Globally hyperbolic flat space–times

We consider (flat) Cauchy-complete GH space–times, i.e., globally hyperbolic flat Lorentzian manifolds admitting some Cauchy hypersurface on which the ambient Lorentzian metric restricts as a complete Riemannian metric. We define a family of such space–times—model space–times—including four subfamilies: translation space–times, Misner space–times, unipotent space–times, and Cauchy-hyperbolic space–times (the last family—undoubtful the most interesting one—is a generalization of standard space–times defined by G. Mess). We prove that, up to finite coverings and (twisted) products by Euclidean linear spaces, any Cauchy-complete GH space–time can be isometrically embedded in a model space–time, or in a twisted product of a Cauchy-hyperbolic space–time by flat Euclidean torus. We obtain as a corollary the classification of maximal GH space–times admitting closed Cauchy hypersurfaces. We also establish the existence of CMC foliations on every model space–time.     

Gravi-inertial reference frames in Schwarzschild and Kerr spaces

Gravi-inertial reference frames — the analogue of inertial frames in two-dimensional space — are constructed in Schwarzschild and Kerr spaces. With their help the energy, momentum, and angular momentum of these systems are determined. A form is found for writing Kerr's solution in Bondi-Sachs coordinates in the slow-rotation approximation. A new solution of Einstein's equations is found in this approximation which describes the gravitational field of a rotating and radiating source.     

A note on teleparallel Killing vector fields in Bianchi type VIII and IX spaceben times in teleparallel theory of gravitation

In this paper we classify Bianchi type VIII and IX space—times according to their teleparallel Killing vector fields in the teleparallel theory of gravitation by using a direct integration technique. It turns out that the dimensions of the teleparallel Killing vector fields are either 4 or 5. From the above study we have shown that the Killing vector fields for Bianchi type VIII and IX space—times in the context of teleparallel theory are different from that in general relativity.     

Unimodular bimode gravity and the coherent scalar-graviton field as galaxy dark matter

An explicit violation of the general gauge invariance/relativity is adopted as the origin of dark matter and dark energy in the context of gravitation. The violation of the local scale invariance alone, with the residual unimodular one, is considered. Besides the four-volume preserving deformation mode—the transverse-tensor graviton—the metric comprises a compression mode—the scalar graviton, or the systolon. A unimodular invariant and general covariant metric theory of the bimode/scalar-tensor gravity is consistently worked out. To reduce the primordial ambiguity of the theory a dynamical global symmetry is imposed, with its subsequent spontaneous breaking revealed. The static spherically symmetric case in empty space, except possibly for the origin, is studied. A three-parameter solution describing a new static space structure—the dark lacuna—is constructed. It enjoys the property of gravitational confinement, with the logarithmic potential of gravitational attraction at the periphery, and results in asymptotically flat rotation curves. Comprising a super-massive dark fracture (a scalar-modified black hole) at the origin surrounded by a cored dark halo, the dark lacunas are proposed as a prototype model of galaxies, implying an ultimate account for the distributed non-gravitational matter and putative asphericity or rotation.     

Stability of the flat space in quasi-Riemannian theories of gravity

The most general action linear in curvature and quadratic in torsion for a quasi-Riemannian theory with tangent space groupSO(1,N-1)×SO(M) is obtained. Stability of the flat space solution of the field equations is studied, by calculating the massless and massive spectrum of excitations. It is shown that some very stringent conditions must be imposed on the parameters of the action in order to avoid instabilities.     

CuCl2-石墨层间化合物导电性能及其机理研究

以2—3μｍ石墨作主体材料合成了不同阶结构的CuCl₂-GICs,并用四探针法测量其导电性能,所得GICs电导率是石墨原料的1.5—2.2倍．阶数升高,电导率递增．微区成分分析发现：氯和铜离子为非计量比例,GICs中存在氯离子空位,提高了载流子的浓度．GICs氯离子空位在ｃ轴方向联通形成格架,增加了该方向载流子活动空间;XPS-ESCA分析证实：GICs中阳离子价态有变化．GICs将良导体的石墨层与绝缘体的氯化物层在分子尺度上结合起来,所形成的阶结构相当于许多导体和绝缘体层组成的“三明治”结构,产生化学键薄弱的通道,提供了垂直c轴方向的载流子通道,隧道效应和格架空间提供了载流子活动空间,这些因素共同作用使得GICs的电导率成倍增加. 关键词：     

溶液pH对羟基苯硫酚同分异构体脱羟基反应影响的SERS研究

金属纳米结构因表面等离激元(SPR)而产生光学增强和催化效应已成为表面科学研究热点之一。SPR和电化学联用可以诱导催化一些非常规反应,并且不同pH值电解质溶液可改变表面吸附分子的存在形式,影响SPR光催化反应。以羟基苯硫酚的同分异构体为探针,采用电化学表面增强拉曼光谱(SERS)研究了取代基羟基位置、溶液pH值等对其在银电极表面吸附和SPR催化反应行为。结果表明,不同羟基取代基位置的羟基苯硫酚SPR催化脱羟基反应对溶液pH值的敏感程度不同,邻羟基苯硫酚(OHTP)的C—O键谱峰强度的变化与溶液pH值相关,其O端更易与金属作用而吸附在表面,且随pH增大而增强。对羟基苯硫酚(PHTP)在碱性条件下被完全抑制的脱羟基反应在间羟基苯硫酚(MHTP)和OHTP中均可发生。MHTP在中性(pH 7)溶液中SPR催化脱羟基反应效率最高,约为酸性(pH 2)的1.36倍,碱性(pH 12)的2.70倍。OHTP在碱性(pH 12)溶液中SPR催化脱羟基反应效率最高,约为酸性(pH 2)的13.71倍,中性(pH 7)的4.95倍。SPR催化脱羟基主要源于非去质子化条件以及形成Ag—O键这两种途径。酸性条件下MHTP及OHTP的脱羟基反应主要是未去质子化的羟基反应,碱性条件主要因去质子化后形成Ag—O键所致。中性条件下,两种贡献同时发生。对MHTP而言,由于位阻效应仅部分分子去质子化后形成Ag—O键而促进SPR催化脱羟基,因此pH 7溶液中两种效应的同时作用导致催化效率最高。对于OHTP分子,去质子化状态的O端更易与电极表面发生作用,且pH升高羟基呈现的去质子化程度更加彻底,更有利于发生脱羟基反应,在pH 12溶液中脱羟基反应主要由于形成Ag—O键,其效率亦最高。同分异构体结构以及介质酸碱度对SPR催化脱羟基反应的研究对于拓宽SPR催化反应类型及从分子水平解析其机理具有重要意义。     

同一种前处理方法测定烟草中砷、铅和镉

采用同一种前处理方法即硝酸和高氯酸消解处理烟草样品后,氢化物发生-原子荧光光谱法测定烟叶中砷、铅;原子吸收光谱法测定烟叶中镉。样品溶液介质为10%的盐酸,对7个样品平行3次重复实验,其相对标准偏差为砷:0.81%—4.96%、铅:2.82%—5.83%、镉:0.96%—4.60%,砷、铅、镉的检测线性范围分别为:0.0—120.0、0.0—60.Oμg·L^-1和0.0—800.0μg·L^-1,加标回收率:砷在94.5%—96.9%之间、铅在92.7%—101.6%之间、镉在102.2%—110.9%之间。     

Application of the Difference Gaussian Rules to Solution of Hyperbolic Problems: II. Global Expansion

This work is the sequel to S. Asvadurov et al. (2000, J. Comput. Phys.158, 116), where we considered a grid refinement approach for second-order finite-difference time domain schemes. This approach permits one to compute solutions of certain wave equations with exponential superconvergence. An algorithm was presented that generates a special sequence of grid steps, called “optimal”, such that a standard finite-difference discretization that uses this grid produces an accurate approximation to the Neumann-to-Dirichlet map. It was demonstrated that the application of this approach to some problems in, e.g., elastodynamics results in a computational cost that is an order of magnitude lower than that of the standard scheme with equally spaced gridnodes, which produces the same accuracy. The main drawback of the presented approach was that the accurate solution could be obtained only at some a priori selected points (receivers). Here we present an algorithm that, given a solution on the coarse “optimal” grid, accurately reconstructs the solution of the corresponding fine equidistant grid with steps that are approximately equal to the minimal step of the optimal (strongly nonuniform) grid. This “expansion” algorithm is based on postprocessing of the approximate solution, is local in time (but not in space), and has a cost comparable to that of the discrete Fourier transform. An approximate inverse to the “expansion” procedure—the “reduction” algorithm—is also presented. We show different applications of the developed procedures, including refinement of a nonmatching grid. Numerical examples for scalar wave propagation and 2.5D cylindrical elasticity are presented.     

Space charge solution of Rittner photoconductor equation for a HgCdTe detector

The steady-state charge continuity equations are linearized to derive a space charge field that accompanies the ambipolar diffusion and drift described by the Rittner equation. The space charge field is evaluated for a typical 14.2 μm cutoff wavelength HgCdTe detector operating at 85 K. It is found that the space charge density is ∼10⁻⁵ times the hole and electron population density generated by photon flux. This corroborates that Rittner's equation gives an accurate solution for the hole and electron densities. But, at relatively high photon flux levels that are found in some Geostationary Operational Environment Satellite instrument channels, the small average space charge field can have a noticable effect on the linearity of detector response. Divergence of electric field terms in the continuity equations, which are absent from the Rittner equation, can also contribute a non-linearity to detector response.     

Simulation of Shock Wave Diffraction over 90° Sharp Corner in Gases of Arbitrary Statistics

The unsteady shock wave diffraction over a 90° sharp corner in gases of arbitrary particle statistics is simulated using an accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space. The numerical method is based on the usage of discrete ordinate method for discretizing the velocity space of the distribution function; whereas a second order accurate TVD scheme (Harten in J. Comput. Phys. 49(3):357–393, 1983) with Van Leer’s limiter (J. Comput. Phys. 32(1):101–136, 1979) is used for evolving the solution in physical space and time. The specular reflection surface boundary condition is assumed. The complete diffraction patterns are recorded using various flow property contours. Different range of relaxation times approximately corresponding to continuum, slip and transitional regimes are considered and the equilibrium Euler limit solution is also computed for comparison. The effects of gas particles that obey the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics are examined and depicted.     

Classical Yang-Mills-Dirac equations: Qualitative analysis of some solutions with a noncompact symmetry group

We consider classical Yang-Mills and Yang-Mills-Dirac equations on Minkowski space, with gauge group SU(2), and look for solutions invariant (up to a gauge transformation) under SO(3)×SO₀(1, 1) and SO₀(2, 1)×SO(2), respectively. In each case, we analyze the qualitative features of the solutions, in particular the asymptotic behavior as the solution approaches its singularities. The method is based on standard theorems from the theory of nonlinear ordinary differential equations.     

盘龙七的提取工艺

将盘龙七粉碎除去泥沙,以饱和的石灰水为溶剂,加热回流提取3次,每次4h、合并提取液,常压浓缩至溶液密度为1.15-1.20g/cm<'3>.冷至室温调pH为2-3.70℃保温结晶得岩白菜素粗品.后用95%乙醇加活性炭煮沸脱色,趁热过滤,得精品.     

New approach to nonlinear dynamics of fullerenes and fullerites

A new type of nonlinear (anharmonic) excitations—bushes of vibrational modes—in physical systems with point or space symmetry is discussed. All infrared-active and Raman-active bushes for C₆₀ fullerene are found by means of special group-theoretical methods.     

A real-time sound field renderer based on digital Huygens' model

Modeling acoustical behavior in a room is complicated and computationally intense. Although many methods have been proposed for computer simulation and computers have become faster and faster, the procedure is deeply time-consuming as sound space increases. With the development of semiconductor technology, an alternative solution is to simulate and rebuild the sound field distribution using hardware. Compared with other methods, the method based on digital Huygens' model (DHM) is simple and easily implemented by hardware. In this paper, two schemes of DHM are derived to analyze sound propagation in a two-dimensional space, and are implemented by field programmable gate array (FPGA). In a two-dimensional space of size 2 m×2 m, surrounded by rigid walls, the hardware simulation results of both schemes agree well with the software simulation result, and the calculation errors are relatively small. Compared with the software-based FDTD, original scheme, and updated scheme, a hardware system with 1024 nodes implemented by a Xilinx FPGA chip XC5VLX330T-FF1738 speeds up 7.1, 5.5, and 3.6 times, respectively.     

A Note on Classification of Cylindrically Symmetric Non-static Space–Times According to Their Teleparallel Killing Vector Fields in the Teleparallel Theory of Gravitation

In this paper, we explored the conservation laws of cylindrically symmetric non-static space–times by using direct integration technique. This classification also covers non-static plane symmetric space–times, static cylindrically symmetric space–times and plane symmetric static space–times. In this paper, we will only present the results of non-static cylindrically symmetric and non-static plane symmetric space–times. The results of static cylindrically symmetric space–times and plane static space–times can be found in Shabbir and Khan (Mod Phys Lett A 25:525, 2010). It turns out that the non-static cylindrically symmetric space–times admit four, five, or seven conservation laws. It is important to note that the above space–times admit at least one or at the most four extra conservation laws.     

Typical applications of MARY spectroscopy: Radical ions of substituted benzenes

The paper describes the underlying principles and discusses the most important advantages and limitations of the experimental technique of magnetically affected reaction yield spectroscopy as developed in the authors’ laboratory and guides the reader step by step through a typical experimental sequence using as example the problem of short-lived radical cations of a series of methyl-substituted benzenes in X-irradiated nonpolar solutions. For two of the eight target substances — benzene itself and mesithylene — the paper reports the first unequivocal observation of their radical cations in liquid alkane solution at room temperature and provides a lower estimate of about 10 ns for their relaxation times in low magnetic field.     

The Hubbard model beyond the two-pole approximation: a composite operator method study

Within the framework of the Composite Operator Method, a three-pole solution for the two-dimensional Hubbard model is presented and analyzed in detail. In addition to the two Hubbard operators, the operatorial basis comprises a third operator describing electronic transitions dressed by nearest-neighbor spin fluctuations. These latter, compared to charge and pair fluctuations, are assumed to be preeminent in the region of model-parameter space — small doping, low temperature and large on-site Coulomb repulsion — where one expects strong electronic correlations to dominate the physics of the system. This assumption and the consequent choice for the basic field, as well as the whole analytical approximation framework, have been validated through a comprehensive comparison with data for local and single-particle properties obtained by different numerical methods on varying all model parameters. The results systematically agree, both quantitatively and qualitatively, up to coincide in many cases. Many relevant features of the model, reflected by the numerical data, are exactly caught by the proposed solution and, in particular, the crossover between weak and intermediate-strong correlations as well as the shape of the occupied portion of the dispersion. A comprehensive comparison with other n-pole solutions is also reported in order to explore and possibly understand the reasons of such good performance.     

The classical limit for quantum mechanical correlation functions

For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx- andp-space around? ^?1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space. In the same sense,? ^?1/2 [(quantum operator) (t) — (classical function) (t)] converges to the solution of the linear quantum mechanical system, which is obtained by linearizing the non-linear Heisenberg equations of motion around the classical orbit.