminescence quenching to n-body acceptors we have discovered a new law of power d/(nS−(n−1)d)$d/(nS-(n-1)d)$ time dependence (d=1,2,3$d=1,2,3$ is the space dimension, S=6,8,10$S=6,8,10$ is the multipolarty of interaction: dipole–dipole, dipole–quadrupole, or quadrupole–quadrupole). The detailed numerical simulation of cooperative quenching by Monte-Carlo method confirms the theoretical result.     

Formation of Si-nanoparticles in a microwave reactor: Comparison between experiments and modelling

The formation and growth of silicon-nanoparticles from silane in a microwave reactor was investigated. Experiments were performed for the following conditions: precursor concentration 380–2530 ppm, pressures of 20–30 mbar, microwave powers 120–300 W. The formed particles were examined in-situ with a particle mass spectrometer. Additionally, particles were collected on grids and analyzed by transmission electron microscopy, X-ray diffraction, and by determining the specific surface area by BET. The particle size was found to be in the range of 5–8 nm in diameter. A simple model was used to simulate the particle formation processes taking place inside the reactor. The microwave energy coupled into the reactor flow was treated as a spatially distributed energy source resulting in a local temperature increase. The particles were assumed to have a monodisperse size distribution. To allow an approximation of their shape they were characterized by their volume and surface area. The model takes nucleation, convection, coagulation, and coalescence into account. The fluid flow inside the microwave reactor was simulated with the commercial CFD-code Fluent.     

Automatic Symmetrization and Energy Estimates Using Local Operators for Partial Differential Equations

We develop a method for automatically symmetrizing Petrowsky well-posed Cauchy problems for constant coefficient linear partial differential equations. The method is rooted in the Sturm sequence technique for establishing the location of the roots of a complex polynomial and can be automated using standard symbolic computation tools. In the special case of homogeneous strictly hyperbolic scalar equations, we show that the resulting estimates are strong enough to control all principal order derivatives and thus can be used in place of the Leray energies. We also illustrate the method by applying it to various problems of mixed type.     

Energy Dispersive X-Ray Fluorescence Analysis and X-Ray Microanalysis of Medieval Silver Coins

 Austrian medieval silver/copper coins were investigated at their surfaces by energy dispersive X-ray fluorescence analysis (EDXRF) and at the cross-sections by X-ray microanalysis in the scanning electron microscope (SEM/EDX) in order to estimate the error occurring when corroded objects of art and archaeology are analyzed on the surface by non-destructive methods. Additionally, Ag/Cu-standards were treated in diluted sulphuric acid and the depletion of copper on the surface was measured by EDXRF. By calculating the ratio of the Ag-K/Ag-L intensity the process of blanching could be studied.     

A High‐Barrier Molecular Balance for Studying Face‐to‐Face Arene–Arene Interactions in the Solid State and in Solution

An atropisomeric molecular balance was developed to study face‐to‐face arene–arene interactions. The balance has a large central 1,4,5,8‐naphthalene diimide surface that forms intramolecular arene–arene interactions with two pendent arms. The balance adopts distinct syn and anti isomers with varying numbers of intramolecular interactions. Thus, the strength of the arene–arene interaction could be quantitatively measured by NMR spectroscopy from the anti/syn ratios. The size of the arene arms was easily varied, which allowed examination of the relationship between arene size and strength of the interaction. A nonlinear size dependence was observed in solution with larger arene arms having a disproportionately stronger arene–arene interaction. The intramolecular arene–arene interactions were also characterized in the solid state by X‐ray crystallography. These studies were facilitated by the kinetic stability of the syn and anti isomers at room temperature due to the high isomerization barrier (ΔG=27.0 kcal mol^?1). Thus, the anti isomer could be selectively isolated and crystallized in its folded conformation. The X‐ray structures confirmed that the anti isomers formed two strong intramolecular arene–arene interactions with face‐to‐face geometries. The solid‐state structure analysis also reveals that the rigid framework may contribute to the observed nonlinear size trend. The acetate linker is slightly too long, which selectively destabilizes the balances with smaller arene arms. The larger arene arms are able to compensate for the longer linker and form effective intramolecular arene–arene interactions.     

Luminescent energy transfer between cadmium telluride nanoparticle and lanthanide(III) chelate in competitive bioaffinity assays of biotin and estradiol

Fluorescence resonance energy transfer has been studied between lanthanide(III) chelates as donors and protein-coupled CdTe semiconductor nanoparticles as acceptors. Wide excitation spectra and large Stokes shift of semiconductor nanoparticles and timeresolved fluorescence detection were shown to provide a combination for successful energy transfer assay. Different intrinsically fluorescent europium(III) and terbium(III) chelates coupled to single biotin molecules were studied for optimal energy transfer with streptavidin labeled semiconductor nanoparticles. No significant differences between the studied chelates were observed. The strength of the methodology was demonstrated in a clinically relevant competitive and separation-free immunoassay of estradiol, where subnanomolar limit of detection was achieved with the coefficient of variation 2-11%. The data suggested that relatively short distance was needed to obtain adequate energy transfer. Therefore, biomolecules were coupled onto the semiconductor nanoparticles without any spacers.     

Design of Functional Carbon Composite Materials for Energy Conversion and Storage

The carbon composite materials have been a research hotspot in the fields of catalysis, energy conversion and so on, because of their features of large structure and morphology variety, good chemical and electrochemical stability, and high electronic conductivity, large specific surface area and rich active sites. This paper summarizes some research progress of carbon composite materials, including assembly methodologies, their structure regulation, properties, and related applications. Moreover, the current challenges and the prospects of these materials are also discussed.