Modern Physics Letters B

This paper deals with $M$-soliton solution of the (2+1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation by virtue of the Hirota bilinear operator method. The obtained solutions for solving the current equation represent some localized waves including soliton, periodic and cross-kink solutions, which have been investigated by the approach of the bilinear method. Mainly, by choosing specific parameter constraints in the $M$-soliton solutions, all cases of the periodic and cross-kink solutions can be captured from the one-, two- and three-soliton solutions. The obtained solutions are extended with numerical simulation to analyze graphically, which results into one-, two- and three-soliton solutions and also periodic and cross-kink solutions profiles. That will be extensively used to report many attractive physical phenomena in the fields of acoustics, heat transfer, fluid dynamics, classical mechanics and so on.

Small amount of Ni was added in the ${\mathrm{\text{Gd}}}_{50}{\mathrm{\text{Co}}}_{50}$ binary alloy to replace the Co element for improving the formability and magnetic properties of the binary amorphous alloy. It was found that the glass formability of the ${\mathrm{\text{Gd}}}_{50}{\mathrm{\text{Co}}}_{50}$ amorphous alloy was significantly improved by Ni addition. The Curie temperature $(T_c)$ of the ${\mathrm{\text{Gd}}}_{50}{\mathrm{\text{Co}}}_{50-x}{\mathrm{\text{Ni}}}_x$ metallic glasses decreases with the Ni addition, and the maximum magnetic entropy change $(-\mathrm{\Delta }{S}_m^{\mathrm{\text{peak}}})$ was also improved. The mechanism for the effect of adding a small quantity of Ni on the $T_c$ and $-\mathrm{\Delta }{S}_m^{\mathrm{\text{peak}}}$ of the ${\mathrm{\text{Gd}}}_{50}{\mathrm{\text{Co}}}_{50}$ amorphous alloy was studied.

In this work, two numerical schemes were developed to overcome the problem of shock waves that appear in the solutions of one/two-layer shallow water models. The proposed numerical schemes were based on the method of lines and artificial viscosity concept. The robustness and efficiency of the proposed schemes are validated on many applications such as dam-break problem and the problem of interface propagation of two-layer shallow water model. The von Neumann stability of proposed schemes is studied and hence, the sufficient condition for stability is deduced. The results were presented graphically. The verification of the obtained results is achieved by comparing them with exact solutions or another numerical solutions founded in literature. The results are satisfactory and in much have a close agreement with existing results.

The glass powder with a relatively complicated composition of 64.02SiO₂–10.05B₂O₃–7.84Na₂O–14.07ZnO–4.02Al₂O₃ (in wt.%) was first synthesized via sol–gel route. The optimal synthesis conditions for the amorphous gel are obtained. The glass transition temperature $(T_{\mathrm{\text{g}}})$ of xerogel was detected as 552${}^{\circ }$C and the glass network structure formed by the [SiO₄], [BO₄] and [AlO₄] units were confirmed by the Fourier Transform-Infrared Spectroscopy (FT-IR). The phase structure and morphologies of glass powder were characterized by X-ray diffractometer (XRD) and Field Emission-Scanning Electron Microscope (FE-SEM), the xerogels and sol–gel glasses exhibit amorphous phase when the heat-treatment temperature increases from $300^{\circ }$C to $700^{\circ }$C. The prepared glass powder with high specific surface areas and a large amount of pores contribute to the synthesis of a composite of glass-mullite-$\beta$-eucryptite at a relatively low sintering temperature of $800^{\circ }$C, which present a relatively low coefficient of thermal expansion (CTE) and high mechanical strength.

In this paper, the performance of copper-indium-gallium-diselenide Cu(In,Ga)Se₂ solar cell, with ZnO window layer, ZnSe buffer layer, CIGS absorber layer and InGaP reflector layer was studied. The study was performed using the TCAD Silvaco simulator. The effects of grading the band gap of CIGS absorber layer, the various thicknesses and doping concentrations of different layers have been investigated. By optimizing the solar cell structure, we have obtained a maximum open circuit voltage of 0.91901 V, a short circuit current density of 39.89910 mA/cm², a fill factor (FF) of 86.67040% and an efficiency of 31.78% which is much higher than the values for similar CIGS solar cells reported so far.

In this paper, the Riemann–Hilbert approach is applied to investigate a higher-order Chen–Lee–Liu equation with third-order dispersion and quintic nonlinearity terms. Based on the analytical, symmetric and asymptotic properties of eigenfunctions, a generalized Riemann–Hilbert problem associated with Chen–Lee–Liu equation with nonzero boundary conditions is constructed. Further, the $N$-soliton solution is found by solving the generalized Riemann–Hilbert problem. As an illustrative example, two kinds of one-soliton solutions with different forms of parameters are obtained.

In this paper, the $N$-solitary wave solution to the (2+1)-dimensional potential Kadomstev–Petviashvili (PKP) equation is obtained with the Hirota bilinear method. Via the limit technique of long wave, the $M$-lump solution can be derived from resulting $N$-solitary wave solution. In addition, interactional solutions consisting of lumps and solitary waves for the PKP equation are obtained, which can describe elastic interactions of lumps and solitary waves. These results are illustrated by graphics of several sample examples.

The high energy density beam welding techniques, such as laser and electron beam welding process, have been widely used in industrial applications. In this study, the butt structures of Ti-6Al-4V alloys with the thickness up to 8 mm are successfully joined by the laser welding process. The macromorphology and microstructures of the welded joints are investigated by a scanning electron microscope (SEM). The penetration increases from 5.91 mm to 9.37 mm with the decrease of welding speed from 1.2 m/min to 0.8 m/min under the condition of equal laser power. The acicular ${\alpha }^{\prime }$ is formed in the fusion zone, resulting from high cooling rate during the process. The metallurgical porosity formation is proposed by investigating the distribution of Al and H elements around the pores. It is concluded that the pores in the weld bead are induced by aluminum vapor and hydrogen gas from the molten pool. The diameter of metallurgical pore has a tendency to increase with the decrease of welding speed.

Compared with the other wireless communication band, X-ray carrier has the merits of lower wavelength, higher frequency and photon energy, which could provide a novel method to solve the communication problems of re-entry blackout region. In this paper, transmission characteristics of X-ray carrier in the re-entry dusty plasma medium were analyzed first, simulation results indicate that dusty particles were more likely to impede the microwave signal than X-ray carrier. Then an alkali metal plasma source was designed to simulate the re-entry dusty plasma sheath for simplification. Transmission co-efficiency under different X-ray energy were tested, which pointed out that X-ray signal would obtain more than 79.4% transmission co-efficiency on condition of dynamic and dusty plasma medium. Finally, we give our proposal and potential capability of X-ray communication in the re-entry plasma condition.

The three kinds of vortex identification methods, namely, ${\omega }_z$ criterion, $Q$ criterion and $\mathrm{\Omega }$ method, are then employed to investigate the physical interactions between the cavitation and vortex dynamics around two-dimensional Clark-Y hydrofoil. The results show that compared to the ${\omega }_z$ and $Q$ criterion, the $\mathrm{\Omega }$ method can capture the vortex structures with both strong and weak vortices, especially for the weak vortices located in the boundary of the cavity and the back region of the re-entrant flow. A proper value of $𝜀$ in $\mathrm{\Omega }$ method based on the previous studies is then suggested to avoid the pseudo-vortex structure in cavitating flow field due to division by zero. The modified $\mathrm{\Omega }$ method with a proper $𝜀$ is then applied to analyze the details of vortical structures in the growth of attached cavity, the re-entrant flow development stage and the cloud cavity shedding stage. The results show that the vortical structures are captured in the boundary and rear region of the attached cavity, the intensity and complexity of strong vortices in the rear boundary region of re-entrant flow increased with its development, and the strength and area of vortical structures at the trailing edge of hydrofoil increased with propulsion of cloud cavity before it sheds completely.

Symmetric and anti-symmetric trapped modes in a cylindrical tube with a segment of higher density are studied. The problem is reduced to an eigenvalue problem of the spatial Helmholtz equation subject to vanishing Dirichlet boundary condition in the cylindrical coordinate system. Through the domain decomposition method and matching technique, multiple frequency parameters are determined by solving the characteristic equation, and the corresponding n-fold periodic trapped modes can be constructed. It is found that in addition to the fundamental mode, the second- and higher-order trapped modes exist, which depend on the density ratio and length of the inhomogeneity. The local inhomogeneity leads to a decrease of the cutoff frequencies of the homogeneous tube and the corresponding vibration mode is localized near the inhomogeneous segment.

In this paper, the modulation instability (MI) of a $(1+1)$-dimensional nonlocal nonlinear Schrödinger equation with general polynomial law nonlinearity and an external potential is investigated. Some new dark and bright soliton solutions are obtained for polynomial law nonlinearities of third and fifth orders.

The investigation on the terbium gallium garnet (TGG) crystal waveguides in the visible and near-infrared bands is significant for potential applications in science and technology. In this work, we report on a TGG planar waveguide based on the proton irradiation with an energy of 400 keV and a dose of $8\times 10^{16}$ ions/cm². The annealing treatments are adopted to improve optical performances of the waveguide on the conditions of 260${}^{\circ }$C and 410${}^{\circ }$C severally for 1 h. The dark-mode spectra and the refractive index distributions of the TGG waveguide are obtained before and after the thermal treatments. There is a strange phenomenon that nine modes are observed on the m-line curve after the annealing treatment at 410${}^{\circ }$C. The theoretical and experimental results demonstrate that the fabricated waveguide annealed at the temperature of 410${}^{\circ }$C can propagate more guided modes and have better capacity to confine light.

With heralded pair coherent states (HPCS), orbital angular momentum (OAM) states and pulse position modulation (PPM) technology, a decoy-state measurement-device-independent quantum key distribution (MDI-QKD) protocol is proposed. OAM states and PPM technology are used to realize the coding of the signal states in the HPCS light source. The use of HPCS light source, OAM coding and PPM coding cannot only reduce the error rate but also improve the key generation rate and communication distance. The new MDI-QKD protocol also employs three-intensity decoy states to avoid the attacks against the light source. By calculating the error rate and key generation rate, the performance of the MDI-QKD protocol is analyzed. Numerical simulation shows that the protocol has very low error rate and very high key generation rate. Moreover, the maximum communication distance can reach 455 km.