Nonlinear perturbation of a high-order exceptional point:Skin discrete breathers and the hierarchical power-law scaling

We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a class of discrete breathers that aggregate to one boundary,here named as skin discrete breathers(SDBs).The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.Specifically,the response of nonlinear energy to the perturbation is given by E_(m)∝Γ~(α_(m)),whereα_(m)=3^(m-1)is the power with m=1,...,L labeling the nonlinear energy bands.This is in sharp contrast to the L-th root of a linear perturbation in general.These SDBs decay in a double-exponential manner,unlike the edge states or skin modes in linear systems,which decay exponentially.Furthermore,these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity.They are also stable,as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis.As nonreciprocal nonlinear models may be experimentally realized in various platforms,such as the classical platform of optical waveguides,where Kerr nonlinearity is naturally present,and the quantum platform of optical lattices with Bose-Einstein condensates,our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity,particularly on high-order EPs,and benchmark the relevant simulations.

Selection of quantum path in high-order harmonics and isolated sub-100 attosecond generation in few-cycle spatially inhomogeneous laser fields

We theoretically study the selection of the quantum path in high-order harmonics（HHG） and isolated attosecond pulse generation from a one-dimensional（1D） model of a H_2~＋ molecule in few-cycle inhomogeneous laser fields.We show that the inhomogeneity of the laser fields play an important role in the HHG process.The cutoff of the harmonics can be extended remarkably,and the harmonic spectrum becomes smooth and has fewer modulations.We investigate the time-frequency profile of the time-dependent dipole,which shows that the short quantum path is enhanced and the long quantum path disappears in spatially inhomogeneous fields.The semi-classical three-step model is also applied to illustrate the physical mechanism of HHG.The influence of driving field carrier-envelop phase（CEP） on HHG is also discussed.By superposing a series of properly selected harmonics,an isolated attosecond pulse（IAP） with duration 53 as can be obtained by a 15-fs,1600-nm laser pulse with the parameter ε = 0.0013（e is the parameter that determines the order of inhomogeneity of the laser field）.

Restraint of spatial distribution in high-order harmonic generation from a model of hydrogen molecular ion

The spatial distribution in high-order harmonic generation（HHG） is theoretically investigated by using a few-cycle laser pulse from a two-dimensional model of a hydrogen molecular ion. The spatial distribution in HHG demonstrates that the harmonic spectra are sensitive to the carrier envelope phase and the duration of the laser pulse. The HHG can be restrained by a pulse with the duration of 5 fs in the region from the 90 th to 320th order. This characteristic is illustrated by the probability density of electron wave packet distribution. The electron is mainly located near the nucleus along the positive-x direction from 3.0 o.c. to 3.2 o.c., which is an important time to generate the HHG in the plateau area. We also demonstrate the time-frequency distribution in the region of the positive-and negative-x direction to explain the physical mechanism.

Carrier envelope phase effect on the spatial distribution of high-order harmonic generation in asymmetric molecule

The spatial distribution in high-order harmonic generation（HHG） from the asymmetric diatomic molecule He H^（2＋） is investigated by numerically solving the non-Born–Oppenheimer time-dependent Schr？dinger equation（TDSE）. The spatial distribution of the HHG spectra shows that there is little contribution in HHG around the geometric center of two nuclei（z = 1.17 a.u.） and the equilibrium internuclear position of the H nucleus（z = 3.11 a.u.）. We demonstrate the carrier envelope phase（CEP） effect on the spatial distribution of HHG in a few-cycle laser pulse. The HHG process is investigated by the time evolution of the electronic density distribution. The time–frequency analysis of HHG from two nuclei in HeH^（2＋） is presented to further explain the underlying physical mechanism.

Convergence to Steady-State Solutions of the New Type of High-Order Multi-resolution WENO Schemes: a Numerical Study

A new type of high-order multi-resolution weighted essentially non-oscillatory(WENO)schemes(Zhu and Shu in J Comput Phys,375:659-683,2018)is applied to solve for steady-state problems on structured meshes.Since the classical WENO schemes(Jiang and Shu in J Comput Phys,126:202-228,1996)might suffer from slight post-shock oscillations(which are responsible for the residue to hang at a truncation error level),this new type of high-order finite-difference and finite-volume multi-resolution WENO schemes is applied to control the slight post-shock oscillations and push the residue to settle down to machine zero in steady-state simulations.This new type of multi-resolution WENO schemes uses the same large stencils as that of the same order classical WENO schemes,could obtain fifth-order,seventh-order,and ninth-order in smooth regions,and could gradually degrade to first-order so as to suppress spurious oscillations near strong discontinuities.The linear weights of such new multi-resolution WENO schemes can be any positive numbers on the condition that their sum is one.This is the first time that a series of unequal-sized hierarchical central spatial stencils are used in designing high-order finitedifference and finite-volume WENO schemes for solving steady-state problems.In comparison with the classical fifth-order finite-difference and finite-volume WENO schemes,the residue of these new high-order multi-resolution WENO schemes can converge to a tiny number close to machine zero for some benchmark steady-state problems.

A gas-kinetic theory based multidimensional high-order method for the compressible Navier–Stokes solutions

This paper presents a gas-kinetic theory based multidimensional high-order method for the compressible Naiver–Stokes solutions. In our previous study, a spatially and temporally dependent third-order flux scheme with the use of a third-order gas distribution function is employed.However, the third-order flux scheme is quite complicated and less robust than the second-order scheme. In order to reduce its complexity and improve its robustness, the secondorder flux scheme is adopted instead in this paper, while the temporal order of method is maintained by using a two stage temporal discretization. In addition, its CPU cost is relatively lower than the previous scheme. Several test cases in two and three dimensions, containing high Mach number compressible flows and low speed high Reynolds number laminar flows, are presented to demonstrate the method capacity.

Spectral redshift of high-order harmonics by adding a weak pulse in the falling part of the trapezoidal laser pulse

We investigate the spectral redshift of high-order harmonics of the H_2~＋（D_2~＋） molecule by numerically solving the non-Born–Oppenheimer time-dependent Schr ¨odinger equation（TDSE）. The results show that the spectral redshift of highorder harmonics can be observed by adding a weak pulse in the falling part of the trapezoidal laser pulses. Comparing with the H_2~＋ molecule, the shift of high-order harmonic generation（HHG） spectrum for the D_2~＋ molecule is more obvious.We employ the spatial distribution in HHG and time-frequency analysis to illustrate the physical mechanism of the spectral redshift of high-order harmonics.

SPATIAL－TEMPORAL DISCRETE COORDINATION OF FEM AND DIRECT INTEGRAL METHOD FOR TRANSIENT DYNAMIC PROBLEMS

In this paper, the coordination of spatial-temporal discrets of FEM and direct integral method is investigates.By analyzing the numespatial-temporal discrete,the principle of balancing the principle of balancing the energy error induced by spatialdiscrete and the energy error induced by temporal discrete is presented, and the prioriprocess and adaptive method for the coordination of spatial discerand temporal discrete is obtained.

基于图卷积的一维平流方程空间离散化数值求解加速方法

本文提出了一种基于图卷积神经网络的偏微分方程空间离散化数值求解加速方法,并将该方法应用于求解一维平流方程的研究中,实现了一维平流方程的加速求解。并设计了基于图卷积的一维平流方程空间离散化神经网络模型(GCPNN),其在物理先验知识指导下基于图模型利用空间图结构特征进行一维平流方程空间离散化求解加速方案建模,在构建图结构关系过程中,基于物理先验知识建立邻接矩阵,利用邻接矩阵融合了全局信息,从而实现了一维平流方程的加速求解。并且通过设计对比实验和消融实验验证了基于GCPNN的求解器相较于基线求解器和CNN求解器在求解精度和计算成本方面的优势,且验证了加入物理先验知识指导及全局信息融合的有效性。

一类时间离散反应扩散对流模型的全局动力学

时间离散空间连续的反应扩散方程模型是描述物种扩散行为的一类重要的研究工具。考虑到物种除了随机扩散外还会存在依赖于局部环境的扩散,文章建立了单个物种关于时间离散空间连续的反应扩散对流模型,然后利用主特征值理论分析了模型平衡点的存在性和稳定性。研究表明,加入依赖于局部环境的扩散对种群的生存是有利的。

基于GD-SPCA法的闽西南地区滑坡易发性评价

合理选择滑坡易发性评价因子是揭示滑坡易发区空间分布特征的重要前提。通过考虑因子最优离散分类,结合地理探测器(Geodetector,GD)与空间主成分分析法(Spatial Principal Component,SPCA)构建滑坡易发性指数。发现评价因子普遍呈现离散分类数越大,因子解释度越高的趋势,且自然断点法与分位数分类法的离散分类结果较好;因子间的交互作用对因子的解释度有一定影响,归一化植被指数(NDVI)的单因子解释度为0.453,但在交互作用下其耦合解释度范围仅为[0.03,0.226];研究区滑坡易发性指数为0.589,属于中度易发区,高度易发区与极易发区主要分布在研究区北部高植被覆盖的山地丘陵处;研究区的滑坡易发性指数具有显著空间聚集特征,高-高聚集区主要分布在该区北部中低山丘陵处,低-低聚集区主要分布在该区南部低缓河谷处。

智能优化算法在土木工程领域的应用综述

为进一步提高建筑施工智能化水平,对遗传算法和粒子群算法等典型算法在土木工程领域的应用进行了调查。通过分析调查结果,总结了各类算法在典型场景下的应用情况,并基于大型复杂结构施工过程,提出了智能优化算法的具体应用场景。

基于时间序列分配和多频率分量压缩的人体行为识别

为解决基于三维卷积神经网络(three dimensional convolutional neural network,3D-CNN)的人体行为识别在时间序列特征提取和特征压缩方面存在的不足,提出了更强的基于3D-CNN的骨架动作识别(stronger 3D-CNN-based approach for skeleton-based action recognition,S-PoseConv3D)网络。该网络通过引入时间序列分配策略(time series allocation strategy,TSAS)和多频率分量特征压缩(multi-frequency component feature compression fusion,M3F)有效提升了PoseConv3D的性能。TSAS通过计算时间序列权重,动态调整不同时间序列在特征提取过程中的比重,从而增强了模型对人体行为时空特征的捕捉能力。M3F则利用离散余弦变换对特征图进行多频率分量的压缩和融合,进而保留了更多的时空信息,减少了全局池化导致的特征丢失。该网络在基于体操视频的数据集(dataset built on top of gymnastic videos,FineGYM)和南洋理工大学骨架行为识别数据集60分类扩展版子集(Nanyang university of technology skeleton behavior recognition dataset 60 classification extended subset,NTU60-XSub)上进行了实验,其相比于原始PoseConv3D在FineGYM数据集上提升了3.93%的平均最高准确率,在NTU60-XSub数据集上也有显著的性能提升,表现出更高的准确率和鲁棒性。该网络能够应用在安防监控、人机交互等领域。

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.

Effect of multiple rescattering processes on harmonic emission in spatially inhomogeneous field

The effect of multiple rescattering processes on the harmonic emission from He atom in a spatially inhomogeneous field is discussed by solving the one-dimensional time-dependent Schrtdinger equation and the classical equation of motion. By establishing the physical model of the harmonic emission in the inhomogeneous field, we discuss the related characters of the multiple rescatterings process in the harmonic generation process. It shows that the second rescattering rather than the first rescattering tends to determine the harmonic cutoff energy when the inhomogeneous parameter is larger than 0.0055. Additionally, with the classica/simulation, the underlying physical mechanism of the continuum-continuum harmonics is also revealed. Moreover, this work may provide new physical insight into the harmonic generation in an inhomogeneous field, and is beneficial to further extract the harnaonic emission from molecular systems.

High-resolution algorithm based on temporal-spatial extrapolation

To enhance the resolution of parameter estimation with limited samples received by a short passive array, an iterative nonparametric algorithm for estimating the frequencies and direction-of-arrivals （DOAs） of signals is proposed. The cost function is constructed using 12-norm Gaussian entropy combined with an additional constraint, 12-norm constraint or linear constraint. By minimizing the cost functions in the temporal and the spatial dimensions using corresponding iteration algorithms respectively, the sparse discrete Fourier transforms （DFTs） of temporal and spatial samples are obtained to represent the extrapolated sequences with much larger sizes than the original samples. Then frequency and angle estimates are obtained by performing the traditional simple methods on the extrapolated sequences. It is shown that the proposed algorithm offers increased resolution and significantly reduced sidelobes compared with the periodogram and beamforming based methods. And it achieves high precision compared with the high-resolution method with lower computational burden. Some numerical simulations and real data processing results are presented to verify the effectiveness of the method.

Influence of nonlinear spatial distribution of stress and strain on solving problems of solid mechanics

The stress and the strain should be defined as statistical variables averaged over the representative volume elements for any real continuum system.It is shown that their nonlinear spatial distributions undermine the classical framework of solid mechanics and may cause non-ignorable errors to the solutions.With considering the high-order gradients of the stress and the strain,a two-step solution scheme is proposed to compensate for the influence.Through a revisit to three simple but typical problems,i.e.,the hole size-dependence of the fracture strength of perforated plates,the indentation depth-dependence of the measured elastic modulus by micro-indentation tests,and the tensile necking of metallic materials as well as hyperelastic materials,the effect of the nonlinear spatial distribution of stress and strain on solving these problems is illustrated.The observed size effect and the instability of deformation can be quantitatively explained if the effect is properly considered by the proposed method.

时间-空间高阶精度矩形交错网格隐式有限差分声波正演模拟

有限差分方法因其操作简单、计算消耗低而成为地震勘探领域中最为常用的数值模拟方法之一,然而用离散的显式差分算子数值逼近地震波动方程中的连续导数容易导致数值频散,并且基于正方形网格离散形式的有限差分方法对不同地质模型的适应性较低.针对一阶变密度声波方程的数值模拟,本文发展了一种适用于矩形网格离散形式的时间高阶空间隐式有限差分格式,可以有效压制时间和空间频散,同时灵活的网格剖分增强了其应用的广泛性.基于本文矩形交错网格时间高阶空间隐式有限差分格式的时空域频散关系和变量替换的思想,首先采用泰勒级数展开方法求解不同方向的非轴上时间差分系数及轴上空间差分系数,使本文差分格式可以获得任意偶数阶时间和空间精度.为了进一步提高本文差分格式在更大波数区域的空间模拟精度,我们采用线性优化方法来求取新的轴上空间差分系数用于一阶变密度声波方程的波场迭代求解中.频散、稳定性分析及数值模拟算例表明:相比于传统十字形空间域隐式有限差分格式,本文矩形交错网格时间高阶空间隐式有限差分格式在精度、稳定性和效率方面均具有优势.

基于EDEM的挖掘机斗齿载荷离散元仿真分析

特大型矿用液压挖掘机对提高露天矿山开采效率和保障开采质量具有不可替代的重要性。挖掘机作业载荷谱规律研究是提升其智能化水平和高效可靠运行的重要基础。基于增强离散元(EDEM)仿真软件对挖掘机斗齿载荷进行仿真分析,从斗齿间载荷夹角和幅值分布两个方面探究工作装置的空间分布规律。仿真分析表明,典型工况下斗齿载荷具有相似时间历程、相应峰值载荷与空间分布规律,为后续挖掘机工作装置的性能退化与寿命预测研究提供理论与数据基础。

商业综合体消费者行为决策机制及空间优化模拟研究

商业综合体的业态组合及空间布局呈现同质化趋势,难以与电商网络背景下消费者体验式随机消费行为相匹配。研究通过分析商业综合体内消费者行为的影响因素建立离散选择模型,并运用多智能体仿真建模技术模拟空间优化策略的实施效果。针对不同类型消费者存在的消费偏好差异,通过提升品牌知名度、调整业态布局,可以有效改善商业空间的客流分布,为商业动态运营提供可视化的决策工具。