Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

One-dimensional dynamic equations of a piezoelectric semiconductor beam with a rectangular cross section and their application in static and dynamic characteristic analysis

Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional （1D） equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.

Prediction of one-dimensional CrN nanostructure as a promising ferromagnetic half-metal

Searching for one-dimensional(1D)nanostructure with ferromagnetic(FM)half-metallicity is of significance for the development of miniature spintronic devices.Here,based on the first-principles calculations,we propose that the 1D CrN nanostructure is a FM half-metal,which can generate the fully spin-polarized current.The ab initio molecular dynamic simulation and the phonon spectrum calculation demonstrate that the 1D CrN nanostructure is thermodynamically stable.The partially occupied Cr-d orbitals endow the nanostructure with FM half-metallicity,in which the half-metallic gap(?s)reaches up to 1.58 eV.The ferromagnetism in the nanostructure is attributed to the superexchange interaction between the magnetic Cr atoms,and a sizable magnetocrystalline anisotropy energy(MAE)is obtained.Moreover,the transverse stretching of nanostructure can effectively modulate?s and MAE,accompanied by the preservation of half-metallicity.A nanocable is designed by encapsulating the CrN nanostructure with a BN nanotube,and the intriguing magnetic and electronic properties of the nanostructure are retained.These novel characteristics render the 1D CrN nanostructure as a compelling candidate for exploiting high-performance spintronic devices.

Size effect on light propagation modulation near band edges in one-dimensional periodic structures

Periodic photonic structures can provide rich modulation in propagation of light due to well-defined band structures.Especially near band edges,light localization and the effect of near-zero refractive index have attracted wide attention.However,the practically fabricated structures can only have finite size,i.e.,limited numbers of periods,leading to changes of the light propagation modulation compared with infinite structures.Here,we study the size effect on light localization and near-zero refractive-index propagation near band edges in one-dimensional periodic structures.Near edges of the band gap,as the structure's size shrinks,the broadening of the band gap and the weakening of the light localization are discovered.When the size is small,an added layer on the surface will perform large modulation in the group velocity.Near the degenerate point with Dirac-like dispersion,the zero-refractive-index effects like the zero-phase difference and near-unity transmittance retain as the size changes,while absolute group velocity fluctuates when the size shrinks.

A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping,the physical plane problems are transformed into regular mathematical problems in quasicrystals(QCs).The analytical solution to an elliptical orifice problem with asymmetric cracks in one-dimensional(1D)orthorhombic QCs is obtained.By using the Dugdale-Barenblatt model,the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed.Finally,the size of the atomic cohesive force zone is determined precisely,and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.

Robust Damage Detection and Localization Under Complex Environmental Conditions Using Singular Value Decomposition-based Feature Extraction and One-dimensional Convolutional Neural Network

Ultrasonic guided wave is an attractive monitoring technique for large-scale structures but is vulnerable to changes in environmental and operational conditions(EOC),which are inevitable in the normal inspection of civil and mechanical structures.This paper thus presents a robust guided wave-based method for damage detection and localization under complex environmental conditions by singular value decomposition-based feature extraction and one-dimensional convolutional neural network(1D-CNN).After singular value decomposition-based feature extraction processing,a temporal robust damage index(TRDI)is extracted,and the effect of EOCs is well removed.Hence,even for the signals with a very large temperature-varying range and low signal-to-noise ratios(SNRs),the final damage detection and localization accuracy retain perfect 100%.Verifications are conducted on two different experimental datasets.The first dataset consists of guided wave signals collected from a thin aluminum plate with artificial noises,and the second is a publicly available experimental dataset of guided wave signals acquired on a composite plate with a temperature ranging from 20℃to 60℃.It is demonstrated that the proposed method can detect and localize the damage accurately and rapidly,showing great potential for application in complex and unknown EOC.

Analysis of Dynamical Behavior of One-Dimensional Real Maps: An Executable Dynamical Programming Software Approach

The dynamical behavior of real-world phenomena is implausible graphically due to the complexity of mathematical coding. The present article has mainly focused on some one-dimensional real maps’ dynamical behavior irrespective of using coding. In continuation, linear, quadratic, cubic, higher-order, exponential, logarithmic, and absolute value maps have been used to scrutinize their dynamical behavior, including the characteristics of the orbit of points. Dynamical programming software (DPS.exe) will be proposed as a new technique to ascertain the dynamical behavior of said maps. Thus, a mathematician can automatically determine one-dimensional real maps’ dynamical behavior apart from complicated programming code and analytical solutions.

Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film

In this paper,we investigate the interfacial behavior of a thin one-dimensional(1D)hexagonal quasicrystal(QC)film bonded on an elastic substrate subjected to a mismatch strain due to thermal variation.The contact interface is assumed to be nonslipping,with both perfectly bonded and debonded boundary conditions.The Fourier transform technique is adopted to establish the integral equations in terms of interfacial shear stress,which are solved as a linear algebraic system by approximating the unknown phonon interfacial shear stress via the series expansion of the Chebyshev polynomials.The expressions are explicitly obtained for the phonon interfacial shear stress,internal normal stress,and stress intensity factors(SIFs).Finally,based on numerical calculations,we briefly discuss the effects of the material mismatch,the geometry of the QC film,and the debonded length and location on stresses and SIFs.

Beam Training and Tracking in mmWave Communication:A Survey

Communicating on millimeter wave(mmWave)bands is ushering in a new epoch of mobile communication which provides the availability of 10 Gbps high data rate transmission.However,mmWave links are easily prone to short transmission range communication because of the serious free space path loss and the blockage by obstacles.To overcome these challenges,highly directional beams are exploited to achieve robust links by hybrid beamforming.Accurately aligning the transmitter and receiver beams,i.e.beam training,is vitally important to high data rate transmission.However,it may cause huge overhead which has negative effects on initial access,handover,and tracking.Besides,the mobility patterns of users are complicated and dynamic,which may cause tracking error and large tracking latency.An efficient beam tracking method has a positive effect on sustaining robust links.This article provides an overview of the beam training and tracking technologies on mmWave bands and reveals the insights for future research in the 6th Generation(6G)mobile network.Especially,some open research problems are proposed to realize fast,accurate,and robust beam training and tracking.We hope that this survey provides guidelines for the researchers in the area of mmWave communications.

Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.

Resistive field generation in intense proton beam interaction with solid targets

The Brown-Preston-Singleton(BPS)stopping power model is added to our previously developed hybrid code to model ion beam-plasma interaction.Hybrid simulations show that both resistive field and ion scattering effects are important for proton beam transport in a solid target,in which they compete with each other.When the target is not completely ionized,the self-generated resistive field effect dominates over the ion scattering effect.However,when the target is completely ionized,this situation is reversed.Moreover,it is found that Ohmic heating is important for higher current densities and materials with high resistivity.The energy fraction deposited as Ohmic heating can be as high as 20%-30%.Typical ion divergences with half-angles of about 5°-10°will modify the proton energy deposition substantially and should be taken into account.

Using harmonic beam combining to generate pulse-burst in nonlinear optical laser

The ultrashort lasers working in pulse-burst mode reveal great machining performance in recent years. The number of pulses in bursts effects greatly on the removal rate and roughness. To generate a more equal amplitude of pulses in burst with linear polarization output and time gap adjustable, we propose a new method by the harmonic beam combining(HBC).The beam combining is commonly used in adding pulses into the output beam while maintaining the pulse waveform and beam quality. In the HBC, dichroic mirrors are used to combine laser pulses of fundamental wave(FW) into harmonic wave(HW), and nonlinear crystals are used to convert the FW into HW. Therefore, HBC can add arbitrarily more HW pulses to generate pulse-burst in linear polarization with simple structure. The amplitude of each pulse in bursts can be adjusted the same to increase the stability of the burst, the time gap of each pulse can be adjusted precisely by proper time delay. Because HBC adds pulses sequentially, the peak power density of the burst is the same as each pulse, pulses can be combined without concern of back-conversion which often occurs in high peak power density. In the demonstration, the extendibility of HBC was verified by combining two beams with a third beam. The combined efficiency rates were larger than 99%, and the beam quality of each beam was maintained at M^(2)≈1.4.

Optical trapping capability of tornado circular Pearcey beams

We systemically investigate optical trapping capability of a kind of tornado waves on Rayleigh particles.Such tornado waves are named as tornado circular Pearcey beams(TCPBs)and produced by combining two circular Pearcey beams with different radii.Our theoretical exploration delves into various aspects,including the propagation dynamics,energy flux,orbital angular momentum,trapping force,and torque characteristics of TCPBs.The results reveal that the orbital angular momentum,trapping force,and torque of these beams can be finely tuned through the judicious manipulation of their topological charges(l_(1)and l_(2)).Notably,we observe a precise control mechanism wherein the force diminishes with|l_(1)+l_(2)|and|l_(1)-l_(2)|,while the torque exhibits enhancement by decreasing solely with|l_(1)+l_(2)|or increasing with|l_(1)-l_(2)|.These results not only provide quantitative insights into the optical trapping performance of TCPBs but also serve as a valuable reference for the ongoing development of innovative photonic tools.

Development of a scintillating-fiber-based beam monitor for the coherent muon-to-electron transition experiment

The coherent muon-to-electron transition(COMET)experiment is a leading experiment for the coherent conversion of μ^(-)N→e^(-)N using a high-intensity pulsed muon beamline,produced using innovative slow-extraction techniques.Therefore,it is critical to measure the muon beam characteristics.We set up a muon beam monitor(MBM),where scintillating fibers woven in a cross shape were coupled to silicon photomultipliers to measure the spatial profile and timing structure of the extracted muon beam for the COMET.The MBM detector was tested successfully with a proton beamline at the China Spallation Neutron Source and took data with good performance in the commissioning run.The development of the MBM,including its mechanical structure,electronic readout,and beam measurement results,are discussed.

A 1-bit electronically reconfigurable beam steerable metasurface reflectarray with multiple polarization manipulations

A 1-bit electronically controlled metasurface reflectarray is presented to achieve beam steering with multiple polarization manipulations. A metsurface unit cell loaded by two PIN diodes is designed. By switching the two PIN diodes between ON and OFF states, the isotropic and anisotropic reflections can be flexibly achieved. For either the isotropic reflection or the anisotropic reflection, the two operation states achieve the reflection coefficients with approximately equal magnitude and 180°out of phase, thus giving rise to the isotropic/anisotropic 1-bit metasurface unit cells. With the 1-bit unit cells, a 12-by-12 metasurface reflectarray is optimally designed and fabricated. Under either y-or x-polarized incident wave illumination, the reflectarray can achieve the co-polarized and cross-polarized beam scanning, respectively, with the peak gains of 20.08 d Bi and 17.26 d Bi within the scan range of about ±50°. With the right-handed circular polarization(RHCP) excitation, the left-handed circular polarization(LHCP) radiation with the peak gain of 16.98 d Bic can be achieved within the scan range of ±50°. Good agreement between the experimental results and the simulation results are observed for 2D beam steering and polarization manipulation capabilities.

Uniformity Control of Scanned Beam in 300 MeV Proton and Heavy Ion Accelerator Complex at SESRI

In recent years,heavy ion accelerator technology has been rapidly developing worldwide and widely applied in the fields of space radiation simulation and particle therapy.Usually,a very high uniformity in the irradiation area is required for the extracted ion beams,which is crucial because it directly affects the experimental precision and therapeutic effect.Specifically,ultra-large-area and high-uniformity scanning are crucial requirements for spacecraft radiation effects assessment and serve as core specification for beamline terminal design.In the 300 MeV proton and heavy ion accelerator complex at the Space Environment Simulation and Research Infrastructure(SESRI),proton and heavy ion beams will be accelerated and ultimately delivered to three irradiation terminals.In order to achieve the required large irradiation area of 320 mm×320 mm,horizontal and vertical scanning magnets are used in the extraction beam line.However,considering the various requirements for beam species and energies,the tracking accuracy of power supplies(PSs),the eddy current effect of scanning magnets,and the fluctuation of ion bunch structure will reduce the irradiation uniformity.To mitigate these effects,a beam uniformity optimization method based on the measured beam distribution was proposed and applied in the accelerator complex at SESRI.In the experiment,the uniformity is successfully optimized from 75%to over 90%after five iterations of adjustment to the PS waveforms.In this paper,the method and experimental results were introduced.

Properties of focused Laguerre–Gaussian beam propagating in anisotropic ocean turbulence

We analyze the properties of a focused Laguerre–Gaussian(LG)beam propagating through anisotropic ocean turbulence based on the Huygens–Fresnel principle.Under the Rytov approximation theory,we derive the analytical formula of the channel capacity of the focused LG beam in the anisotropic ocean turbulence,and analyze the relationship between the capacity and the light source parameters as well as the turbulent ocean parameters.It is found that the focusing mirror can greatly enhance the channel capacity of the system at the geometric focal plane in oceanic turbulence.The results also demonstrate that the communication link can obtain high channel capacity by adopting longer beam wavelength,greater initial beam waist radius,and larger number of transmission channels.Further,the capacity of the system increases with the decrease of the mean squared temperature dissipation rate,temperature-salinity contribution ratio and turbulence outer scale factor,and with the increase of the kinetic energy dissipation rate per unit mass of fluid,turbulence inner scale factor and anisotropy factor.Compared to a Hankel–Bessel beam with diffraction-free characteristics and unfocused LG beam,the focused LG beam shows superior anti-turbulence interference properties,which provide a theoretical reference for research and development of underwater optical communication links using focused LG beams.

Miniature tunable Airy beam optical meta-device

Tunable Airy beams with controllable propagation trajectories have sparked interest in various fields,such as optical manipulation and laser fabrication.Existing research approaches encounter challenges related to insufficient compactness and integration feasibility,or they require enhanced tunability to enable real-time dynamic manipulation of the propagation trajectory.In this work,we present a novel method that utilizes a dual metasurface system to surpass these limitations,significantly enhancing the practical potential of the Airy beam.Our approach involves encoding a cubic phase profile and two off-axis Fresnel lens phase profiles across the two metasurfaces.The validity of the proposed strategy has been confirmed through simulation and experimental results.The proposed meta-device addresses the existing limitations and lays the foundation for broadening the applicability of Airy beams across diverse domains,encompassing light-sheet microscopy,laser fabrication,optical tweezers,etc.

Experimental and numerical analyses of the effect of fibre content on the close-in blast performance of a UHPFRC beam

Limited research has been conducted on the influences of fiber content on close-in blasting characteristics for ultrahigh-performance fiber-reinforced concrete(UHPFRC)beams.This paper aims to address this knowledge gap through experimental and mesoscale numerical methods.Experiments were conducted on ten UHPFRC beams built with varying steel fiber volumetric fractions subjected to close-in explosive conditions.Additionally,this study considered other parameters,such as the longitudinal reinforcement type and ratio.In the case of UHPFRC beams featuring normal-strength longitudinal reinforcement of diametersΦ12,Φ16,andΦ20,a reduction in maximum displacement by magnitudes of19.6%,19.5%,and 17.4%was observed,respectively,as the volumetric fractions of fiber increased from1.0%to 2.5%.In addition,increasing the longitudinal reinforcement ratio and using high-strength steel longitudinal reinforcement both significantly reduced the deformation characteristics and increase the blasting resistances of UHPFRC beams.However,the effects on the local crushing and spalling damage were not significant.A mesoscale finite element model,which considers the impacts of fiber parameters on UHPFRC beam behaviors,was also established and well correlated with the test findings.Nevertheless,parametric analyses were further conducted to examine the impacts of the steel fiber content and length and the hybrid effects of various types of microfibers and steel fibers on the blasting performance of UHPFRC beams.

Sensing-Assisted Accurate and Fast Beam Management for Cellular-Connected mmWave UAV Network

Beam management,including initial access(IA)and beam tracking,is essential to the millimeter-wave Unmanned Aerial Vehicle(UAV)network.However,the conventional communicationonly and feedback-based schemes suffer a high delay and low accuracy of beam alignment,since they only enable the receiver to passively“hear”the information of the transmitter from the radio domain.This paper presents a novel sensing-assisted beam management approach,the first solution that fully utilizes the information from the visual domain to improve communication performance.We employ both integrated sensing and communication and computer vision techniques and design an extended Kalman filtering method for beam tracking and prediction.Besides,we also propose a novel dual identity association solution to distinguish multiple UAVs in dynamic environments.Real-world experiments and numerical results show that the proposed solution outperforms the conventional methods in IA delay,association accuracy,tracking error,and communication performance.