Exact Finite-Dimensional Filter for Exponential Functionals of the State of Beneš Systems

The purpose of this article is to derive finite-dimensional filters for exponential functionals of the state of nonlinear Bene? type filtering systems with correlated noises. These new filters can be applied in the state reconstruction of doubly–stochastic auto–regressive processes.     

The structural and catalytic properties of nanoparticles@MOF composites: A case study of Au@ZIF-8 hybrid crystals

Strain analysis of the MOF and its composites using high-resolution X-ray diffractionmeter (XRD) was carried out and the presence of non-uniform, depth-related strain in the MOF crystals was confirmed. Further analysis showed that the magnitude and distribution of strain in MOF crystals can be tuned with the incorporation of nanoparticles (NPs). Moreover, the spatial controlled structures can also optimize functionalities of the NPs@MOF, which was exemplified by their applications on the catalytic reduction of nitroarenes. It is anticipated that the investigation of MOF structure evolution through controlling the architectures of the MOF/NPs hybrid materials will shed a light on the study of optimizing the mechanical and chemical properties of MOF composites.     

Energy structure and absorption spectra of colloidal CdS nanocrystals in gelatin matrix

We investigate the energy structure of colloidal CdS nanocrystals by measuring the UV–vis absorption spectra. Nanocrystals were synthesized by sol–gel method in a gelatin matrix in the size range from 2.5 to 3.9 (±0.2) nm. In order to interpret the UV–vis absorption spectra we calculate the energy spectrum of electron quasi-stationary states using the model of open nanocrystal as well as the hole stationary spectrum in a two-band approach. It is shown that the main contribution to the absorption spectrum is made by interband transitions 1S_3/2→1S_e and 1P_3/2→1P_e, and its shape is determined by the size distribution of nanoparticles. For this system the estimated values of the effective masses of the heavy hole and light hole are 1.44m₀ and 0.28m₀, respectively.     

Characterization of the channel walls roughness in photonic crystal fibers

We present electron microscope (FEI NanoSEM) and atomic force microscopy measurements of surface roughness in nanochannels in photonic crystal fibers (PCF). A method was invented to cleave the PCF along the axis without damaging the surface structure in the nanochannels allowing us to characterize the morphology of the nanochannels in the PCF. A multi-wall carbon nanotube mounted onto commercial AFM probes and super sharp silicon non-contact mode AFM probes were used to characterize the wall roughness in the nanochannels. The roughness is shown to have a Gaussian distribution, and has an amplitude smaller than 0.5 nm. The height–height correlation function is an exponential correlation function with an autocorrelation length of 13 nm, and 27 nm corresponding with scan sizes of 200×100 nm², and 1600×200 nm², respectively.     

Free vibration of non-uniform nanobeams using Rayleigh–Ritz method

In this article, boundary characteristic orthogonal polynomials have been implemented in the Rayleigh–Ritz method to investigate free vibration of non-uniform Euler–Bernoulli nanobeams based on nonlocal elasticity theory. Non-uniform cross section of nanobeams has been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinate. Detailed analysis has been reported for all the possible cases of such variations. The objective of the present study is to analyze the effects of nonlocal parameter, boundary condition, length-to-diameter ratio and non-uniform parameter on the frequency parameters. It is found that clamped nanobeams are having highest frequency parameters than other types of boundary conditions for a particular set of parameters. It is also observed that frequency parameters decrease with increase in scaling effect parameter. First four deflection shapes of non-uniform nanobeams have also been incorporated. In this analysis, some of the new results in terms of boundary conditions have also been included.     

Aharonov–Bohm effect in non-uniform crater-like quantum dot with double rim

We study electron energies in a double concentric quantum ring with anisotropy in the rims heights in the presence of the external magnetic field applied along the symmetry axis. To this end, we consider a model in which the thickness grows linearly from the axis up to the inner rim with a slope different from one between the inner and the outer rims. The anisotropy in the rims heights originated by the presence in the structure of various valleys we simulate by periodic dependence of the slope on the radial direction. We show that the wave functions of the electron confined in such structure can be found analytically if the slopes in all radial directions are the same, and by using a simple exact diagonalization procedure otherwise. The behavior of the electron energies as functions of the magnetic field, rings radii and rims heights, as well as the number of the valleys and their depths is consistently described with our formalism. The entanglement of the states with different radial and orbital quantum numbers, the period and the amplitude of the Aharonov–Bohm oscillations are very sensible to any variations of the rims heights.     

The Ising version of the t–J model

The t–J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.