On Scalar Planck Waves

The sound of space-time at the large scale is observed in the form of gravitational waves, which are disturbances in space-time produced by wavelike distortions (or kinks) in the gravitational field of an accelerating parcel or distribution of energy. In this study, we investigate a hypothetical wave mode of quantum space-time, which suggests the existence of scalar Planck waves. According to this hypothesis, the sound of quantum space-time corresponds to kinks propagating in the gravitational displacement field of an oscillating energy density. In evaluating the emission of scalar Planck waves and their effect on the geometry of space-time, one finds that they not only transport a vanishingly small amount of energy but can also be used to simulate gravity.

Helmholtz decomposition with a scalar Poisson equation in elastic anisotropic media

P-and S-wave separation plays an important role in elastic reverse-time migration.It can reduce the artifacts caused by crosstalk between different modes and improve image quality.In addition,P-and Swave separation can also be used to better understand and distinguish wave types in complex media.At present,the methods for separating wave modes in anisotropic media mainly include spatial nonstationary filtering,low-rank approximation,and vector Poisson equation.Most of these methods require multiple Fourier transforms or the calculation of large matrices,which require high computational costs for problems with large scale.In this paper,an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial domain.For 2D problems,the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation.Therefore,compared with existing methods based on pseudoHelmholtz decomposition operators,this method can significantly reduce the computational cost.Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.

A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.

Dynamic of Scalar Bosons in Aharonov-Bohm Magnetic Field

We study the dynamic of scalar bosons in the presence of Aharonov-Bohm magnetic field. First, we give the differential equation that governs this dynamic. Secondly, we use variational techniques to show that the following Schrödinger-Newton equation: , where A is an Aharonov-Bohm magnetic potential, has a unique ground-state solution.

Bi-normalized response spectra and scalar periods for developing uniform seismic design spectra

Aiming at the uniform features of acceleration response spectra, two scalar periods-the response spectral predominant period Tp and the smoothed spectral predominant period To are employed to normalize the abscissa of the normalized response spectra （NRS） of ground motions, respectively. Engineering characteristics of 5% -damped NRS, and the bi-normalized response spectra （BNRS） are investigated accounting for the effects of soil condition and fault distance. Nearly 600 horizontal ground motion components during the Chi-Chi earthquake are included in the analysis. It shows that the NRS strongly depends on soil condition and fault distance. However, soil condition and distance have only a slight influence on two kinds of BNRS. Dispersion analysis indicates that such normalization can reduce scatter in the derivation of response spectral shapes. Finally, a parametric analysis of the scalar periods （Tp, To） is performed and then compared with those of previous studies. These special and particular aspects of earthquake response spectra and scalar periods need to be considered in developing earthquake-resistant design criteria.

理论研究IIB族金属二氢化物分子的基态性质

基于小核能量一致性相对论赝势,采用密度泛函理论和耦合簇理论,分别在标量和二分量水平上计算研究了MH_(2)(M=Zn,Cd,Hg,Cn)分子的平衡键长和振动频率.计算结果显示,HgH_(2)和CnH_(2)的自旋轨道耦合效应较为明显.采用的8种泛函总体较好地评估了自旋轨道耦合效应.耦合簇理论计算的ZnH_(2)、CdH_(2)、HgH_(2)的键长和Σ_(u)振动频率与实验值偏差略大,这可能是由于其多参考态特性较明显.二分量PBE泛函计算的键长和Σ_(u)振动频率与实验值最接近.目前最重的CnH_(2)相关研究未见报道,研究给出了其键长和振动频率的理论值.

Fast and secure elliptic curve scalar multiplication algorithm based on special addition chains

To resist the side chaimel attacks of elliptic curve cryptography, a new fast and secure point multiplication algorithm is proposed. The algorithm is based on a particular kind of addition chains involving only additions, providing a natural protection against side channel attacks. Moreover, the new addition formulae that take into account the specific structure of those chains making point multiplication very efficient are proposed. The point multiplication algorithm only needs 1 719 multiplications for the SAC260 of 160-bit integers. For chains of length from 280 to 260, the proposed method outperforms all the previous methods with a gain of 26% to 31% over double-and add, 16% to22% over NAF, 7% to 13% over4-NAF and 1% to 8% over the present best algorithm--double-base chain.

仿射Khler-Scalar曲率为零的仿射Khler流形

设x:M→An+1是由定义在凸域ΩAn上的某局部严格凸函数xn+1=f(x1,...,xn)给出的超曲面.考虑Hessian度量 g =∑2fxixjdxidxj.若(M,g)是具有非负李奇曲率的紧致Hessian流形且仿射Khler-Scalar曲率为零,作者证明了如果Δρ≤nρ2,则函数f一定是二次多项式,其中ρ=[det(fij)]-1n+2.

仿射Kähler-Scalar曲率为零的紧致仿射Kähler流形

设x:M→A^(n+1)是由定义在凸域ΩA^n上的某局部严格凸函数x_(n+1)=f(x_1,...,x_n)给出的超曲面.考虑Hessian度量g=∑~2f /x_i_jdx_idx_j.若(M,g)是具有0仿射Khler-Scalar曲率的2维紧致Hessian流形,则函数f一定是二次多项式.

TRANSPORTATION OF PASSIVE SCALAR IN INHOMOGENEOUS TURBULENCE

The paper studies the transportation of passive scalar in the inhomogeneous turbulence by means of large eddy simulation. The prediction accuracy is verified by the well-known Comte-Bellot spectrum of the homogeneous turbulence. The mean transportation properties are predicted with satisfaction and the underestimation of the thermal flux by the phenomenological models has been disclosed. The high intermittence of the temperature fluctuations has been found in the inhomogeneous turbulence and it is the reason for the underestimation of turbulent thermal flux by the phenomenological model.

SPACELIKE SUBMANIFOLDS IN THE DE SITTER SPACE S_p^(n+p)(c) WITH CONSTANT SCALAR CURVATURE

Let Mn be a closed spacelike submanifold isometrically immersed in de Sitter space S^n+p _p(c).Denote by R,H and S the normalized scalar curvature,the mean curvature and the square of the length of the second fundamental form of Mn,respectively.Suppose R is constant and R≤c. The pinching problem on S is studied and a rigidity theorem for Mn immersed in ~S^n+p _p(c) with parallel normalized mean curvature vector field is proved.When n≥3, the pinching constant is the best.Thus,the mistake of the paper “Space-like hypersurfaces in de Sitter space with constant scalar curvature”(see Manus Math,1998,95:499-505) is corrected.Moreover,the reduction of the codimension when Mn is a complete submanifold in S^n+p _p(c) with parallel normalized mean curvature vector field is investigated.

Real scalar field scattering in the nearly extremal Schwarzschild de Sitter space

Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild-de Sitter （SdS） space. The approximations naturally lead to the invertible x（r） and the global replacement of the true potential by a PSshl-Teller one. Meanwhile, the Schr6dinger-like wave equation is transformed into a solvable form. Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x, while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate τ.

Interaction of elementary waves of scalar conservation laws with discontinuous flux function

In this paper, the Riemann solutions for scalar conservation laws with discontinuous flux function were constructed. The interactions of elementary waves of the conservation laws were concerned, and the numerical simulations were given.

Real scalar field scattering with polynomial approximation around Schwarzschild–de Sitter black-hole

As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter blackhole. The complicated relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schroedinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm Liouville type problem. Then this boundary value problem can be solved numerically for two limiting cases： the first one is the Nariai black-hole whose horizons are close to each other, the second one is the black-hole with the horizons widely separated. Compared with previous results （Brevik and Tian）, the field near the event horizon and cosmological horizon can have a better description.

POINTWISE CONVERGENCE RATE OF VANISHING VISCOSITY APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITH BOUNDARY

This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...

Review on cochlear implant electrode array tip fold-over and scalar deviation

Objective: Determine the occurrence rate of cochlear implant (CI) electrode tip fold-over and electrode scalar deviation as reported in patient cases with different commercial electrode types. Data-sources: PubMed search for identifying peer-reviewed articles published till 2018 on CI electrode tip fold-over and scalar deviation. Key-words for searching were “Cochlear electrode tip fold-over”,“Cochlear electrode scalar position” and “Cochlear electrode scalar location”. Articles-selection: Only if electrode related issues were investigated in patient cases. 38 articles met the inclusion-criteria. Results: 13 articles on electrode tip fold-over issue covering 3177 implanted ears, out of which 50 ears were identified with electrode tip fold-over with an occurrence rate of 1.57%. Out of 50 ears, 43 were implanted with pre-curved electrodes and the remaining 7 with lateral-wall electrodes. One article reported on both tip fold-over and scalar deviation. 26 articles reported on the electrode scalar deviation covering an overall number of 2046 ears out of which, 458 were identified with electrode scalar deviation at a rate of 22.38%. After removing the studies that did not report on the number of electrodes per electrode type, it was 1324 ears implanted with pre-curved electrode and 507 ears with lateral-wall electrode. Out of 1324 pre-curved electrode implanted ears, 424 were reported with scalar deviation making an occurrence rate of 32%. Out of 507 lateral-wall electrode implanted ears, 43 were associated with scalar deviation at an occurrence rate of 6.7%. Conclusion: This literature review revealing the fact of higher rate of electrode insertion trauma associated with pre-curved electrode type irrespective of CI brand is one step closer to obsolete it from the clinical practice in the interest of patient's cochlear health.

一类新的具有Scalar旗曲率的广义(α,β)-度量(英文)

根据文献[1]构造的几类广义(α,β)-度量,研究了一类新的(α,β)度量并给出它的Scalar旗曲率.

Footprint Characteristics of Scalar Concentration in the Convective Boundary Layer

Footprint characteristics for passive scalar concentration in the convective boundary layer （CBL） are investigated. A backward Lagrangian stochastic （LS） dispersion model and a large eddy simulation （LES） model are used in the investigation. Typical characteristics of the CBL and their responses to the surface heterogeneity are resolved from the LES. Then the turbulence fields are used to drive the backward LS dispersion. To remedy the spoiled description of the turbulence near the surface, MoninObukhov similarity is applied to the lowest LES level and the surface for the modeling of the backward LS dispersion. Simulation results show that the footprint within approximately 1 km upwind predominates in the total contribution. But influence from farther distances also exists and is even slightly greater than that from closer locations. Surface heterogeneity may change the footprint pattern to a certain degree. A comparison to three analytical models provides a validation of the footprint simulations, which shows the possible influence of along-wind turbulence and the large eddies in the CBL, as well as the surface heterogeneity.

Using Affine Quantization to Analyze Non-Renormalizable Scalar Fields and the Quantization of Einstein’s Gravity

Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with non-renormalizable scalar models as well as quantum gravity. The basic applications of this approach lead to the common goals of any quantization, such as Schroedinger’s representation and Schroedinger’s equation. Careful attention is paid toward seeking favored classical variables, which are those that should be promoted to the principal quantum operators. This effort leads toward classical variables that have a constant positive, zero, or negative curvature, which typically characterize such favored variables. This focus leans heavily toward affine variables with a constant negative curvature, which leads to a surprisingly accommodating analysis of non-renormalizable scalar models as well as Einstein’s general relativity.

A rigidity theorem for submanifolds in S^(n+p) with constant scalar curvature

Let Mn be a closed submanifold isometrically immersed in a unit sphere Sn . Denote by R, H and S, the normalized +p scalar curvature, the mean curvature, and the square of the length of the second fundamental form of Mn, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for Mn immersed in Sn +pwith parallel nor- malized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.