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<jats:p>We simulate the gas-atomization process of a close-coupled annular nozzle for vacuum induction gas atomization at a three-dimensional scale. Moreover, the relationship between the simulated droplet type and experimentally metallic powder is established by comparing the morphology of droplets with powders. Herein, the primary atomization process is described by the volume-of-fluid (VOF) approach, whereas the prediction of powder diameter after secondary atomization is realized by the VOF-Lagrangian method. In addition, to completely reflect the breaking and deformation process of the metallic flow, we employ the VOF model to simulate the secondary atomization process of a single ellipsoidal droplet. The results show that the primary atomization process includes the formation of surface liquid film, appearance of serrated ligaments, and shredding of ligaments. Further, gas recirculation zone plays an important role in formation of the umbrella-shaped liquid film. The secondary atomization process is divided into droplet convergence and dispersion stages, and the predicted powder diameter is basically consistent with the experiment. In general, the four main powder shapes are formed by the interaction of five different typical droplets.</jats:p>

<jats:p>Sr-doped Ba<jats:sub>0.7</jats:sub>La<jats:sub>0.3</jats:sub>TiO<jats:sub>3</jats:sub> (BSLTO) thin films are deposited by pulsed laser deposition, and their microstructure, conductivity, carrier transport mechanism, and ferroelectricity are systematically investigated. The x-ray diffraction measurements demonstrate that Sr-doping reduces the lattice constant of BSLTO thin films, resulting in the enhanced phonon energy in the films as evidenced by the Raman measurements. Resistivity-temperature and Hall effect measurements demonstrate that Sr can gradually reduce electrical resistivity while the electron concentration remains almost unchanged at high temperatures. For the films with semiconducting behavior, the charge transport model transforms from variable range hopping to small polaron hopping as the measurement temperature increases. The metalic conductive behaviors in the films with Sr = 0.30, 0.40 conform to thermal phonon scattering mode. The difference in charge transport behavior dependent on the A-site cation doping, is clarified. It is revealed that the increasing of phonon energy by Sr doping is responsible for lower activation energy of small polaron hopping, higher carrier mobility, and lower electrical resistivity. Interestingly, the piezoelectric force microscopy (PFM) results demonstrate that all the BSLTO films can exhibit ferroelectricity, especially for the room temperature metallic conduction film with Sr = 0.40. These results imply that Sr-doping could be a potential way to explore ferroelectric metal materials for other perovskite oxides.</jats:p>

<jats:p>A series of InSb thin films were grown on GaAs substrates by molecular beam epitaxy (MBE). GaSb/AlInSb is used as a compound buffer layer to release the strain caused by the lattice mismatch between the substrate and the epitaxial layer, so as to reduce the system defects. At the same time, the influence of different interface structures of AlInSb on the surface morphology of buffer layer is explored. The propagation mechanism of defects with the growth of buffer layer is compared and analyzed. The relationship between the quality of InSb thin films and the structure of buffer layer is summarized. Finally, the growth of high quality InSb thin films is realized.</jats:p>

<jats:p>We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction, which may have potential applications in electric circuits. Nonlocal infinitely many conservation laws are constructed based on its Lax pair. Nonlocal discrete generalized (<jats:italic>m</jats:italic>, <jats:italic>N</jats:italic> – <jats:italic>m</jats:italic>)-fold Darboux transformation is extended and applied to solve this system. As an application of the method, we obtain multi-soliton solutions in zero seed background via the nonlocal discrete <jats:italic>N</jats:italic>-fold Darboux transformation and rational solutions from nonzero-seed background via the nonlocal discrete generalized (1, <jats:italic>N</jats:italic> – 1)-fold Darboux transformation, respectively. By using the asymptotic and graphic analysis, structures of one-, two-, three- and four-soliton solutions are shown and discussed graphically. We find that single component field in this nonlocal system displays unstable soliton structure whereas the combined potential terms exhibit stable soliton structures. It is shown that the soliton structures are quite different between discrete local and nonlocal systems. Results given in this paper may be helpful for understanding the electrical signals propagation.</jats:p>

<jats:p>This paper is concerned with the global stabilization of state-dependent switching neural networks (SDSNNs) via discontinuous event-triggered control with network-induced communication delay. Aiming at decreasing triggering times, a discontinuous event-trigger scheme is utilized to determine whether the sampling information is required to be sent out or not. Meanwhile, under the effect of communication delay, the trigger condition and SDSNNs are transformed into two tractable models by designing a fictitious delay function. Then, using the Lyapunov–Krasovskii stability theory, some inequality estimation techniques, and extended reciprocally convex combination method, two sufficient criteria are established for ensuring the global stabilization of the resulting closed-loop SDSNNs, respectively. A unified framework is derived that has the ability to handle the simultaneous existence of the communication delay, the properties of discontinuous event-trigger scheme, as well as feedback controller design. Additionally, the developed results demonstrate a quantitative relationship among the event trigger parameter, communication delay, and triggering times. Finally, two numerical examples are presented to illustrate the usefulness of the developed stabilization scheme.</jats:p>

<jats:p>A model predictive inverse method (MPIM) is presented to estimate the time- and space-dependent heat flux on the ablated boundary and the ablation velocity of the two-dimensional ablation system. For the method, first of all, the relationship between the heat flux and the temperatures of the measurement points inside the ablation material is established by the predictive model based on an influence relationship matrix. Meanwhile, the estimation task is formulated as an inverse heat transfer problem (IHTP) with consideration of ablation, which is described by an objective function of the temperatures at the measurement point. Then, the rolling optimization is used to solve the IHTP to online estimate the unknown heat flux on the ablated boundary. Furthermore, the movement law of the ablated boundary is reconstructed according to the estimation of the boundary heat flux. The effects of the temperature measurement errors, the number of future time steps, and the arrangement of the measurement points on the estimation results are analyzed in numerical experiments. On the basis of the numerical results, the effectiveness of the presented method is clarified.</jats:p>

<jats:p>The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate the nonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation before approximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic mode decomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, a novel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid of error data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy. Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.</jats:p>

<jats:p>Entanglement swapping is a key technology for multi-hop communication based on entanglement in quantum networks. However, the end-to-end delay of the traditional sequential entanglement swapping (SEQES) grows rapidly with the increase of network scale. To solve this problem, we first propose a low-delay multi-particle simultaneous entanglement swapping (SES) scheme to establish the remote four-particle Greenberger–Horne–Zeilinger (GHZ) channel states for the bidirectional teleportation of three-particle GHZ states, in which the intermediate nodes perform Bell state measurements, send the measurement results and the Bell state type to the user node Bob (or Alice) through classical channel simultaneously. Bob (or Alice) only needs to carry out a proper unitary operation according to the information he (or she) has received. Further, we put forward a hierarchical simultaneous entanglement swapping (HSES) scheme to reduce the classical information transmission cost, which is composed of level-1 SES and level-2 SES (schemes). The former is an inner segment SES, and the latter is an inter segments SES. Theoretical analysis and simulation results show the HSES can obtain the optimal performance tradeoff between end-to-end delay and classical cost.</jats:p>

<jats:p>We investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radially periodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially periodic potential, we first demonstrate that spin–orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar–core vortex can be observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin–orbit coupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-function phase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase of the ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin–orbit coupling strength can control the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs. Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.</jats:p>

<jats:p>By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, Majorana’s stellar representation provides an intuitive geometric perspective to comprehend the quantum system with high-dimensional Hilbert space. However, the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet. Here, a practical method is presented to resolve the problem for the mixed-spin (<jats:italic>s</jats:italic>, 1/2) system and describe the entanglement of the system. The system can be decomposed into two spins: spin-(<jats:italic>s</jats:italic> + 1/2) and spin-(<jats:italic>s</jats:italic> – 1/2) at the coupling bases, which can be regarded as independent spins. Besides, any pure state may be written as a superposition of two orthonormal states with one spin-(<jats:italic>s</jats:italic> + 1/2) state and the other spin-(<jats:italic>s</jats:italic> – 1/2) state. Thus, the whole initial state can be regarded as a state of a pseudo spin-1/2. In this way, the mixed spin decomposes into three spins. Therefore, the state can be represented by (2<jats:italic>s</jats:italic> + 1) + (2<jats:italic>s</jats:italic> – 1) + 1 = 4<jats:italic>s</jats:italic> + 1 sets of stars on a Bloch sphere. Finally, some examples are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere.</jats:p>