Modern Physics Letters B

In this paper, an $N$-coupled high-order nonlinear Schrödinger system, which describes the properties of the ultrashort optical pulses in an optical fiber, is investigated with the Darboux transformation (DT) method and asymptotic analysis. Starting from the given $(2N+1)$th-order Lax pair, we construct a new form of the DT (with some complex eigenfunctions of a Lax pair involved) to derive the formulas of the $n$th-iterated solutions, where $n$ and $N$ are the positive integers. On the zero background, the first- and second-order solitons are obtained and analyzed through the asymptotic analysis. Multi-parameter adjustment is proceeded since there are $3N+4$ real parameters in the second-order solitons. We find that under certain conditions each of the two interaction patterns (elastic and/or inelastic) holds in the second-order solitons. On the plane wave background, the first-order bright and dark–bright solitons are obtained. Velocities, amplitudes, widths and characteristic lines of the first-order bright and dark–bright solitons are presented and analyzed.

As an artificial periodic material, phononic crystals (PnCs) are suitable for energy harvesting from vibration and noise environments of equipments. A two-dimensional (2D) PnC with a point defect is presented to design a piezoelectric energy-harvesting (PEH) device. Using finite element (FE) simulations, bandwidth and electric power of the initial supercell using the PnC are obtained but do not attain the optimal performance. Therefore, five geometric parameters are considered to perform the numerical experiment using a five-factor and seven-level experimental design. The two relationships between the five geometric parameters and PnCs bandwidth, the five geometric parameters, and output power are finally obtained. The two functional relationships are regarded as a unified objective function to further optimize five geometric parameters. The optimized PnC-based PEH device will achieve better output power within broadband. It is expected to be used to design PEH devices to achieve better output power in wider bandwidth.

In sand mold three-dimensional printing (3DP), penetration of the binder material in the sand bed is a major factor that determines the printing accuracy, but this procedure has not been studied in detail before. This study aims to fill such a gap. In this study, discrete element software EDEM was used to simulate the multilayer sanding process, and a nonuniform sand bed model was constructed. The level set method was applied to track the binder-air interface. Change in the curing state of the binder was characterized by setting different values for the dynamic viscosity of the binder liquid. The multiphysics software COMSOL was used to analyze the seepage flow of the binder in the sand bed. Results showed that the contact angle directly affected the infiltration process of the binder. The smaller the contact angle, the better the penetration effect of the binder. When selecting the binder material, it was desirable to choose a material with a smaller contact angle. Simulation study suggested that when the printing width was 1500 $\mu$m, the layer thickness was 300 $\mu$m, and the binder ejection volume was 200%, the printing quality was optimal among the various cases studied. The adopted technique for modeling the curing state of the binder using varying dynamic viscosity of the binder liquid was proved to work effectively and efficiently, and satisfactorily described the penetration flow of the binder during the molding process.

In this experiment, europium(III)-ibuprofen-phenanthroline complexes, dysprosium(III)-ibuprofen-phenanthroline complexes and terbium(III)-ibuprofen-phenanthroline complexes were prepared separately, established a ternary solid complex system, performed a series of characterization of the system, and studied the application of the rare-earth-ibuprofen-phenanthroline complex system. In the experiment, the three ternary complexes were characterized by elemental analysis, infrared analysis, ultraviolet analysis, fluorescence analysis, thermogravimetric analysis, etc., and the chemical composition of the complexes was determined, and the data and spectra obtained were analyzed. The rare-earth ternary complex was successfully prepared by a simple and feasible method. The analysis results found that the characteristics and performance of the ternary complex were enhanced, and its physical and chemical properties were explored. The successful preparation of rare earth-ibuprofen-phenanthroline ternary complexes provides a certain scientific basis and reference for the study of determining the content of ibuprofen (IBU) in vitro, and also provides a new method for the synthesis of rare-earth ternary complexes. The reason why rare-earth materials can be used as catalysts is determined by their own photoelectric characteristics. In this paper, through the experimental test of catalytic performance of IBU and different rare-earth complexes, it is found that Tb complex has the best catalytic performance, and the degradation rate of phenol can reach 64.8% in 6 h.

The main goal of this paper is to extract the closed-form wave solutions by means of $(G^{\prime }/G)$-expansion method to the DNA flow known as the Peyrard–Bishop model which describes the nonlinear interaction between neighboring displacements and hydrogen bonds. The aforementioned model is investigated for the time-fractional order and the fractional derivatives are used in the sense of conformable derivatives. The projected method provides additional generic and comprehensive wave solutions incorporated with physical parameters whose specific values reveal different shapes of the waveform such as periodic soliton, singular kink soliton, singular anti-kink soliton, and other different types of solitons. The obtained soliton solutions are novel, advanced, distinct, and relevant based on the available information in the literature which may be applied to more complex phenomena. The three-dimensional, two-dimensional, and contour plots of some of the attained results are sketched by assigning individual values of the parameters to scrutinize the dynamic behavior of the waves.

The integrable Lakshmanan–Porsezian–Daniel (LPD) equation originating in nonlinear fiber is studied in this work via the Riemann–Hilbert (RH) approach. First, we give the spectral analysis of the Lax pair, from which an RH problem is formulated. Afterwards, by solving the special RH problem with reflectionless under the conditions of irregularity, the formula of general $N$-soliton solutions can be obtained. In addition, the localized structures and dynamic behaviors of the breathers and solitons corresponding to the real part, imaginary part and modulus of the resulting solution $r(x,t)$ are shown graphically and discussed in detail. Unlike 1- or 2-order breathers and solitons, 3-order breathers and soliton solutions rapidly collapse when they interact with each other. This phenomenon results in unbounded amplitudes which imply that higher-order solitons are not a simple nonlinear superposition of basic soliton solutions.

This paper introduces a new five-dimensional hyper-chaotic system with hyper-chaotic attractors. Its typical dynamical behaviors are also analyzed. The existence of hyper-chaotic attractors has been verified through Multisim and MATLAB simulations as well as circuit experiments. The Lyapunov stability theory is used to realize the stagger and adaptive synchronization of the system. During this process, the two methods are used to demonstrate the feasibility and compare the synchronization speed in different cases. The experimental results show that the staggered synchronization will converge to the synchronized state in a short time than another. This hyper-chaotic system is implemented with simple physical components to illustrate its correctness and rationality.

A novel metasurface is proposed that aims to generate underwater acoustic waves with various functions by only one actuator. Each metasurface unit consists of an air cavity sandwiched on one side by a vibration plate and connecting rubber supports. By properly selecting the ratio of the plate to unit lengths, a phase shift of $\pi$ can be attained to constitute a binary coding metasurface. Three demonstrations, including focusing, branching and self-bending waves, are chosen to validate the functionality of the design. The design is also shown to work over a wide frequency range by changing the ratio. In addition, the design is extremely compact, with the thickness only about 1/100 of the target wavelength. Compared with commonly used phased array transducers that are utilized to generate underwater acoustic waves, this design offers has the advantage of needing only a single actuator as opposed to needing a lumped electrical control system.

New results are obtained with a modified experimental setup, in order to reduce the residual detected signal when the unmodulated beam is strongly attenuated. In the light of these results, the transfer of modulation, from the modulated beam to the unmodulated one, can be attributed to a photon–photon scattering mechanism, operating in the crossing area of the two beams. Even the stochastic character of the process becomes more plausible.

In this work, we study a magnetic nanowire system composed of finite layers, forming a nanobulk. The interaction between the layers (inter-layers) is given by an exchange term $J$ and the interactions within each layer (intra-layer) are given by a magneto-static interaction energy between the nanowires. We propose to create a geometrical pattern inside of each nanobulk in order to decrease the magneto-static energy through three geometrical configurations of the nanobulk: (i) rectangular–rectangular, (ii) rectangular-cylindrical and (iii) cylindrical–cylindrical. In addition, we incorporate surface/interface effects (another material) to study energy variations inside the nanobulk. As a result, we show that there are certain geometries that minimize drastically the magneto-static energy, also that when the intensity of the $J$ coupling between the layers is too intense it implies that the energy tends to dissipate inside the nanobulk. In addition, a drop in the magneto-static energy is observed when the interfaces/surfaces of the finite-layer nanobulk are modified.

A multi-functional terahertz metamaterial with electromagnetically induced transparency (EIT) and broadband absorptions is proposed. The unit cell of the metamaterial is comprised of an E shape and a split-ring resonator on the top of the polyimide. For TE and TM polarization, the temporal coupled-mode theory reveals that the EIT effect arises from coupling two resonators. The transparent windows are experimentally demonstrated at 0.205 THz and 0.44 THz for the TM and TE polarization, respectively. When the vanadium dioxide (${\text{VO}}_2)$ film is added to the bottom of the polyimide and works in the metallic state, the metamaterial could absorb electromagnetic waves in the broadband for the two polarizations, even in the case of oblique incidence. For the TE polarization, the relative bandwidth of the absorption over 60 % absorptance is 119.8 % in the range of 0.307 THz–1.225 THz. Meanwhile, for the TM polarization, the bandwidth over 60 % absorption is 68.8 % within the range of 0.52 THz–1.065 THz. The proposed multi-functional terahertz metamaterial can be widely used in sensing technology, optical storage, stealth technology, and other fields in reality.

If a mean-field spin ring interact with a cold external thermal reservoir, the system might first evolve to the paramagnetic metastable state along the paramagnetic path, and then fluctuate around the metastable state for a long period due to an energy barrier. The spin system must absorb sufficient energy from the thermal reservoir to achieve a phase transition to the final ferromagnetic equilibrium state. However, if an external magnetic field is applied to the system, the energy barrier becomes smaller, which can reduce the relaxation time of the system significantly. Moreover, if the magnetic intensity is strong enough, the energy barrier vanishes and the system evolves directly to the equilibrium state.