Polarization singularities in near-field of Gaussian vortex beam diffracted by a circular aperture

Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory. It is shown that there exist C-points and L-lines, which depend on off-axis displacement parameters along the x and y directions, waist width, wavelength, and topological charge of the diffracted Gaussian vortex beam, as well as on propagation distance. The results are illustrated by numerical calculations.

Thermal field in water pipe cooling concrete hydrostructures simulated with singular boundary method

The embedded water pipe system is often used as a standard cooling technique during the construction of large-scale mass concrete hydrostructures. The prediction of the temperature distribution considering the cooling effects of embedded pipes plays an essential role in the design of the structure and its cooling system. In this study, the singular boundary method, a semi-analytical meshless technique, was employed to analyze the temperature distribution. A numerical algorithm solved the transient temperature field with consideration of the effects of cooling pipe specification, isolation of heat of hydration, and ambient temperature. Numerical results are verified through comparison with those of the finite element method, demonstrating that the proposed approach is accurate in the simulation of the thermal field in concrete structures with a water cooling pipe.

EXPERIMENTAL GH SINGULARITY FIELD AROUND GROWING CRACK-TIP

The displacement fields u_x,u_y at growing crack tip of LYI2-M specimens with double edge cracks are measured using moire method.The experimental singularity fields are compared with GH theoretical field [12-14].The size and shape of the experimental GH singularity fields are obtained.The error in both the experimental and theoretical evaluations is controlled within ±10%.The experiments show that there is (In A/r)^(+1)singularity dominant around a growing crack tip.The shape of this dominant region ranges from butterfly wing to oblate and circular.Inside GH-field,there is a 3-D deformed damage zone where no GH sin- gularity exists.

SINGULAR BEHAVIOUR AND ASYMPTOTIC STRESS FIELD OF A CRACK TERMINATING AT A BIMATERIAL INTERFACE

A crack terminating at an interface of two dissimilar elastic materials is investigated.It is found that the asymptotic stress field near the crack tip is in general composed of two parts with each part be- ing characterized by one singularity.The detailed relation of the two singularities with the bimaterial proper- ties is given for some special cases of the crack.

Some Index Classes of Singularity of Vector Fields on Manifolds with Boundary

V. I. Arnold defined some particular classes of index for singularities of adapted fields. We generalize these index classes for general fields on manifolds with boundary and get some relations of these index classes.

AN ANZAHL THEOREM IN SINGULAR PSEUDO-SYMPLECTIC GEOMETRY OVER FINITE FIELDS

This paper obtains formulas for the number of subspaces of a given type contained in a given subspace in singular pseudo-symplectic geometry.

The Singularities of Gravitational Fields of Static Thin Loop and Double Spheres Reveal the Impossibility of Singularity Black Holes

In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we do not know their solutions up to now. Based on the coordinate transformations of the Kerr and the Kerr-Newman solutions of the Einstein’s equation of gravity field with axial symmetry, the gravity fields of static thin loop and double spheres are obtained. The results indicate that, no matter how much the mass and density are, there are singularities at the central point of thin loop and the contact point of double spheres. What is more, the singularities are completely exposed in vacuum. Space near the surfaces of thin loop and spheres are highly curved, although the gravity fields are very weak. These results are inconsistent with practical experience and completely impossible. By reasonable analogy, black holes with singularity in cosmology and astrophysics are something illusive. Caused by the mathematical description of curved space-time, they do not exist in real world actually. If there are black holes in the universe, they can only be the types of the Newtonian black holes without singularities, rather than the Einstein’s singularity black holes. In order to escape the puzzle of singularity thoroughly, the description of gravity should return to the traditional form of dynamics in flat space. The renormalization of gravity and the unified description of four basic interactions may be possible only based on the frame of flat space-time. Otherwise, theses problems can not be solved forever. Physicists should have a clear understanding about this problem.

POWER LAW NONLINEAR VISCOELASTIC CRACK-TIP FIELDS

The aim of this paper is to derive the power law type nonlinear viscoelastic crack-tip fields.For the requirement of later derivation,the HRR singular fields and the high-order asymp- totic fields are first examined.That they are essentially the isotropic,incompressible,power law type nonlinear elastic crack-tip fields is illustrated.After a concise review of the elasticity recov- ery correspondence principle for solving the nonlinear viscoelastic problems,the correspondence principle for solving the crack problems of power law type nonlinear viscoelastic materials under the first type boundary condition is proposed.The solution of the crack-tip stress,strain fields for the power law type nonlinear viscoelastic materials,especially for the modified polypropylene, is obtained.

Singularities of noncompact charged objects

We formulate a model for noncompact spherical charged objects in the framework of noncommutative field theory.The Einstein-Maxwell field equations are solved with charged anisotropic fluid.We choose matter and charge densities as functions of the two parameters,instead of defining these quantities in terms of the Gaussian distribution function.It is found that the corresponding densities and the Ricci scalar are singular in origin,whereas the metric is nonsingular,indicating a spacelike singularity.The numerical solution of the horizon equation implies that there are two or one or no horizon（s）,depending on the mass.We also evaluate the Hawking temperature and find that a black hole with two horizons is evaporated to an extremal black hole with one horizon.

The Mathematical Origin of Gravitational Singularities

In this note we give a geometrical presentation to the 4D Riemannian curvature as it relates to the Newtonian gravity in the 4D Lorentz manifold. The compacting of the proper time as is necessary for the unification with the Maxwell electrodynamics, as given by Einstein and Kaluza-Klein, should the universe be only of 4D space-time, led to the concept of gravitational field singularity sinks known as black holes, that would not be acceptable under a 5D homogeneous manifold through which the 4D Lorentz manifold evolved by application of the Perelman-Ricci Flow entropy mapping, which is consistent with both Maxwell suggested magnetic monopole, the quantum Higgs vacuum theory and the Gell-Mann standard model for hadrons.

Coherence vortices of partially coherent beams in the far field

Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model correlator in the far field, where our main attention is paid to the evolution of far-field coherence vortices into intensity vortices of fully coherent beams. The results show that, although there are usually no zeros of intensity in partially coherent beams with Gaussian envelope and Schell-model correlator~ zeros of spectral degree of coherence exist. The coherence vortices of spectral degree of coherence depend on the relative coherence length, mode index and positions of pairs of points. If a point and mode index are kept fixed, the position of coherence vortices changes with the increase of the relative coherence length. For the low coherent case there is a circular phase dislocation. In the coherent limit coherence vortices become intensity vortices of fully coherent Laguerre-Gaussian beams.

Quantum Unruh Effect on Singularities of Black Holes

It is generally believed that matter inside or once entering a black hole will gravitationally fall into the center and form a size-less singularity, where the density goes to infinity and the spacetime breaks down with infinite curvature or gravitation. In accordance to the Unruh effect, one of the most surprizing predictions of quantum field theory, however, it is found from this study that such singularity cannot be actually formed because it violates the law of energy conservation. The total Unruh radiation energy of the size-less singularity is shown to be infinite, much greater than that the collapsing matter can generate. All the energies of the collapsing matter including the gravitational potential energy, deducted, are far below the Unruh radiation energy, increased, for the collapsing matter to form the singularity. The collapsing matter actually formed is shown to be not a size-less singular point but a small sphere with a finite radius, which is found to be dependent of the mass of the singularity sphere, approximately proportional to the square root of the mass. The radius of the singularity sphere cannot be zero, unless the mass also approaches to zero. The result obtained from this study not only provides us a quantum solution to the problem of black hole singularity, but also leads to profound implications to the spacetime and cosmology. The Unruh effect excludes a black hole to form a size-less singularity, which has a finite mass but infinite density, curvature, and Unruh radiation energy. A point-like or size-less singularity can only be massless and naked.

Singularity-Free Superstar as an Alternative to Black Hole and Gravastar

Singularity-free superstar is proposed as a model for the collapse of large stars and for GRBs, and as an alternative to black hole and gravastar. Similar to a superconductor, a superstar contains extreme force fields that have non-zero momentum and non-zero wavelength to prevent the inactivation of force field at absolute zero and singularity (infinite interacting energy) at infinite density, respectively, based on the uncertainty principle. Emerging only at an extremely low temperature above absolute zero or an extremely high density below infinite density, extreme force fields are shortrange, and located in between a particle and its ordinary force fields (electromagnetic, weak, strong, and gravitational forces) to prevent the inactivation of force fields at absolute zero and singularity (infinite interacting energy) at infinite density in ordinary force fields. Extreme force fields are manifested as the bonds among electrons in a superconductor and among atoms in a Bose-Einstein condensate. When the stellar core of a large star reaches the critical extreme density during the stellar collapse, the stellar core is transformed into the super matter core with extreme force fields and ordinary force fields without singularity. A pre-superstar contains the super matter core, the ordinary matter region, and the thin phase boundary between the super matter core and the ordinary matter region. The stellar collapse increases the super matter core by converting the in falling ordinary energy and matter from the ordinary matter region into the super matter, and decreases the ordinary matter region. Eventually, the stellar breakup occurs to detach the ordinary matter region and the phase boundary from the super matter core, resulting in GRB to account for the observed high amount of gamma rays and the observed complex light curves in GRBs. Unlike black holes and gravastars that lose information, singularity-free superstars that keep all information exist.

AGN Singularities and Jets Modelled with the Superstar Scenario

In this paper we present solutions with the superstar scenario for the problems of singularity and the relativistic jet in AGN (Active Galactic Nuclei) based on supermassive black hole with singularity. The five-zone structure of superstar from inside to outside consists of the Singularity-Free Superstar Core (SC), the short-range repulsive super force field (SFF) near the event horizon, the superstar lepton sphere (SLS) containing infalling leptons (electron-positron pairs), the superstar ergosphere (SE), and the superstar accretion disk (SAD). As in the Meissner effect in superconductor, the short-range SFF repulses leptons in the SLS preventing singularity, while infalling leptons from the SAD and the SE continue to enter the SLS through the strong gravity of the SC. When the density at the bottom of the SLS reaches the critical density, leptons fall into the SC with the corresponding size increase of the SC to prevent singularity. Without further infalling leptons, the short-range repulsive force from the SFF disintegrates the SLS into the SLS plasma fragments (electron-positron pair plasma), detaching from the SC. Some SLS plasma fragments in the SAD generate the broad relativistic SAD jet, and some SLS plasma fragments in the SE generate the coincident narrow relativistic SE jet. In this two-jet model (the origin of the spine-sheath jet structure), protected by the SAD jet, the fast and narrow SE jet inside the slow and broad SAD jet generates the VHE (very high energy ≥ 100 GeV) Synchrotron Self Compton (SSC) gamma-ray emission without the attenuation by the photons in the BLR (broad line region) of flat spectrum radio quasar (FSRQ). In conclusion, AGN based on supermassive superstar provide the solutions for singularity, VHE gamma-ray emissions in FSRQs and FR1 type radio galaxies, AGN jet structure, and AGN jet type.

基于有限域上奇异线性空间的(m+1,1)型子空间的结合方案的构造

基于有限域上的奇异线性空间,定义X为所有包含一个固定的(m-1,0)型的子空间的(m+1,1)型子空间组成的集合,根据X中任意两个子空间的和的不同类型,构造了一个X上类数为5的结合方案.此外,给出了该结合方案的所有交叉数.

压电材料切口奇异物理场计算

采用切口尖端奇性特征分析与有限元法相结合的思路,计算压电材料切口尖端的力学和电学奇异物理场.首先基于奇性渐近展开技巧,推演压电材料切口的奇性特征方程,引入插值矩阵法求解,获得切口尖端奇性渐近展开式的奇性指数、特征角函数及其导数.再根据有限元法的位移和电势计算结果较应力和电位移高一阶精度的特点,利用稀疏有限元网格,计算出切口附近的位移和电势,代入切口尖端物理场渐近展开式,求出幅值系数.根据计算出的幅值系数、奇性指数、特征角函数及其导数,重构出切口尖端附近的奇异应力场和电位移场,继而计算出切口的应力强度因子和电位移强度因子.本文提出半解析方法,基于有限元稀疏网格计算结果,利用较小的计算量,获得较高精度的奇异物理场.该方法无须对有限元法的插值函数进行改造,适合嵌入商业有限元软件,直接用于工程压电材料结构安全分析.

布劳威尔关于向量分布的研究

布劳威尔通过将球面不动点定理和向量场联系起来,推动了布劳威尔不动点定理的产生,也促进了代数拓扑学的发展。基于相关原始文献,围绕布劳威尔关于向量分布的研究,分析布劳威尔对庞加莱指数工作的推广,及其对二维布劳威尔不动点定理新证明方法的思想演变过程,以期厘清布劳威尔将庞加莱的指数工作应用于一般连续向量分布的过程,及二维不动点定理新证明的具体思想。

压电/压磁复合楔形结构耦合场的奇异性研究:反平面问题

研究了反平面变形状态下压电/压磁复合楔形结构耦合场的奇异性.应用复变函数理论和本征函数展开方法,推导了16种机械、电学和磁学组合边界条件下关于奇异性指数本征方程的显函表达式.基于得到的本征方程,通过数值算例表明了楔角、边界条件和材料组合类型对耦合场奇异性的影响,发现压电效应和压磁效应之间的相互作用导致压电/压磁复合楔磁电弹场的奇异性比压电复合楔电弹场的奇异性更加复杂.

基于模型预测控制的无人机对海面小型目标的隐蔽跟踪

针对具备对空探测防卫能力的海面小型机动目标的跟踪问题,提出了一种基于非线性模型预测控制的隐蔽跟踪方法。首先,搭建了无人机和海面小型机动目标的运动学模型,并对海面小型目标携带的无人机探测装备进行了能力分析;其次,根据海面小型目标携带的探测装备的性能参数,设计出一条隐蔽的期望包围跟踪轨迹,并以此建立相应的无奇点导航向量场;最后,设计非线性模型预测控制器,以跟踪导航向量场给出的期望速度信号,实现单架无人机对非协同海上运动目标的隐蔽跟踪。仿真结果表明,使用非线性模型预测控制器,能在保证较好的控制精度下,显著减少无人机的能量消耗,增加控制器输出的平滑性。

地下水动力场演化图像奇异点检测方法研究

为了增强图像中的细节、完善平滑处理、提高图像中奇异点的检测精度,提出基于改进Renyi熵的地下水动力场演化图像奇异点检测方法。通过求解地下水动力场演化图像的梯度场,计算不同亮度下图像的相对梯度。利用图像增强函数,对地下水动力场演化图像作增强处理。创新性地根据三维直方图将地下水动力场演化图像划分为图像背景域和目标域。利用改进Renyi熵,定义了演化图像在目标域和背景域的三维Renyi熵。结合最大熵分割原理,分割了地下水动力场演化图像。引入平滑尺度,对地下水动力场演化图像进行平滑处理。利用概率函数,建立图像奇异点检测函数。设计了地下水动力场演化图像奇异点检测算法。试验结果表明,所提方法能够准确检测图像中的奇异点,并将检测熵值和检出率分别提高到0.8以上和90%以上。该研究有效提高了地下水动力场演化图像中奇异点的检测性能。