Negative Norm Estimates for Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for Nonlinear Hyperbolic Equations

In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing accuracy-conserving(SIAC)filter is a post-processing technique to enhance the accuracy of the discontinuous Galerkin(DG)solutions.This work is the essential step to extend the SIAC filter to the moving mesh for nonlinear problems.By the post-processing theory,the negative norm estimates are vital to get the superconvergence error estimates of the solutions after post-processing in the L2 norm.Although the SIAC filter has been extended to nonuniform mesh,the analysis of fil-tered solutions on the nonuniform mesh is complicated.We prove superconvergence error estimates in the negative norm for the ALE-DG method on moving meshes.The main dif-ficulties of the analysis are the terms in the ALE-DG scheme brought by the grid velocity field,and the time-dependent function space.The mapping from time-dependent cells to reference cells is very crucial in the proof.The numerical results also confirm the theoreti-cal proof.

Single-Step Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for 1-D Euler Equations

We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity modified by some smoothing,which is found to con-siderably reduce the numerical dissipation introduced by Riemann solvers.The scheme preserves constant states for any mesh motion and we also study its positivity preservation property.Local grid refinement and coarsening are performed to maintain the mesh qual-ity and avoid the appearance of very small or large cells.Second,higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.

A hybrid subcell-remapping algorithm for staggered multi-material arbitrary Lagrangian-Eulerian methods

A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV,M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.

Simulation of sheet metal extrusion processes with Arbitrary Lagrangian-Eulerian method

An Arbitrary Lagrangian-Eulerian(ALE) method was employed to simulate the sheet metal extrusion process,aiming at avoiding mesh distortion and improving the computational accuracy.The method was implemented based on MSC/MARC by using a fractional step method,i.e.a Lagrangian step followed by an Euler step.The Lagrangian step was a pure updated Lagrangian calculation and the Euler step was performed using mesh smoothing and remapping scheme.Due to the extreme distortion of deformation domain,it was almost impossible to complete the whole simulation with only one mesh topology.Therefore,global remeshing combined with the ALE method was used in the simulation work.Based on the numerical model of the process,some deformation features of the sheet metal extrusion process,such as distribution of localized equivalent plastic strain,and shrinkage cavity,were revealed.Furthermore,the differences between conventional extrusion and sheet metal extrusion process were also analyzed.

A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow

In this paper,we present a new vertex-centered arbitrary LagrangianEulerian(ALE)finite volume scheme for two-dimensional compressible flow.In our scheme,the momentum equation is discretized on the vertex control volume,while the mass equation and the energy equation are discretized on the sub-cells which are included in the vertex control volume.We attain the average of the fluid velocity on the vertex control volume directly by solving the conservation equations.Then we can obtain the fluid velocity at vertex with the reconstructed polynomial of the velocity.This fluid velocity is chosen as the mesh velocity,which makes the mesh move in a Lagrangian manner.Two WENO(Weighted Essentially Non-Oscillatory)reconstructions for the density(the total energy)and the velocity are used to make our scheme achieve the anticipated accuracy.Compared with the general vertexcentered schemes,our scheme with the new approach for the space discretization can simulate some multi-material flows which do not involve large deformations.In addition,our scheme has good robustness,and some numerical examples are presented to demonstrate the anticipated accuracy and the good properties of our scheme.

Complete-basis-reprogrammable coding metasurface for generating dynamicallycontrolled holograms under arbitrary polarization states

Reprogrammable metasurfaces,which establish a fascinating bridge between physical and information domains,can dynamically control electromagnetic(EM)waves in real time and thus have attracted great attentions from researchers around the world.To control EM waves with an arbitrary polarization state,it is desirable that a complete set of basis states be controlled independently since incident EM waves with an arbitrary polarization state can be decomposed as a linear sum of these basis states.In this work,we present the concept of complete-basis-reprogrammable coding metasurface(CBR-CM)in reflective manners,which can achieve independently dynamic controls over the reflection phases while maintaining the same amplitude for left-handed circularly polarized(LCP)waves and right-handed circularly polarized(RCP)waves.Since LCP and RCP waves together constitute a complete basis set of planar EM waves,dynamicallycontrolled holograms can be generated under arbitrarily polarized wave incidence.The dynamically reconfigurable metaparticle is implemented to demonstrate the CBR-CM’s robust capability of controlling the longitudinal and transverse positions of holograms under LCP and RCP waves independently.It’s expected that the proposed CBR-CM opens up ways of realizing more sophisticated and advanced devices with multiple independent information channels,which may provide technical assistance for digital EM environment reproduction.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

A numerical study of passenger side airbag deployment based on arbitrary Lagrangian-eulerian method

The passenger side airbags(PAB)are usually larger than the driver airbags.Therefore,the inflator of PAB is more powerful with high mass rate.In this paper,an Arbitrary Lagrangian-Eulerian(ALE)method based computational method is developed to simulate the deployment of a PAB.The tank test is used to test the property of the inflator.Through comparison of numerical and experimental results,the ALE method is validated.Based on a failed airbag test,a smaller sub-airbag is placed inside PAB to disperse the gas flow to directions which are less damaging.By applying dynamic relaxation,the initial mesh corresponding to the experimental terms is obtained.The results indicate that the interior pressure and impact force coincide with the test data,and the method in this paper is capable of capturing airbag deploying process of the PAB module accurately.

Efficient modeling of cable-pulley system with friction based on arbitrary-Lagrangian-Eulerian approach

In conventional modeling of a cable-pulley system, the cable must be finely meshed with Lagrangian elements for valid contact detections with pulleys, leading to extremely low efficiency. The sliding joint method based on the arbitrary-Lagrangian- Eulerian （ALE） formulation still lacks an efficient cable element, and in particular, modeling of friction between a sliding joint and the cable has not been studied. This paper presents efficient multi-body modeling of a cable-pulley system with friction. A variable- length cable element with a node movable along the cable, which is described with ALE, is developed to mesh the cable. A transitional cable element is then proposed to model the contact part of the cable by fixing its two nodes to the two corresponding locations of the pulley. Friction of the cable-pulley is derived as a simple law of tension decay and embedded in the multi-body system modeling. It is simplified as a generalized friction force acting only on the arc-length coordinate. This approach can use a rough mesh on the cable, and is free of contact detections, thus significantly saving computation time. Several examples are presented to validate the proposed method, and show its effectiveness in real engineering applications.

Hybrid Approach for Privacy Enhancement in Data Mining Using Arbitrariness and Perturbation

Imagine numerous clients,each with personal data;individual inputs are severely corrupt,and a server only concerns the collective,statistically essential facets of this data.In several data mining methods,privacy has become highly critical.As a result,various privacy-preserving data analysis technologies have emerged.Hence,we use the randomization process to reconstruct composite data attributes accurately.Also,we use privacy measures to estimate how much deception is required to guarantee privacy.There are several viable privacy protections;however,determining which one is the best is still a work in progress.This paper discusses the difficulty of measuring privacy while also offering numerous random sampling procedures and statistical and categorized data results.Further-more,this paper investigates the use of arbitrary nature with perturbations in privacy preservation.According to the research,arbitrary objects(most notably random matrices)have"predicted"frequency patterns.It shows how to recover crucial information from a sample damaged by a random number using an arbi-trary lattice spectral selection strategy.Thisfiltration system's conceptual frame-work posits,and extensive practicalfindings indicate that sparse data distortions preserve relatively modest privacy protection in various situations.As a result,the research framework is efficient and effective in maintaining data privacy and security.

Arbitrary Decode-Forward Relaying with Re-Encoded Bits Selection Strategy for Polar Codes

In this paper,we propose an arbitrary decode-forward single-relay scheme for finite blocklength polar codes,which can be applied to the general symmetric discrete memoryless relay channel with orthogonal receiver components.The relay node decodes the received message.The relay node selectively re-encodes the message and transmits it to the destination node.Furthermore,in order to minimize the upper-bound of the block error probability,we propose a selection strategy to decide the proper re-encoded bit set by the relay.Simulation results are presented to illustrate the improvement in decoding performance of the proposed scheme compared to conventional relay schemes in both additive white Gaussian noise(AWGN)channel and Rayleigh fading channel(RFC).

荀子不是任意说的中国总代表——基于体认语言学的思考

语言具有像似性还是任意性,这一争论由来已久。随着认知语言学和体认语言学的流行,学界现已普遍接受像似性的观点。在索绪尔结构主义语言学中的任意说传入我国后,学界有人寻找我国先哲以作呼应,如将荀子在《正名篇》中所言“名无固宜……”引为佐证,误把他视为索氏任意说的中国总代表。经过多年的研读和思考,我们发现这是一个严重的误读,荀子在这篇文章中阐发的论点其实是当今体认语言学所提出的体认观和像似性之先声。本文从5个方面批评了学界所谓“荀子是任意说的中国总代表”的观点,以期为荀子正名,倡导“我思故我云”之研究风尚。

收放伞绳对十字型伞静态气动特性影响的数值模拟研究

为研究十字型降落伞作为主动控制装置时,其可控性与气动特性的规律,建立了不同伞绳收缩比δ为0、10.0%、12.5%、15.0%、20.0%、25.0%时十字型伞无限质量充气的有限元模型,基于任意拉格朗日-欧拉方法进行数值模拟,分析了十字型降落伞收缩伞绳,引起伞面几何构型不对称对气动特性的影响.结果表明:不同攻角为0°、5°、10°时,十字型降落伞的平均阻力系数随伞绳收缩比δ的增大而减小;十字型伞的瞬时升力峰值随着伞绳收缩比δ的增加而增大,方向始终由伞绳收缩一侧指向另一侧,具有较强的时变特性.

6061铝合金超声辅助搅拌摩擦焊温度场分析

为了分析超声振动对6061铝合金超声辅助搅拌摩擦焊接过程温度场的影响,采用解析建模和数值模拟的方法,建立了超声辅助搅拌摩擦焊过程中接触界面摩擦系数模型和热力耦合有限元分析模型,开展了6061铝合金超声辅助搅拌摩擦焊温度测量试验,结合有限元与试验结果进行对比分析.结果表明,仿真得到的工件表面温度分布曲线及取样点温度都与试验结果基本吻合,验证了建立模型的准确性;超声振动可以改变摩擦状态,降低焊接摩擦产热,减少峰值温度及高温区域的面积,振幅对焊接峰值温度影响的显著性高于频率.

任意起伏地形下重力异常三维正演及并行计算

为了进一步提高空间-波数域三维重力异常正演算法的适用范围和计算效率,本文采用任意傅里叶变换算法实现了空间-波数域三维重力异常正演,且在NVIDIA CUDA平台上进行CPU-GPU并行加速.任意傅里叶变换算法的基本思想是将二维傅里叶变换转化为两个一维傅里叶变换,一维傅里叶变换积分离散为多个单元积分累加和,离散单元中原函数采用二次插值形函数拟合,求出单元积分的解析表达式.相比现有的傅里叶变换算法,新方法具有采样灵活、积分精度高、计算速度快和傅里叶变换的截断效应小等优势.利用空间-波数域算法的高度并行性,采用CPU并行求解常微分方程,GPU并行计算任意傅里叶变换,实现了CPU-GPU并行加速方案,进一步提升了本文算法效率.利用常密度模型,对比数值解和解析解,结果表明本文算法正确;利用变密度模型对比了任意傅里叶变换算法与高斯快速傅里叶变换算法的计算效率与精度,在相近的数值精度下,本文算法波数选取少,效率高;测试CPU-GPU并行效果,结果表明相比CPU串行算法,CPU-GPU并行算法的计算效率大大提升,千万数量级节点数模型正演仅耗时数秒.最后利用实际地形数据进行三维重力异常场数值模拟,证明了新方法的高效性与实用性,对实现大规模复杂条件下重力异常精细化反演成像与综合解释有重要意义.

下卧软弱夹层地基ALE法强夯加固数值分析

随着高能级强夯快速发展,软弱夹层对地基加固影响问题凸显,其吸能缓冲作用机理尚不清晰,夯击参数选取经验性强。基于现场试验和任意拉格朗日-欧拉(arbitrary Lagrange-Euler, ALE)法强夯加固仿真开展地基应力波传播过程研究,探讨下卧软弱夹层对加固效果影响机理。对夯击能级、夹层埋深、夹层厚度等因素进行参数研究,改进强夯参数设计流程。结果表明:软弱夹层对夯击应力波向下传播过程有迟滞作用,地基应力场在此深度内发生断层;当首击地基加固深度为1/2软弱夹层埋深时,可兼顾能级控制与施工效率需要;当软弱夹层埋深大于10 m或厚度超过2 m时加固难度较大,需配合其他工法共同加固处理。

水-空气耦合介质中冰载荷对闸墩的撞击影响研究

西北干寒地区长距离输水工程中河道修建的闸墩受到冰载荷撞击破坏,为确保冬季安全稳定供水,需进行冰载荷对闸墩撞击破坏力学特性研究。该文采用任意拉格朗日-欧拉(arbitrary Lagrangian-Eulerian, ALE)流固耦合(fluid structure interaction, FSI)方法模拟不同碰撞工况下冰体楔入闸墩碰撞过程,并通过对比实验,验证了冰材料模型参数和ALE算法的适用性,分析了网格尺寸对撞击力的影响。研究结果表明:计算得到冰载荷对闸墩撞击力极值与实验值具有良好的吻合性,表明该模拟所采用的冰材料模型参数、ALE算法和网格尺寸能够较准确模拟冰载荷对闸墩的作用力;闸墩损伤变形与冰排破损主要集中在碰撞接触区,接触区撞击力大小受到“水垫效应”的影响,空气介质对撞击力影响较小;不同冰厚和冰速工况下撞击力时程曲线呈现“Sawtooth”(上下波动)现象,撞击力加载-卸载时间较短;冰排楔入闸墩的过程中,撞击力极值出现在0°正碰接触区,在冰速1.2 m/s~3.0 m/s范围内,撞击力逐渐减小,在不改变冰速工况下,随着冰厚的增加,墩体结构响应越大,冰速和冰厚两种影响工况下闸墩顶端位移均为周期性振动。其仿真结果拟为西北干寒地区冰期河道中墩体结构安全提供指导。

基于改进傅里叶级数的黏弹性夹层板动力问题的数值算法研究

本文提出了一种基于改进傅里叶级数的新型数值算法,用于求解任意边界条件下黏弹性夹层板的自由振动特性。该算法利用一阶剪切理论建立面外位移场,采用改进的傅里叶级数拟合位移容许函数,结合Rayleigh-Ritz法计算动能和势能,并利用Hamilton变分原理得到振动特征矩阵方程。计算结果表明,无论是梁式板结构还是各种边界条件下的夹层板结构,该算法得到的自振频率和损耗因子与解析解、2D有限元解、数值计算法和ABAQUS有限元软件等计算结果相比,误差均不超过1%,计算效率提高了10倍,并且克服了传统方法只能求解特定边界下振动问题的局限性。本文建立的方法具有收敛性好、计算效率高和适应性强等特点。

基于多重机制优化YOLOv8的复杂环境下安全帽检测方法

为了解决建筑工地、隧道、煤矿等施工场景中现有安全帽检测算法对于小目标、密集目标以及复杂环境下的检测精度低的问题,提出了一种基于多重机制的安全帽检测方法。以YOLOv8n为基础将Backbone部分的C2f模块加入可扩张残差(DWR)注意力模块,使得网络能够更灵活地适应不同尺度的特征,以而更准确地识别图像中的物体;采用可变形卷积AKConv模块取代主干部分中的原始Conv,为卷积神经网络带来了显著的性能提升,从而实现更高效的特征提取。此外引用了大型可分离核注意力LSKA模块与SPPF结构相结合,大大增强了模型核心的融合能力。在Safety helmet数据集的实验结果表明,改进后的算法相较于原模型,mAP@0.5指标上提升了10.5个百分点,在mAP@0.5-0.95指标上提升了3.7个百分点,能有效提高复杂场景下的安全帽佩戴检测精度。

不定期继续性合同任意解除的生效时点

《民法典》第563条第2款规定了不定期继续性合同的任意解除制度,该制度最核心的问题是确定合同解除的时点。该款“当事人可以随时解除合同”的表述存在歧义,极易引发误解,法律和司法解释规定的不明确导致学界观点模糊不清,司法裁判立场也存在明显差异。不定期继续性合同任意解除的生效时点应为解除通知到达对方当事人后的合理期限届满时,从而有利于保护相对方合理信赖,给予相对方必要准备时间,合理规避损害赔偿的难题。具体衡量不定期继续性合同任意解除的生效时点,应从合同持续时间与履行情况、当事人对合同的依赖程度、寻求替代交易的难易程度几方面进行客观衡量,妥善平衡合同双方当事人的利益。