Modern Physics Letters B

Chromium-doped manganese–zinc ferrite samples were prepared by solid-state reaction route to probe the effect of chromium ion on the crystal and lattice structure of mixed manganese–zinc ferrite. X-ray diffraction patterns reveal that Mn${}_{0.5}$Zn${}_{0.5-x}$Cr${}_x$Fe${}_2$O${}_4$ ($x$ = 0.0, 0.1, 0.2, 0.3, 0.4 and 0.5) ferrite has polycrystalline cubic spinel structure with some secondary phase of $\alpha$–Fe${}_2$O${}_3$. The Raman spectra reveal four Raman active phonon modes in the measurement range of 200–750 cm${}^{-1}$ with small shift in Raman modes towards higher wave number. The average particle size for Mn${}_{0.5}$Zn${}_{0.5}$Fe${}_2$O${}_4$ is found to be 37.28 nm which reduces to 33.64 nm for Mn${}_{0.5}$Cr${}_{0.5}$Fe${}_2$O${}_4$. As the ion doping of chromium increases, the modes of vibration are found to shift towards higher wavelength and blueshift is attributed to the higher ionic radii of Cr${}^{2+}$ as compared to Zn${}^{2+}$.

In order to detect weld defects in laser welding T-joint of Al–Li alloy, a real-time X-ray image system is set up for quality inspection. Experiments on real-time radiography procedure of the weldment are conducted by using this system. Twin fillet welding seam radiographic arrangement is designed according to the structural characteristics of the weldment. The critical parameters including magnification times, focal length, tube current and tube voltage are studied to acquire high quality weld images. Through the theoretical and data analysis, optimum parameters are settled and expected digital images are captured, which is conductive to automatic defect detection.

The electronic structure, density of states (DOS), effective mass are calculated for tetragonal TlInSe₂ from first principle in the framework of density functional theory (DFT). The electronic structure of TlInSe₂ has been investigated by Quantum Wise within GGA. The calculated band structure by Hartwigsen–Goedecker–Hutter (HGH) pseudopotentials (psp) shows both the valence band maximum and conduction band minimum located at the T point of the Brillouin zone. Valence band maximum at the T point and the surrounding parts originate mainly from 6s states of univalent Tl ions. Bottom of the conduction band is due to the contribution of 6p-states of Tl and 5s-states of In atoms. Calculated DOS effective mass for holes and electrons are $m_{{\mathrm{\text{DOS}}}_h}^{\ast }=0.830m_e$, $m_{{\mathrm{\text{DOS}}}_h}^{\ast }=0.492m_e$, respectively. Electron effective masses are fairly isotropic, while the hole effective masses show strong anisotropy. The calculated electronic structure, density of states and DOS effective masses of TlInSe₂ are in good agreement with existing theoretical and experimental results.

A novel model of hexagonal photonic crystal fiber (PCF) composed of fluoride-doped silicate and plasma materials for estimating the off-axis band structure has been presented. The well-known plane wave expansion (PWE) method has been adopted for the analysis of band structure. We have observed the influence of intensity of field on photonic band gap (PBG) by creating different types of defect in the holes of the PCF structure for the design of waveguide and narrow-band filter. A dynamic shift in bands and photonic band gaps (PBGs) has been reported and compared with other designs. The PCF containing the defect of high index material in the presence of plasma has been found to be more suitable to control the propagation of photon for nonlinear waves. The PWE calculations have shown that the four off-axis PBGs for the different contribution of plasma holes could exceed by 1.0 normalized frequency or they could compensate within 0.24 normalized frequencies on introducing alternate distribution of high index material like SF57 in the cladding.

The lump soliton solutions of a (2 + 1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation are obtained by making use of its bilinear form. We discuss the conditions to guarantee the analyticity, positiveness and localization of lump solutions. The solutions of interaction between a lump and a stripe are presented. It is proved that the interaction between the two solitary waves is non-elastic. The three-wave method is employed to investigate the periodic lump solutions. Figures are presented to illustrate the dynamical features of these solutions.

The formality of signed relationships has been recently adopted in a lot of complicated systems. The relations among these entities are complicated and multifarious. We cannot indicate these relationships only by positive links, and signed networks have been becoming more and more universal in the study of social networks when community is being significant. In this paper, to identify communities in signed networks, we exploit a new greedy algorithm, taking signs and the density of these links into account. The main idea of the algorithm is the initial procedure of signed modularity and the corresponding update rules. Specially, we employ the “Asymmetric and Constrained Belief Evolution” procedure to evaluate the optimal number of communities. According to the experimental results, the algorithm is proved to be able to run well. More specifically, the proposed algorithm is very efficient for these networks with medium size, both dense and sparse.

This paper investigates the mixed $H_{\infty }$ and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks with time delays. Our aim is to design a controller such that, though the unavoidable phenomena of time delay and external disturbances is fully considered, the resulting closed-loop system is stable with a mixed $H_{\infty }$ and passive performance level. By combining sliding mode control and adaptive control methods, a novel adaptive sliding mode control strategy is designed for the synchronization of time-delayed FO dynamic networks. Via the application of FO system stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequalities. Based on the conditions, a desired controller which can guarantee the stability of the closed-loop system and also ensure a mixed $H_{\infty }$ and passive performance level is designed. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.

In this paper, theoretical solutions for degree distribution of decreasing random birth-and-death networks $(0<p<1/2)$ are provided. First, we prove that the degree distribution has the form of Poisson summation, for which degree distribution equations under steady state and probability generating function approach are employed. Then, based on the form of Poisson summation, we further confirm the tail characteristic of degree distribution is Poisson tail. Finally, simulations are carried out to verify these results by comparing the theoretical solutions with computer simulations.

Currently, with the rapid development of information technology, the electronic media for social communication is becoming more and more popular. Discovery of communities is a very effective way to understand the properties of complex networks. However, traditional community detection algorithms consider the structural characteristics of a social organization only, with more information about nodes and edges wasted. In the meanwhile, these algorithms do not consider each node on its merits.

Label propagation algorithm (LPA) is a near linear time algorithm which aims to find the community in the network. It attracts many scholars owing to its high efficiency. In recent years, there are more improved algorithms that were put forward based on LPA. In this paper, an improved LPA based on random walk and node importance (NILPA) is proposed. Firstly, a list of node importance is obtained through calculation. The nodes in the network are sorted in descending order of importance. On the basis of random walk, a matrix is constructed to measure the similarity of nodes and it avoids the random choice in the LPA. Secondly, a new metric IAS (importance and similarity) is calculated by node importance and similarity matrix, which we can use to avoid the random selection in the original LPA and improve the algorithm stability.

Finally, a test in real-world and synthetic networks is given. The result shows that this algorithm has better performance than existing methods in finding community structure.

This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati–Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.