Vacuum polarization by a scalar field in de Sitter spacetime in the presence of a global monopole

We analyze vacuum polarization effects associated with massive scalar quantum fields in a higher-dimensional de Sitter space in the presence of a global monopole. Because this analysis has been developed in pure de Sitter space, we are mainly interested on the effects induced by the presence of the global monopole. So, to achieve this objective, we calculate the corresponding Wightman function, which is expressed in an integral representation and explicitly depends on the parameters associated with the presence of the monopole and the cosmological constant. Admitting that the former is closed to unity, which corresponds to a realistic value predicted by Grand Unified Theories, it is possible to express this function as a sum of two terms: the first one corresponds to the Wightman function on the bulk where the global monopole is absent, and the second one is a contribution induced by the presence of the monopole.     

Laplace transform inversions using optimal contours in the complex plane

A numerical method for computing inverse Laplace transforms is proposed. In this method, the complex contour integral defining the inverse transform is computed over an equivalent contour as proposed by Talbot and Evans. Special contours, called optimal contours, are constructed so that the transformed real integrand decreases exponentially to zero as z runs along such a contour to infinity. The efficient Clenshaw-Curtis quadrature is employed for the final evaluation. The presented method is competitive and compares favourably with those of Talbot and Evans.     

Dark energy and inflation in a gravitational wave dominated universe

The empty space (with no matter fields) is not really empty because of natural metric fluctuations, quantum (gravitons) and classical (gravitational waves). We show that gravitons as well as classical gravitational waves of super-horizon wavelengths are able to form a de Sitter state of the empty homogeneous isotropic Universe. This state is an exact solution to the self-consistent equations of finite one-loop quantum gravity for gravitons in the empty FLRW space. It is also an exact solution to the selfconsistent equations of back-reaction for classical gravitational waves in the same space. Technically, to get this de Sitter solution in both quantum and classical cases, it is necessary to carry out a transition to imaginary time and then to return to real time, which is possible because this de Sitter state is invariant with respect to Wick rotation. Such a procedure means that time was used as a complex variable, and this fact has a deep but still not understood significance. The de Sitter accelerated expansion of the empty Universe naturally explains the origin of dark energy and inflation because the Universe is empty at the start (inflation) and by the end (dark energy) of its evolution. This theory is consistent with the existing observational data. The CMB anisotropy of the order of 10^?5 is produced by fluctuations in the number of gravitons. The existence of a threshold and a unique coincidence of topologically impenetrable barriers for tunneling takes place for the matter-dominated epoch and de Sitter State only. These facts provide a solution to the coincidence problem. The theoretical prediction that the equation-of-state parameter should be w > ?1 for inflation and w < ?1 for dark energy is consistentwith the observational data. To provide the reader with a complete picture, this paper gather together new and some published results of the graviton theory of the origin of inflation and dark energy.     

A hybrid method for the solution of crack problems based on the cauchy integral formula and the Riemann-Hilbert problem

Using the values of a complex potential on a closed contour surrounding a crack (derived either by an experimental or by a numerical method), this potential (as well as the corresponding stress intensity factors) is determined inside the contour by using the classical theory of the Riemann-Hilbert boundary value problem together with the well-known Cauchy integral formula. The case of an array of periodic collinear cracks is considered in detail and the corresponding numerical results (based on the trapezoidal quadrature role) are displayed.     

基于遗传算法的主动轮廓模型

由 Kass等人提出的主动轮廓模型 ,本质上是一条能量最小化的轮廓曲线 .它作为一种全新的采用自上而下机制的图象目标提取方法 ,由于它有效地利用了高级信息 ,从而提高了目标提取的速度和准确性 ,已经在数字图象处理和计算机视觉领域得到了广泛的应用 .原始的主动轮廓模型算法可以分为构造能量函数、推导欧拉方程、离散化和迭代求解 4步 .但该算法存在许多问题 ,为此在分析原始主动轮廓模型算法和一些改进算法的基础上 ,提出了一种基于遗传算法的主动轮廓模型算法 ,并给出实验结果 .实验结果证明 ,基于遗传算法的主动轮廓模型不仅成功地解决了原方法收敛易陷入局部最小值的问题 ,也提高了目标提取的成功率 .     

Geodesic portrait of de Sitter-Schwarzschild spacetime

De Sitter-Schwarzschild space-time is a globally regular spherically symmetric spacetime which is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild as r → ∞. A source term in the Einstein equations smoothly connects de Sitter vacuum at the origin with Minkowski vacuum at infinity and corresponds to an anisotropic vacuum fluid defined by symmetry of its stress-energy tensor which is invariant under radial boosts. In the range of the mass parameter M ≥ M _crit, de Sitter-Schwarzschild spacetime represents a vacuum nonsingular black hole, while M < M _crit corresponds to a compact gravitationally bound vacuum object without horizons, called a G-lump. Masses of objects are related to both de Sitter vacuum trapped inside and to smooth breaking of the spacetime symmetry from the de Sitter group at the origin to the Poincaré group at infinity. We here present a geodesic survey of de Sitter-Schwarzschild spacetime.     

Numerical contour integration for loop integrals

A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and efficient numerical integrations an along appropriate contour can be performed for scalar and tensor integrals appearing in loop calculations of the standard model. Examples of 3- and 4-point diagrams in 1-loop integrals and 2- and 3-point diagrams in 2-loop integrals with arbitrary masses are shown.Moreover it is shown that numerical evaluations of the Hypergeometric function, which often appears in the loop integrals, can be performed using the numerical contour-integration method.     

Hybrid path planning method based on skeleton contour partitioning for robotic additive manufacturing

Establishing manufacturability design criteria for multidimensional complex parts can significantly reduce the production cost, shorten the manufacturing cycle, and improve the production quality of directed energy deposition. Therefore, there is an urgent need to establish a high-performance manufacturing design strategy for complex parts. Proposed here is a skeleton contour partitioning hybrid path-planning method that takes full advantage of the excellent geometric reducibility of the contour offset method and the outstanding flexibility of the zigzag path method, eliminating the influences of sharp corners and degradation on forming quality in the contour offset method. First, reference contours are obtained by subjecting the original contours to an inward–outward twice-offset process; incompletely filled regions are obtained by Boolean operations on the original and reference contours, and these regions are the ones to be optimized. Second, the optimized regions are merged into skeleton fill regions, and the fill paths are generated by a polygon trapezoidal partitioning recombination algorithm and an algorithm for generating optimal zigzag paths. Finally, the contour offset paths are split and regrouped based on the skeleton regions and are connected into a continuous forming path for each subregion, then all the forming paths are converted into robot printing tool paths from the skeleton-region filling paths to the contour-offset ones. The actual forming results for several parts with different geometric features are verified and compared with those of the traditional path-planning method, and it is concluded that the proposed method converges rapidly to the details of complex components and is highly feasible and applicable.     

A search for observational manifestations of de Sitter relativity

De Sitter-invariant special relativity is a natural extension of Einstein’s special relativity. Within this framework, extension of special relativity to de Sitter space-time introduces a new length scale R, serving as an origin of the geometrical cosmological constant Λ = 3/R ². De Sitter relativity predicts a departure from the Lorentz invariance due to space-time curvature, related to the geometrical cosmological constant. In this paper, the impact of de Sitter special relativity effects on threshold particle processes and equivalence principle violation is considered. The main conclusion is that the constraints coming from cosmological fine structure constant variations render this effects nowadays undetectable. A brief outlook is given thereafter.     

Regular Rotating Black Holes and Solitons

Solutions describing regular rotating black holes are typically obtained by applying the Newman-Janis complex translation to spherical metrics of the Kerr-Schild class. Regular solutions of this class are specified by T _t ^t = T _r ^r and have necessarily de Sitter centers provided that the source terms T _k ⁱ satisfy the weak energy condition. Rotation transforms a de Sitter center into a de Sitter vacuum disk which is the generic common constituent of all regular rotating objects. In nonlinear electrodynamics coupled to gravity all metrics belong to the Kerr-Schild class and have the Kerr-Newman asymptotic for a distant observer. The ring singularity is replaced with the superconducting ring current which represents an electromagnetic nondissipative source of any asymptotically Kerr-Newman geometry. We outline the basic generic features of regular rotating black holes and solitons which are regular compact objects without event horizons, replacing naked singularities.     

Cosmological acceleration from a scalar field and classical and quantum gravitational waves (Inflation and dark energy)

We show that, on the average, a homogeneous and isotropic scalar field and, on the average, homogeneous and isotropic ensembles of classical and quantum gravitational waves generate the de Sitter expansion of empty (with no matter) space-time. At the start and by the end of its cosmological evolution, the Universe is empty. The contemporary Universe is about 70% empty, so the effect of cosmological acceleration should be very noticeable. One can assume that itmanifests itself as dark energy. At the start of the cosmological evolution, before the firstmatter was born, the Universe was also empty. The cosmological acceleration of such empty space-time can manifests itself as inflation. To get the de Sitter accelerated expansion of empty space-time under influence of scalar fields and classical and quantum gravitational waves, one needs to make a mandatory Wick rotation, i.e., one needs to make a transition to Euclidean space of imaginary time. One can assume that the very existence of inflation and dark energy could be considered as a possible observable evidence for the fact that time by its nature could be a complex value which manifests itself precisely at the start and by the end of the evolution of the Universe, i.e., in those periods when the Universe is empty (or nearly empty).     

Schwarzschild–De Sitter Thin Shell Wormholes Supported by a Generalized Cosmic Chaplygin Gas

The dynamics of spherically symmetric thin-shell wormholes (TSW), supported by a generalized cosmic Chaplygin gas in Schwarzschild- de Sitter space-time, is studied using the cut-and-paste technique (the Darmois–Israel formalism). A mechanical stability analysis of spherically symmetric thinshell wormhole is is carried out. by using the standard potential method. The existence of stable static solutions depends on the value of some parameters.     

A non-mapped complex variable method for the computation of unseparated airfoil flows

A new complex variable method is developed for the analysis of incompressible potential flow over lifting airfoils. The method is built around the numerical solution of a principal-value Cauchy integral equation. Unlike previous complex variable methods, no mappings are required, and the numerical solution is obtained entirely in the physical ($\text{Z}$) plane. Zero normal velocity over the airfoil is satisfied analytically at every point on the surface, not merely at discrete locations. No restrictions are placed on the airfoil contour, and the solution method producers both the potential distribution around the airfoil and the circulation.     

De Sitter Special Relativity: Effects on cosmology

The main consequences of de Sitter Special Relativity for the Standard Model of physical cosmology are examined. The cosmological constant Λ appears, in this theory, as a manifestation of the proper conformal current which must be added to the usual energy-momentum density when the Poincaré kinematics of special relativity is replaced by a de Sitter kinematics. Since that conformal current itself vanishes in the absence of sources, Λ is ultimately dependent on the matter content and can in principle be calculated. A present-day value very close to that given by the crossed supernova/BBR data is obtained through simple and reasonable assumptions. Also, a primeval inflation of polynomial type is found, and the usual notion of a comoving observer is shown to be slightly modified.     

基于扫描线的等高线树生成法

等高线树在地图的产生、地形分析等应用中具有较重要的应用。对于产生等高线树,提出了一种基于扫描线的方法,该方法把扫描线和等高线之间的交点对解释为区域,利用区域之间的包含关系对应等高线之间的包含关系,以这种方式来确定父等高线与子等高线之间的“一对多”直接包含关系。与其他方法相比,该方法较容易理解与实现,且执行速度较快。     

Parallel eigenvalue calculation based on multiple shift–invert Lanczos and contour integral based spectral projection method

We discuss the possibility of using multiple shift–invert Lanczos and contour integral based spectral projection method to compute a relatively large number of eigenvalues of a large sparse and symmetric matrix on distributed memory parallel computers. The key to achieving high parallel efficiency in this type of computation is to divide the spectrum into several intervals in a way that leads to optimal use of computational resources. We discuss strategies for dividing the spectrum. Our strategies make use of an eigenvalue distribution profile that can be estimated through inertial counts and cubic spline fitting. Parallel sparse direct methods are used in both approaches. We use a simple cost model that describes the cost of computing k eigenvalues within a single interval in terms of the asymptotic cost of sparse matrix factorization and triangular substitutions. Several computational experiments are performed to demonstrate the effect of different spectrum division strategies on the overall performance of both multiple shift–invert Lanczos and the contour integral based method. We also show the parallel scalability of both approaches in the strong and weak scaling sense. In addition, we compare the performance of multiple shift–invert Lanczos and the contour integral based spectral projection method on a set of problems from density functional theory (DFT).     

De sitter relativity: a natural scenario for an evolving Λ

In de Sitter special relativity, spacetime translations are replaced by a combination of translations and proper conformal transformations. As a consequence, the energy-momentum current is replaced by a combination of ordinary energy-momentum and proper conformal currents. Whereas the ordinary energy-momentumtensor remains to be a dynamic source of the spacetime curvature, the proper conformal current appears as a kinematic source of ??. The de Sitter special relativity, therefore, allows for a new interpretation of dark energy as an entity encoded in the kinematic group of spacetime. Furthermore, since ordinary energy is allowed to transform into dark energy and vice versa, it provides a natural scenario for an evolving cosmological term. A qualitative discussion on how a ??-evolving universe would behave is presented.     

一种评估颅骨和颅面相似性的方法

针对评估颅面和颅骨轮廓相似性过程中的离散点对应、曲线拟合带来的误差以及人工干预问题, 提出一种基于重采样和Fourier变换的离散轮廓像素点的相似度量方法。首先使用Canny算子和滑动窗口方法进行边缘检测和边界跟踪, 得到待比较颅骨和颅面的边缘轮廓像素集合; 然后对轮廓统一重采样, 解决了两者离散点的对应问题; 最后直接对数据进行规格化和离散傅里叶变换, 利用傅里叶描述子进行相似性度量, 避免了曲线拟合导致的误差和手工介入问题。实验表明, 该算法提高了颅骨和颅面相似性度量的准确率, 复杂度较低, 可实现评价过程自动化, 为颅像重合身份认证奠定了基础。