On fractal properties of non-normal numbers with respect to Rényi f-expansions generated by piecewise linear functions

The paper is devoted to the study of fractal properties of subsets of the set of non-normal numbers with respect to Rényi f  -expansions generated by continuous increasing piecewise linear functions defined on [0,+∞)$[0,+\infty )$. All such expansions are expansions for real numbers generated by infinite linear IFS f={_f0,_f1,…,_fn,…}$f=\{f_0,f_1,\dots ,f_n,\dots \}$ with the following list of ratios _Q∞=(_q0,_q1,…,_qn,…)$Q_{\infty }=(q_0,q_1,\dots ,q_n,\dots )$.     

Phase transitions of nonlinear waves in quadratic waveguide arrays

We study two-color parametric nonlinear modes in waveguide arrays with a quadratic nonlinear response. We predict theoretically and observe experimentally a new type of phase transition manifested in an abrupt power-controlled change of the mode structure from unstaggered to staggered, due to the interplay of localization and synchronization in parametrically driven discrete systems.     

Anti-Stokes Luminescence in Multi-Resonance-Type Thermally-Activated Delayed Fluorescence Molecules

Photon-upconversion in organic molecular systems is one of the promising technologies for future energy harvesting systems because these systems can generate excitons that possess higher energy than excitation energy. The photon-upconversion caused by absorbing ambient heat as additional energy is particularly interesting because it could ideally provide a light-driving cooling system. However, only a few organic molecular systems have been reported. Here, we report the anti-Stokes photoluminescence (ASPL) derived from hot-band absorption in a series of multi-resonance-type thermally-activated delayed fluorescence (MR-TADF) molecules. The MR-TADF molecules exhibited an anti-Stokes shift of approximately 0.1 eV with a high PL quantum yield in the solution state. The anti-Stokes shift corresponded well to the 1–0 vibration transition from the ground state to the excited singlet state, and we further evaluated a correlation between the activation energy for the ASPL intensity and the TADF process. Our demonstration underlines that MR-TADF molecules have become a novel class of ASPL materials for various future applications, such as light-driving cooling systems.     

Microcrystalline composite particles of carbon nanotubes and calcium carbonate

Coprecipitation of urea-melt modified carbon nanotubes and calcium carbonate from an aqueous solution by two methods yielded microcrystalline composite particles. Powders obtained by colloidal crystallization from a supersaturated solution that were isolated and dried soon after precipitation were a mixture of raspberry-shaped and rhombohedral particles. These were shown by infrared and X-ray diffraction analyses to be mainly calcite. Particles that were kept wet for 1 day or longer before being isolated were typically entirely rhombohedral with edge lengths in the range of 5-30 microm. Scanning electron microscopy investigations revealed that the nanotubes were adsorbed on the particle surface and also incorporated into the interior matrix. Removal of the calcium carbonate component by treating the particles with acid yielded nanotube shells whose size and shape reflected those of the original particles.     

Iron-catalysed green synthesis of carboxylic esters by the intermolecular addition of carboxylic acids to alkenes

Iron triflate, in situ-formed from FeCl3 and triflic acid, or FeCl3 and silver triflate efficiently catalyse the intermolecular addition of carboxylic acids to various alkenes to yield carboxylic esters; the reaction is applicable to the synthesis of unstable esters, such as acrylates.     

Pseudoisocyanine J-aggregate to optical waveguiding crystallite transition: microscopic and microspectroscopic exploration

Using fluorescent microscopy and microspectroscopy, optical properties and morphology transformations in individual pseudoisocyanine (PIC) J-aggregates in aqueous electrolyte solutions have been explored. A stringlike structure of J-aggregates with a string diameter much less than 1 microm has been observed. Photodestruction of the strings under short-wavelength excitation has been revealed. Rodlike PIC crystallites, about 1 microm in diameter, have been observed with time. The fluorescence spectrum of rodlike crystallites has been found to differ from that of stringlike J-aggregate and from PIC crystal powder spectra. The crystallites are very stable, and their photodestruction has not been observed under any excitation conditions. It has been found that rodlike crystallites in contrast to stringlike J-aggregates possess optical waveguide properties. The luminescence of crystallites can be observed only at the excitation spot and at butt ends located up to hundreds of micrometers from the excitation spot.     

Experimental and modeling studies of B atom number density distributions in hot filament activated B2H6/H2 and B2H6/CH4/H2 gas mixtures

Experimental and modeling studies of the gas-phase chemistry occurring in dilute, hot filament (HF) activated B2H6/H2 and B2H6/CH4/H2 gas mixtures are reported. Spatially resolved relative number densities of B (and H) atoms have been measured by resonance enhanced multiphoton ionization methods, as a function of process conditions (e.g. the HF material and its temperature, the B2H6/H2 mixing ratio, and the presence (or not) of added CH4). Three-dimensional modeling of the H/B chemistry prevailing in such HF activated gas mixtures using a simplified representation of the gas phase chemistry succeeds in reproducing all of the experimentally observed trends, and in illustrating the key role of the "H-shifting" reactions BHx + H <= => BHx-1 + H2 (x = 1-3) in enabling rapid interconversion between the various BHx (x = 0-3) species. CH4 addition, at partial pressures appropriate for growth of boron-doped diamond by chemical vapor deposition methods, leads to approximately 30% reduction in the measured B atom signal near the HF. The modeling suggests that this is mainly due to concomitant H atom depletion near the HF, but it also allows us a first assessment of the possible contributions from B/C coupling reactions upon CH4 addition to HF activated B2H6/H2 gas mixtures.     

Effect of agents modifying the membrane dipole potential on properties of syringomycin E channels

We evaluated the effect of agents modifying the membrane dipole potential: phloretin, 6-ketocholestanol and RH 421 on the properties of single channels formed by lipodepsipeptide syringomycin E (SRE) in planar lipid bilayers. SRE forms two conductive states in lipid bilayers: "small" and "large." Large SRE channels are clusters of several small ones, demonstrating synchronous openings and closures. The increase in the membrane dipole potential led to (i) an increase in SRE channel conductance, (ii) an increase in the channel's lifetime, and (iii) a decrease in a number of synchronously operating small channels in the clusters. Overall, the results support the model of the small SRE channel synchronization in the cluster as voltage-dependent orientation of the lipid dipoles associated with the channel pores.     

Solution of the master equation for Wigner's quasiprobability distribution in phase space for the Brownian motion of a particle in a double well potential

Quantum effects in the Brownian motion of a particle in the symmetric double well potential V(x)=ax(2)2+bx(4)4 are treated using the semiclassical master equation for the time evolution of the Wigner distribution function W(x,p,t) in phase space (x,p). The equilibrium position autocorrelation function, dynamic susceptibility, and escape rate are evaluated via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The escape rate so yielded has a quantum correction depending strongly on the barrier height and is compared with that given analytically by the quantum mechanical reaction rate solution of the Kramers turnover problem. The matrix continued fraction solution substantially agrees with the analytic solution. Moreover, the low-frequency part of the spectrum associated with noise assisted Kramers transitions across the potential barrier may be accurately described by a single Lorentzian with characteristic frequency given by the quantum mechanical reaction rate.