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.

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.

Anomalous scaling in a non-Gaussian random shell model for passive scalars

In this paper, we have introduced a shell-model of Kraichnan＇s passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and σ correlated in time, and its introduction is inspired by She and Levveque （Phys. Rev. Lett. 72, 336 （1994））. For comparison, we also give the passive scalar advected by the Gaussian random velocity field. The anomalous scaling exponents H（p） of passive scalar advected by these two kinds of random velocities above are determined for structure function with values of p up to 15 by Monte Carlo simulations of the random shell model, with Gear methods used to solve the stochastic differential equations. We find that the H（p） advected by the non-Gaussian random velocity is not more anomalous than that advected by the Gaussian random velocity. Whether the advecting velocity is non-Gaussian or Gaussian, similar scaling exponents of passive scalar are obtained with the same molecular diffusivity.

MAPPING CLOSURE APPROXIMATION FOR REACTIVE SCALARS IN RANDOM FLOWS

The Mapping Closure Approximation(MCA)approach is developed to describe the statistics of both conserved and reactive scalars in random flows.The statistics include Probability Density Function(PDF),Conditional Dissipation Rate(CDR)and Conditional Laplacian(CL).The statistical quantities are calculated using the MCA and compared with the results of the Direct Nu- merical Simulation(DNS).The results obtained from the MCA are in agreement with those from the DNS.It is shown that the MCA approach can predict the statistics of reactive scalars in random flows.

Influence of velocity spatiotemporal correlations on the anomalous scaling exponents of passive scalars

In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer-Ohkitani-Yamada （GOY） shell model, we show that the correlation function decays exponentially. The advecting velocity field is regarded as a colored noise field, which is spatially and temporally correlative. For comparison, we are also given the scaling exponents of passive scalars obtained by the Gaussian random velocity field, the multi-dimensional normal velocity field and the She-Leveque velocity field, introduced by She, et al. We observe that extended self-similarity sealing exponents H（p）/H（2） of passive scalar obtained by the colored noise field are more anomalous than those obtained by the other three velocity fields.

Probability Distribution Function of Passive Scalars in Shell Models

A shell-model version of passive scalar problem is introduced, which is inspired by the model of K. Ohkitani and M. Yakhot [K. Ohkitani and M. Yakhot, Phys. Rev. Lett. 60 （1988） 983; K. Ohkitani and M. Yakhot, Prog. Theor. Phys. 81 （1988） 329]. As in the original problem, the prescribed random velocity field is Gaussian and 5 correlated in time. Deterministic differential equations are regarded as nonlinear Langevin equation. Then, the Fokker-Planck equations of PDF for passive scalars are obtained and solved numerically. In energy input range （n 〈 5, n is the shell number.）, the probability distribution function （PDF） of passive scalars is near the Gaussian distribution. In inertial range （5≤ n ≤ 16） and dissipation range （n ≥ 17）, the probability distribution function （PDF） of passive scalars has obvious intermittence. And the scaling power of passive scalar is anomalous. The results of numerical simulations are compared with experimental measurements.

Influence of Velocity Shell Correlations on Anomalous Scaling Exponents of Passive Scalars in Shell Models

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of passive scalars of turbulence. Different to the original problem, the distribution function of the prescribed random velocity field is multi-dimensional normal and delta-correlated in time. Here, our random velocity field is spatially correlative. For comparison, we also give the result obtained by the Gaussian random velocity field without spatial correlation. The anomalous scaling exponents H（p） of passive scalar advected by two kinds of random velocity above are determined for structure function up to p= 15 by numerical simulations of the random shell model with Runge-Kutta methods to solve the stochastic differential equations. We observed that the H（p） ＇s obtained by the multi-dimeasional normal distribution random velocity are more anomalous than those obtained by the independent Gaussian random velocity.

Production of Charged Scalars from the Littlest Higgs Model Associated with Top Quark at LHC

The littlest Higgs （LH） model is the most economical one among various little Higgs models, which predicts the existence of the charged scalars Φ^±. In this paper, we study the production of the charged Higgs boson Φ^- with single top quark via the process gb →tΦ^- at the CERN Large Hadron Collider （LHC）. The numerical results show that the production cross section is sma/ler than 0.2 pb in most of the parameters space, it is very difficult to observe the signatures of the charged scalars via the process pp → gb ＋ X → tΦ^- ＋ X at the LHC experiments. However, it can open a window to distinguish the top-pions in the TC2 model or charged Higgs in the MSSM from Φ^±.

Approximate Reformulation a Recent Non-Renormalizable QFT’s Methodology and Einstein’s Gravity

We revisit, advancing a useful approximation, a recently formulated QFT treatment that successfully overcomes any troubles with infinities for non-renormalizable QFTs [J. Phys. Comm. 2 115029 (2018)]. Such methodology was able to successfully deal, in non-relativistic fashion, with Newton’s gravitation potential [Annals of Physics 412, 168013 (2020)]. Our present approximation to the QFT method of [J. Phys. Comm. 2 115029 (2018)] is based on the Einstein’s Lagrangian (EG) elaborated by Gupta [1], save for a different constraint’s selection. This choice allows one to avoid the lack of unitarity for the S matrix that impaired the proceedings of Gupta and Feynman. Moreover, we are able to simplify the handling of such constraint by eliminating the need to involve ghosts for guarantying unitarity. Our approximation consists in setting the graviton field ∅μν=γμν∅, where γμνis a constant tensor and ∅a scalar (graviton) field. The ensuing approximate approach is non-renormalizable, an inconvenience that we are able to overcome in [J. Phys. Comm. 2 115029 (2018)].

Upper Bound of Scalars in the Integer Sub-decomposition Method： The Theoretical Aspects

The focal point of this paper is to present the theoretical aspects of the building blocks of the upper bounds of ISD （integer sub-decomposition） method defined by kP = k11P ＋ k12ψ1 （P） ＋ k21P ＋ k22ψ2 （P） with max {｜k11｜, ｜k12｜} 〈 Ca√n and max{｜k21｜, ｜k22｜}≤C√, where C=I that uses efficiently computable endomorphisms ψj for j=1,2 to compute any multiple kP of a point P of order n lying on an elliptic curve E. The upper bounds of sub-scalars in ISD method are presented and utilized to enhance the rate of successful computation of scalar multiplication kP. Important theorems that establish the upper bounds of the kernel vectors of the ISD reduction map are generalized and proved in this work. The values of C in the upper bounds, that are greater than 1, have been proven in two cases of characteristic polynomials （with degree 1 or 2） of the endomorphisms. The upper bound of ISD method with the case of the endomorphism rings over an integer ring Z results in a higher rate of successful computations kP. Compared to the case of endomorphism rings, which is embedded over an imaginary quadratic field Q = [4-D]. The determination of the upper bounds is considered as a key point in developing the ISD elliptic scalar multiplication technique.

Space-time correlations of passive scalar in Kraichnan model

We consider the two-point,two-time(space-time)correlation of passive scalar R(r,τ)in the Kraichnan model under the assumption of homogeneity and isotropy.Using the fine-gird PDF method,we find that R(r,τ)satisfies a diffusion equation with constant diffusion coefficient determined by velocity variance and molecular diffusion.Itssolution can be expressed in terms of the two-point,one time correlation of passive scalar,i.e.,R(r,0).Moreover,the decorrelation o R(k,τ),which is the Fourier transform of R(r,τ),is determined byR(k,0)and a diffusion kernal.

锥形束CT评价人工耳蜗植入的电极深度和位置

目的分析人工耳蜗植入后电极植入深度、位置与耳蜗大小、盘旋方式的关系,探讨植入后电极深度的影响因素和电极移位的原因。方法选取植入CI24RE(CA)弯电极30例和SONATA ti100 Standard直电极人工耳蜗装置41例,利用锥形束CT测量术后电极植入长度、植入深度角、电极在耳蜗内的位置,分析上述指标与术前CT评估的耳蜗大小、倾斜角度的关系。结果①术后电极植入深度角和长度均存在较大的个体差异。直电极组平均植入深度角为702±53度,平均植入长度为30.02±1.29 mm;弯电极组平均植入深度角为441±45度,平均植入长度为18.4±1.0 mm,两组间差异有统计学意义(P<0.001)。②电极植入深度角与耳蜗底回的长径和宽径均呈负相关:直电极组r=-0.768(P<0.001)、r=-0.678(P<0.001),弯电极组r=-0.467(P=0.008)、r=-0.471(P=0.008)。电极植入长度与植入深度角呈正相关:直电极组r=0.578(P<0.001),弯电极组r=0.748(P<0.001)。③术后电极移位6例,均为弯电极且位于耳蜗180度位置。弯电极组中电极移位者与未移位者耳蜗底回倾斜角以及第一回和第二回之间的夹角差异有统计学意义(10.28度vs 8.75度,P=0.006;15.23度vs 14.00度,P=0.033)。结论人工耳蜗植入术后电极植入长度和深度角存在较大的个体差异,与耳蜗大小密切相关;耳蜗盘旋方式不同是引起电极移位的原因之一。

数量对合矩阵与数量反对合矩阵的迹与谱

应用相似关系下保持特征值与迹不变的性质,避开了计算特征多项式,得到了数量对合矩阵和数量反对合矩阵的只用迹表示的谱、行列式的计算公式及其相似等价类。作为应用,得到了通常对合矩阵、反对合矩阵、对称正交矩阵和反对称正交矩阵的相关结论。

全面精细化管理对血站批量无偿献血工作中非标量血液产生率的影响

目的分析全面精细化管理对血站批量无偿献血工作中非标量血液产生率的影响。方法选取2021年2月—2023年2月中国人民解放军联勤保障部队第924医院输血医学科的13名工作人员为研究对象,其中2021年2月—2022年2月实施常规化管理为对照组,该阶段献血总人数5469人;2022年3月—2023年2月实施全面精细化管理后为观察组,该阶段献血总人数4679人。探究全面精细化管理对血站批量无偿献血工作中非标量血液产生率的影响。结果观察组非标量血液产生率低于对照组,差异有统计学意义(χ^(2)=5.247,P<0.05);观察组血液采集时间显著短于对照组,差异有统计学意义(P<0.05);观察组满意度(92.31%)高于对照组(69.23%),差异有统计学意义(P<0.05)。结论全面精细化管理能显著降低血站批量无偿献血工作中非标量血液产生率,缩短采血时间,进一步提升血站工作人员的满意度。

轻量级位置隐私的安全查询方案

随着各类位置服务相关应用的快速发展,出现了需要对特定兴趣区域的访问用户进行查询和统计的服务需求。现有的查询方案可实现对访问用户的隐私保护,但采用的同态加密协议会引入较高的计算开销,无法实现对移动终端的实时统计,且存在不同兴趣区域的误判问题。基于布隆过滤器和安全向量内积协议,提出一种新的轻量级位置隐私查询方案。该方案设计了一种复合空间布隆过滤器,实现多种类位置数据的高效编码,与一种安全的向量内积计算协议结合,在保护用户位置隐私的前提下允许服务提供商完成对特定兴趣区域用户的访问统计。从理论上证明了方案的正确性和安全性,分析了其计算和通信开销。实验结果表明,该方案与典型代表方案相比,避免了用户在不同兴趣区域的误判问题,提高了查询准确度;在所设定实验条件下,离线和在线计算开销可降低2个数量级,同时可减少约50%通信开销。

“哪里是A,简直是B”的量级构式研究

从“量级构式”这一特殊视角出发,对“哪里是A,简直是B”进行全新的研究。“哪里是A,简直是B”不仅是构式,更是一个量级构式,具有标记量级信息的功能。“哪里是A,简直是B”有多种构式变体形式、特殊量级形式和量级语义维度,其形成机制是构式互动和构式压制。

一种基于径向基隐式曲面的地质三维建模方法

针对目前基于钻孔数据生成地质三维模型过程繁琐、算法复杂、中间数据庞大的弊端,本文使用钻孔点和径向基隐函数模型描述地层曲面,以多边形标量场提取曲面函数模型的等势面生成地质曲面进行可视化;再提取曲面的边框,根据网格大小长度提取边框的转折点数据;根据上下相邻两个地层曲面的边框转折点,绘制侧立面;合并侧立面与上下相邻两地质层曲面,生成地质三维模型。并使用郑州市高新区地质钻孔数据作为数据源进行实验,快速完整地生成了研究区的地质体三维模型。