Boundedness of semilinear Duffing equations with singularity

We prove the boundedness of all solutions for the equation x＂ ＋ V＇（x） = DxG（x,t）, where V（x） is of singular potential, i.e., limx→-1 Y（x） = ∞, and G（x, t） is bounded and periodic in t. We give sufficient conditions on V（x） and G（x, t） to ensure that all solutions are bounded.     

Dynamics of a self-propelled particle under different driving modes in a channel flow

In this paper, a model that combines the lattice Boltzmann method with the singularity distribution method is proposed to simulate a self-propelled particle swimming(exhibiting translation and rotation) in a channel flow. The results show that the velocity distribution for a self-propelled particle swimming deviates from a Maxwellian distribution and exhibits highvelocity tails. The influence of an eccentric potential doublet on the translation velocity of the particle is significant. The velocity decay process can be described using a double exponential model form. No large differences in the velocity distribution were observed for different translation Reynolds numbers, rotation Reynolds numbers, or regular intervals.     

Determination of stress intensity factor with direct stress approach using finite element analysis

In this article,a direct stress approach based on finite element analysis to determine the stress intensity fac-tor is improved.Firstly,by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack,we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity fac-tor,which is nearly equal to the stress intensity factor given by the asymptotic solution.Secondly,the crack problem is solved numerically by the finite element method.Depending on the modeling capability of the software,we designed an adaptive mesh model to simulate the stress singularity.Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corre-sponding crack problem.Therefore,the stress intensity factor may be calculated from the stress distribution in the appro-priate interval,with a high accuracy.     

插值矩阵法分析与复合材料界面相交的平面裂纹奇异应力场

提出了用插值矩阵法分析与各向异性材料界面相交的平面裂纹应力奇异性。基于V形切口尖端附近区域位移场渐近展开,将位移场的渐近展开式的典型项代入线弹性力学基本方程,得到关于平面内与复合材料界面相交的裂纹应力奇异性指数的一组非线性常微分方程的特征值问题,运用插值矩阵法求解,获得了平面内各向异性结合材料中与界面以任意角相交的裂纹尖端的应力奇异性指数随裂纹角的变化规律,数值计算结果与已有结果比较表明,本文方法具有很高的精度和效率。     

Large eddy simulation of turbulent premixed and stratified combustion using flame surface density model coupled with tabulation method

Large eddy simulations (LESs) are performed to investigate the Cambridge premixed and stratified flames, SwB1 and SwB5, respectively. The flame surface density (FSD) model incorporated with two different wrinkling factor models, i.e., the Muppala and Charlette2 wrinkling factor models, is used to describe combustion/turbulence interaction, and the flamelet generated manifolds (FGM) method is employed to determine major scalars. This coupled sub-grid scale (SGS) combustion model is named as the FSD-FGM model. The FGM method can provide the detailed species in the flame which cannot be obtained from the origin FSD model. The LES results show that the FSD-FGM model has the ability of describing flame propagation, especially for stratified flames. The Charlette2 wrinkling factor model performs better than the Muppala wrinkling factor model in predicting the flame surface area change by the turbulence. The combustion characteristics are analyzed in detail by the flame index and probability distributions of the equivalence ratio and the orientation angle, which confirms that for the investigated stratified flame, the dominant combustion modes in the upstream and downstream regions are the premixed mode and the back-supported mode, respectively.     

Universal absorption of two-dimensional materials within k ⋅ p method

The universal optical absorption is a fascinating property existing in certain two-dimensional (2D) materials. By introducing a general two-band $\mathbf{k}?\mathbf{p}$ effective Hamiltonian, we demonstrate that the absorptance can manifest an universal value at the direct band-edge of 2D materials in three specific cases. However, for general 2D materials, the absorptance becomes nonuniversal. We investigate the dependency of absorptance on the band parameters of general 2D materials. The influences of band-anisotropy and band warping are also considered. Interestingly, we find that the coherent interband coupling and the band warping are responsible for the occurrence of the saddle-point type of Van Hove singularity, which leads to strong light-matter interactions in 2D materials.     

Destroying a Near-Extremal Kerr-Newman-AdS Black Hole with Test Particles

If radiative and self-force effects are neglected, we find that feeding a test particle into a near-extremal KerrNewman-Ad S black hole could lead to destroy their event horizon, giving rise to naked singularities. Hence radiative and self-force effects must be taken into account to further test cosmic censorship. Moreover, the allowed parameter range for this test particle is very narrow, this leaves the possibility of radiative and self-force effects considerations to cure the problem of WCC violation in Kerr-Newman-Ad S spacetime.     

On the singularities of composition of entire functions

Let f be an entire function. A point zo is called a critical point of f if f'(zo) = 0, and f(zo) is called a critical value (or an algebraic singularity) of f. Next a ∈ (C^) is said to be an asymptotic value (or a transcendental singularity) of f if there exists a curve Γ:[0,1]→(C^) such that limt→1Γ(t)=∞ and limt→1(foΓ)(t)=a. In this paper we find relations between the asymptotic values of f, g and f o g, relations between critical points of f, g and f o g and also in the case when the two functions f and g are semi-conjugated with another entire function.     

断裂或接触力学问题中第二类柯西奇异积分方程的一种解析方法

第二类柯西奇异积分方程因涉及复奇异因子往往造成求解困难,而适用第一类奇异积分方程的高效数值方法并不能推广至第二类奇异积分方程,即便是第二类奇异积分方程,其数值解法仍是一个难题.为此提出了构造第二类奇异积分方程解析解的一种新方法.通过分解柯西奇异项,并利用雅克比多项式的正交性,推导针对右端载荷项为单项式(monomial)的递推解析解,进而借助级数展开的方法推广至一般的载荷问题.提出的基于递推的解析解构造方案,能完美地结合maple软件编程,从而提供一种方便、快捷、有效的算法.由给出的算例可见,本方法适用于处理界面断裂或接触分析问题中含复数奇异因子的复杂情形,从而为研究该类典型力学问题提供了一种可供选择的方法.     

Bifurcation of multi-freedom gear system with spalling defect

This study focuses on the bifurcation characteristics of the four degree-of-freedom gear system with local spalling defect to explore the spalling nonlinear dynamic mechanism. The dynamic model of the gear system with spalling defect, time-variant mesh stiffness, and nonlinear clearance is established to investigate the effect of spalling defect on mesh stiffness and dynamic bifurcation. The primary resonance and internal resonance responses of the spalling model are analyzed by the averaging method, and the bifurcation characteristics with the evolvement of spall and internal excitation are studied by employing the singularity theory for the two-state variable system, which reveal the different bifurcation characteristics caused by the spalling defect. The results obtained herein can provide a theoretical basis to spalling fault diagnosis of gearbox.