Comment on “Exponential ultimate boundedness of fractional-order differential system via periodically intermittent control” [Nonlinear Dyn 2019;92(2), 247–265]

Nonlinear Dynamics - In this note, some points to paper (Xu L.G., Liu W.,” Hu ”H.X.:“Exponential ultimate boundedness of fractional-order differential system via periodically...     

Some phenomena for weak spring Duffing equation in subharmonic and ultrasubharmonic region

In this paper the situation in which weak spring Duffing equation gets into the chaos on account of small perturbation is discussed with Melnikov-Holmes’ method, and some phenomena in which the different subharmonic and the ultrasubharmonic coexist with the chaos are discovered.     

CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES

Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi- contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L . B . Ciric , Q . H. Liu , H. E. Rhoades and H. K. Xu , et al. , but also give an affirmative answer to the open question of Rhoades-Naimpally-Singh in convex metric spaces .     

Defect and improvement of Two-Time Expansion method in nonlinear oscillations

In this paper, the defect of the Two-Time Expansion method is indicated and an improvement of this method is suggested. Certain examples in which the present method is used, are given. Moreover, the paper shows the equivalence of the improved Two-Time Expansion Method and the method of KBM (Krylov-Bogoliubov-Mitropolski).Finally, we Thank Prof. Xu Zhao for his help.     

SOME IDENTITY RELATIONS BETWEEN PLANE PROBLEMS FOR VISCO-AND ELASTICITY

I.IntroductionThereareimportantapplicationsfortheor}:ofplanea'iscoelasticit}'Inthefieldsofgeology,miningandconstructingetc.,butformostproblemsofviscoelastici[}'.theirsolutionsareobtainedfromthecorrespondingelasticsolutionsb}'"leansofthecorrespondenceprinc…     

关于具有激波的流动的稳定性

<正> 1、引言 流体运动总是同时受动力学和热力学规律的约制,通常处理流动问题时这两方面的考虑也总是交织在一起,例如,为了定义描述流动现象的诸流动变量,首先要假定每个流体质点微团是处于热力学平衡态,即假定流动系统满足“局域热平衡”条件。这样才可以定义各“点”的压力、密度、熵等变量。由于流动系统同时又是一个热力学系统,因此它的     

Two-stage fourth-order gas-kinetic scheme for three-dimensional Euler and Navier-Stokes solutions

ABSTRACT

For the one-stage third-order gas-kinetic scheme (GKS), successful applications have been achieved for the three-dimensional compressible flows [Pan, L., K. Xu, Q. Li, and J. Li. 2016. “An Efficient and Accurate Two-stage Fourth-order Gas-kinetic Scheme for the Navier-Stokes Equations.” Journal of Computational Physics 326: 197–221]. The high-order accuracy of the scheme is obtained by integrating a multidimensional time-accurate gas distribution function over the cell interface within a time step without using Gaussian quadrature points and Runge-Kutta time-stepping technique. However, to the further increase of the order of the scheme, such as the fourth-order one, the one step formulation becomes very complicated for the multidimensional flow. Recently, a two-stage fourth-order GKS with high efficiency has been constructed for two-dimensional inviscid and viscous flow computations ([Li, J., and Z. Du. 2016. “A Two-stage Fourth Order Time-accurate Discretization for Lax-Wendroff Type Flow Solvers I. Hyperbolic Conservation Laws.” SIAM Journal on Scientific Computing 38: 3046–3069]; Pan et al. 2016), and the scheme uses the time accurate flux function and its time derivatives. In this paper, a fourth-order GKS is developed for the three-dimensional flows under the two-stage framework. Based on the three-dimensional WENO reconstruction and flux evaluation at Gaussian quadrature points on a cell interface, the high-order accuracy in space is achieved first. Then, the two-stage time stepping method provides the high accuracy in time. In comparison with the formal third-order GKS [Pan, L., and K. Xu. 2015. “A Third-order Gas-kinetic Scheme for Three-dimensional Inviscid and Viscous Flow Computations.” Computers & Fluids 119: 250–260], the current fourth-order method not only improves the accuracy of the scheme, but also reduces the complexity of the gas-kinetic flux solver greatly. More importantly, the fourth-order GKS has the same robustness as the second-order shock capturing scheme [Xu, K. 2001. “A Gas-kinetic BGK Scheme for the Navier-Stokes Equations and its Connection with Artificial Dissipation and Godunov Method.” Journal of Computational Physics 171: 289–335]. Numerical results validate the outstanding reliability and applicability of the scheme for three-dimensional flows, such as the cases related to turbulent simulations.     

Une méthode de calcul des coefficients de réflexion et de transmission d'une houle bidimensionnelle en milieu confinéA new method for the calculation of transmission and reflection coefficients for water waves in a small basin

This paper presents a method to estimate reflected and transmitted wave amplitude spectra in a bounded domain such as a wave tank, when available data signals must be shortened due to interferences and wall effects. This paper extends the well known Goda and Suzuki two-probe method to three probes. The paper also suggests solutions to compute reliable transmission and reflection coefficients in spite of problems linked to higher harmonics and to the interference between different wave trains propagating in the tank. To cite this article: G. Duclos, A.H. Clément, C. R. Mecanique 331 (2003).     

钢管混凝土拱稳定分析的有限元法

在 2 0结点三维块体等参元及 1 6结点相对位移板壳元 [1 ] 的基础上、引入梁的基本假定 ,采用等效数值积分法 ,构造出 1 2 - 2 0结点三维退化平面和柱面层合曲梁单元 ,同时给出用于梁或拱线弹性稳定性分析的有限元列式 ,最后 ,以绍兴轻纺大桥为工程背景 ,计算出轻纺大桥钢管混凝土拱面内屈曲及面外侧倾屈曲的临界荷载。     

Creep damage constitutive equations for multi-axial states of stress for 0.5Cr0.5Mo0.25V ferritic steel at 590°C

Multi-axial creep damage constitutive equations are developed for 0.5Cr0.5Mo0.25V ferritic steel at 590°C. It is aimed to overcome the deficiency of inconsistency in predicted and observed creep strains existed in previous formulations [Q. Xu, in: European Conference on Advances in Mechanical Behaviour, Plasticity and Damage, 7–9 November 2000, Tours, France; Creep Damage Mechanics Research Report, The School of Engineering, The University of Huddersfield, 2000; I.J. Perrin, D.R. Hayhurst, J. Strain Anal. 31 (4) (1996) 299]. In this paper, the lifetime and strain at failure are qualitatively validated in a wider range of states of stress by which the capability of producing consistent results is demonstrated.     

气体动理学统一算法中相容性条件不满足引起的数值误差及其影响研究

求解玻尔兹曼(Boltzmann) 模型方程的气体动理学统一算法(unified gas kinetic scheme,UGKS) 是为模拟存在显著稀薄气体效应流动而建立的. 在该方法中,如果速度空间离散采用传统的离散速度坐标法(discreteordinate method,DOM),将会导致相容性条件得不到严格满足,从而引入数值误差. 本文从理论分析及数值试验两方面说明了该数值误差,正比于来流马赫数,反比于来流努森数. 引入了守恒型的离散速度坐标法(conservativediscrete ordinate method,CDOM),在离散层面上确保了相容性条件得到严格满足. 圆柱绕流计算结果表明,来流马赫数较高、努森数较小时,相容性条件满足与否对计算结果影响较大,采用CDOM 可以在较稀的速度空间网格上得到网格无关解,缩减计算量最大可达2/3.      

Singular Characteristics of Nonlinear Normal Modes in a Two Degrees of Freedom Asymmetric Systems with Cubic Nonlinearities

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｍｏｄｅｒｎａｎａｌｙｓｉｓａｎｄｍｅｔｈｏｄｓｆｏｒｎｏｎｌｉｎｅａｒｄｙｎａｍｉｃｓｈａｖｅｇｒｅａｔｌｙｐｒｏｍｏｔｅｄｔｈｅｄｅｖｅｌｏｐｍｅｎｔｉｎｎｏｎｌｉｎｅａｒｓｃｉｅｎｃｅ.ＴｈｅｓｅｉｎｃｌｕｄｅＬ＿Ｓｒｅｄｕｃｅ[1],ｓｉｎｇｕｌａｒｉｔｙｔｈｅｏｒｙ[2 ],ｐｅｒｔｕｒｂａｔｉｏｎｔｅｃｈｎｉｑｕｅ[3 ],Ｍｅｌｎｉｋｏｖｆｕｎｃｔｉｏｎ[4 ],Ｃ＿Ｌｍｅｔｈｏｄ[5 ]ａｎｄｃｅｎｔｅｒｍａｎｉｆｏｌｄ[6],ｅｔｃ .Ｈｏｗｅｖｅｒ,ｔｈｅｃｏｕｐｌｉｎｇｂｅ…     

基于Mask R-CNN网络的磨损颗粒智能识别与应用

针对设备磨损故障诊断中磨粒识别技术难度高、工作主观经验影响大等问题,采用深度学习技术开展了磨粒智能识别的研究,提出了基于Mask R-CNN卷积神经网络的磨粒数字化表征方法. 该方法利用迁移学习训练基于Mask R-CNN网络的磨粒识别模型对图像中磨粒进行识别和实例分割,然后使用Suzuki85算法、迭代算法、等比例计算方法计算出磨粒的真实尺寸,解决了磨粒分析中难定量分析的问题. 结果表明:基于Mask R-CNN网络(采用R-101-FPN骨干网络)训练的磨粒识别模型可以对图像中多个异常磨损颗粒进行识别,综合准确率和召回率达到当前图像识别领域的主流水平. 辅以上述Suzuki85等算法,成功实现磨粒图像的定量评价分析,对促进设备故障诊断技术的自动化发展和工业应用具有一定的实际应用价值.      

Assessment of gas and liquid velocities induced by an impacting liquid drop

A two-phase flow model using the boundary element method was applied to investigate the physics of a liquid drop impacting onto a solid, dry plate. Xu et al. showed that air pressure plays an important role in splashing: as air pressure was reduced, splashing of an ethanol drop with a Weber number of 838 was suppressed. This remarkable observation provided the motivation for the current modeling effort. We numerically investigate how air pressure affects the behavior of an impacting drop. Surveying both inside and outside the impacting drop, velocities of both the liquid and gas are computed. Simulations show that gas speed, as it is displaced by the falling drop, is more than three times higher than the incoming drop speed. Air entrainment induced by the displaced gas seems to be an important contributor to corona formation, which always precedes any instability, fingering, or splashing of the liquid. To describe drop-impact phenomena, the maximum spreading diameter of the drop and the topology of the impacting fluid are reported as functions of Weber number and gas density.     

DSMC approach to nonstationary Mach reflection of strong incoming shock waves using a smoothing technique

The direct simulation Monte Carlo (DSMC) method is applied to simulation of nonstationary Mach reflection of strong shock waves. Normally the DSMC method is very time consuming in solving unsteady flow field problems especially for high Mach numbers, because of the necessity of iterative calculations to eliminate the inherent statistical fluctuation caused by a finite sample size. A central weighted smoothing technique is introduced to process the DSMC results, so that the iteration time can be significantly reduced. In spite of some relaxations of the shock wave structure, the smoothing technique is verified to be useful to estima te the flow fields qualitatively and even quantitatively by using a relatively small sample size. The comparison between the present approach and the kineticmodel approach (Xu et al. 1991a, 1991b) on the application to unsteady rarefied flow fields was also carried out.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Harmonic model of graphene based on a tight binding interatomic potential

Like in many other materials, the presence of topological defects in graphene has been demonstrated to modify its behavior, thus enhancing features aimed at several technological applications, more specifically, its electronic and transport properties. In particular, pristine defect-free graphene has been shown to be of limited use for semiconductor-based electronics, whereas the presence of individual or cluster defect rings along grain boundaries hinders electron transport and introduce a transport gap, unveiling the possibility of novel electronic device applications based on the structural engineering of graphene-based materials. In this work, we present an atomic bondwise force-constant model from the tight binding potential by Xu et al. (1992), that accounts for the electron-mechanical coupling effects in graphene. First we verify that this computational scheme is capable of accurately predicting the defect energies and core structures of dislocation dipoles based on the theory of discrete dislocations of Ariza and Ortiz (2005). In order to demonstrate our ability to characterize the effect of patterned distributions of structural defects on the electronic structure of graphene, we present the electronic band structures and density of states curves of several defective graphene sheets.     

One-dimensional quasistatic nonisothermal evolution of shape-memory material inside the hysteresis loop

We study in this paper the quasistatic nonisothermal processes of a onedimensional bar consisting of a two-phase shape-memory material. The system of p.d.e.'s governing the evolution of the bar is obtained by means of a temperature-dependent hysteretic stress-strain law that we formulate as a plasticity criterion and a hysteresis operator. The constitutive theory is developed here on the basis of the mixture approach proposed by Mtiller [t] and of a natural extrapolation of the isothermal experimental data regarding the behavior of the material inside the hysteresis loop recently described by Miiller and Xu [2]. Numerical simulations are presented for three initial and boundary-value problems of interest with regard to uniaxial stretching experimental tests.     

An instrumented vehicle for offroad dynamics testing

The paper presents an instrumented vehicle that was equipped with measuring systems to perform complete dynamics tests, especially in off-road conditions. The equipment consists of four wheel dynamometers, a steering robot, and a differential GPS system together with an inertial platform, a non-contact vehicle speed sensor, and an on-board computer with software to control the devices and collect experimental data. The four wheel dynamometers measure six elements; based on strain gage force transducers, it measures three orthogonal forces and three moments. The steering robot can control the steering wheel of the vehicle at a variety of excitation modes; it can carry out typical vehicle dynamics tests (ISO 7401, ISO 4138, ISO/TR3888, etc.) as well as custom engineered tests at a wide range of setting parameters (steer angle rate up to 1600 deg/s). The differential GPS system gives true time vehicle kinematics data (velocities, accelerations, angles, etc.) at 10-ns sample rate and 20-mm accuracy. The base vehicle, a Suzuki Vitara 4 × 4, required no special modifications or changes to install the measuring equipment. The paper also describes typical tests performed with the use of the instrumented vehicle together with sample results.     

Zero singularity of codimension two or three in a four-neuron BAM neural network model with multiple delays

In this paper, a four-neuron BAM neural network model with multiple delays is considered. The existence conditions under which that the origin of the system is Bogdanov–Takens (B–T) or triple zero singularity are given. By choosing the connected weights as bifurcation parameters and using the center manifold reduction and the normal form theory and the formula developed by Xu and Huang (J Differ Equ 244:582–598 2008) and Qiao et al. (Chinese Ann Math Ser A 31:59–70 2010), the versal unfoldings and the normal forms for this singularity were given to analyze the behaviors of the system. This paper is a further study of paper Cao and Xiao (IEEE Trans Neural Netw 18:416–430 2007).