Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data ReleaseⅠ

Observing and timing a group of millisecond pulsars with high rotational stability enables the direct detection of gravitational waves(GWs).The GW signals can be identified from the spatial correlations encoded in the times-of-arrival of widely spaced pulsar-pairs.The Chinese Pulsar Timing Array(CPTA)is a collaboration aiming at the direct GW detection with observations carried out using Chinese radio telescopes.This short article serves as a“table of contents”for a forthcoming series of papers related to the CPTA Data Release 1(CPTA DR1)which uses observations from the Five-hundred-meter Aperture Spherical radio Telescope.Here,after summarizing the time span and accuracy of CPTA DR1,we report the key results of our statistical inference finding a correlated signal with amplitude logA_(c)=-14.4_(-2.8)^(+1.0)for spectral index in the range ofα∈[-1.8,1.5]assuming a GW background(GWB)induced quadrupolar correlation.The search for the Hellings–Downs(HD)correlation curve is also presented,where some evidence for the HD correlation has been found that a 4.6σstatistical significance is achieved using the discrete frequency method around the frequency of 14 n Hz.We expect that the future International Pulsar Timing Array data analysis and the next CPTA data release will be more sensitive to the n Hz GWB,which could verify the current results.

Efficient and rapid accuracy estimation of the Earth's gravitational field from next-generation GOCE Follow-On by the analytical method

Firstly, a new analytical error model of the cumulative geoid height using the three-dimensional diagonal tensors of satellite gravity gradiometry （SGG） is introduced based on the variance-covariance matrix principle. Secondly, a study for the requirements demonstration on the next-generation GOCE Follow-On satellite gravity gradiometry system is developed using different satellite orbital altitudes and measurement accuracies of satellite gravity gradiometer by the new analytical error model of SGG. The research results show that it is preferable to design satellite orbital altitudes of 300 km–400km and choose the measurement accuracies of 10-13/s2 –10-15/s2 from satellite gravity gradiometer. Finally, the complementarity of the four-stage satellite gravity missions, including past CHAMP, current GRACE, and GOCE, and next-generation GOCE Follow-On, is contrastively demonstrated for precisely recovering the Earth’s full-frequency gravitational field with high spatial resolution.

Development of hybrid optimization algorithm for structures furnished with seismic damper devices using the particle swarm optimization method and gravitational search algorithm

Previous studies about optimizing earthquake structural energy dissipation systems indicated that most existing techniques employ merely one or a few parameters as design variables in the optimization process,and thereby are only applicable only to simple,single,or multiple degree-of-freedom structures.The current approaches to optimization procedures take a specific damper with its properties and observe the effect of applying time history data to the building;however,there are many different dampers and isolators that can be used.Furthermore,there is a lack of studies regarding the optimum location for various viscous and wall dampers.The main aim of this study is hybridization of the particle swarm optimization(PSO) and gravitational search algorithm(GSA) to optimize the performance of earthquake energy dissipation systems(i.e.,damper devices) simultaneously with optimizing the characteristics of the structure.Four types of structural dampers device are considered in this study:(ⅰ) variable stiffness bracing(VSB) system,(ⅱ) rubber wall damper(RWD),(ⅲ) nonlinear conical spring bracing(NCSB) device,(iv) and multi-action stiffener(MAS) device.Since many parameters may affect the design of seismic resistant structures,this study proposes a hybrid of PSO and GSA to develop a hybrid,multi-objective optimization method to resolve the aforementioned problems.The characteristics of the above-mentioned damper devices as well as the section size for structural beams and columns are considered as variables for development of the PSO-GSA optimization algorithm to minimize structural seismic response in terms of nodal displacement(in three directions) as well as plastic hinge formation in structural members simultaneously with the weight of the structure.After that,the optimization algorithm is implemented to identify the best position of the damper device in the structural frame to have the maximum effect and minimize the seismic structure response.To examine the performance of the proposed PSO-GSA optimization method,it has been applied to a three-story reinforced structure equipped with a seismic damper device.The results revealed that the method successfully optimized the earthquake energy dissipation systems and reduced the effects of earthquakes on structures,which significantly increase the building’s stability and safety during seismic excitation.The analysis results showed a reduction in the seismic response of the structure regarding the formation of plastic hinges in structural members as well as the displacement of each story to approximately 99.63%,60.5%,79.13% and 57.42% for the VSB device,RWD,NCSB device,and MAS device,respectively.This shows that using the PSO-GSA optimization algorithm and optimized damper devices in the structure resulted in no structural damage due to earthquake vibration.

Weakly Singular Symmetric Galerkin Boundary Element Method for Fracture Analysis of Three-Dimensional Structures Considering Rotational Inertia and Gravitational Forces

The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.

Correction of cosine oscillation to the improved correlation method of estimating the amplitude of gravitational background signal

In the measurement of G with the angular acceleration method,the improved correlation method developed by Wu et al.（Wu W H,Tian Y,Luo J,Shao C G,Xu J H and Wang DH 2016 Rev.Sci.Instrum.87 094501） is used to accurately estimate the amplitudes of the prominent harmonic components of the gravitational background signal with time-varying frequency.Except the quadratic slow drift,the angular frequency of the gravitational background signal also includes a cosine oscillation coming from the useful angular acceleration signal,which leads to a deviation from the estimated amplitude.We calculate the correction of the cosine oscillation to the amplitude estimation.The result shows that the corrections of the cosine oscillation to the amplitudes of the fundamental frequency and second harmonic components obtained by the improved correlation method are within respective errors.

Application of Gravitational Methods to Prospecting Salt(Potash) Rocks in the Kuqa Depression

The Kuqa depression deposited thick rock salt,which has a lower density than surrounding rocks.When salt bodies form a certain scale,obvious negative gravity anomalies can be detected in the surface.Therefore,gravitational method can quickly obtain the shape,plane distribution of deep-seated salt bodies and overall tectonic morphology of the basin.

From Sustainability to Gravity: The Research Path of an Engineer

My career as a scientist has been a passionate pursuit of knowledge,objective knowledge devoid of ideology,that could prove useful in understanding and transforming the world.As an engineer,I aimed to produce planning solutions which would be economically feasible,technically viable,and socially acceptable.Disappointed by the ineffectiveness of methodology and planning initiatives to attain sustainability,I turned to the history of science to find answers,and finally to physics,searching for an explanation of gravity.I traced a path from social to natural sciences.My attachment to my values and ideals,my commitment to my goals costed me dearly.It led me to quit applied research,to move to a desert island in the Atlantic Ocean,to be consumed for years by a Galileo-like obsession.“I must create a system,or be enslaved by another man’s.I will not reason and compare:my business is to create”(Blake,2002,p.210),has been my life’s motto.Have I succeeded in my self-appointed task or have I just wasted valuable years of creative research building sand castles?I don’t have the answer to this question.What I know for sure is that I do not regret hanging to what I thought to be right.

The mini-GWAC optical follow-up of gravitational wave alerts – results from the O2 campaign and prospects for the upcoming O3 run

The second(O2)observational campaign of gravitational waves(GWs)organized by the LIGO/Virgo Collaborations has led to several breakthroughs such as the detection of GW signals from merger systems involving black holes or neutrons stars.During O2,14 GW alerts were sent to the astronomical community with sky regions mostly covering over hundreds of square degrees.Among them,six were finally confirmed as real astrophysical events.Since 2013,a new set of ground-based robotic telescopes called Ground-based Wide Angle Camera system(GWAC)project and its pathfinder mini-GWAC has been developed to contribute to the various challenges of multi-messenger and time domain astronomy.The GWAC system is built up in the framework of the ground-segment system of the SVOM mission that will be devoted to the study of the multi-wavelength transient sky in the next decade.During O2,only the mini-GWAC telescope network was fully operational.Due to the wide field of view and fast automatic follow-up capabilities of the mini-GWAC telescopes,they were adept to efficiently cover the sky localization areas of GW event candidates.In this paper,we present the mini-GWAC pipeline we have set up to respond to GW alerts and we report our optical follow-up observations of eight GW alerts detected during the O2 run.Our observations provided the largest coverage of the GW localization areas with a short latency made by any optical facility.We found tens of optical transient candidates in our images,but none of those could be securely associated with any confirmed black hole-black hole merger event.Based on this first experience and the near future technical improvements of our network system,we will be more competitive in detecting the optical counterparts from some GW events that will be identified during the upcoming O3 run,especially those emerging from binary neutron star mergers.

A Series Solution Approach to the Circular Restricted Gravitational Three-Body Dynamical Problem

The present manuscript examines the circular restricted gravitational three-body problem (CRGTBP) by the introduction of a new approach through the power series method. In addition, certain computational algorithms with the aid of Mathematica software are specifically designed for the problem. The algorithms or rather mathematical modules are established to determine the velocity and position of the third body’s motion. In fact, the modules led to accurate results and thus proved the new approach to be efficient.

An Independent Degree-eight Mars Gravity Field Model and the Expected Results from the Tianwen-1 Mission

Tianwen-1 is China's first independent interplanetary exploration mission,targeting Mars,and includes orbiting,landing,and rover phases.Similar to previous Mars missions,the Tianwen-1 orbiter was designed for polar orbits during the scientific mission period but has an exceptional eccentricity of approximately 0.59.We provide the first independent eight-degree Martian gravity field model in this paper,which was developed exclusively by a team working in China with our independent software as well,based on about two months of radiometric Doppler and range data from only the Tianwen-1 mission.This model is independent from the models created by the groups at NASA Jet Propulsion Laboratory and Goddard Space Flight Center in the United States,as well as the Centre National d'Etudes Spatiales in France.Furthermore,in order to optimize the engineering and scientific benefits,we proposed a number of potential orbits for the extended Tianwen-1 mission.In order to solve a higher-degree independent Mars gravity field model,the viability of modifying the perigee height was investigated,with the priority considerations of fuel savings and implementation hazards being controlled.

Statistical improvement in detection level of gravitational microlensing events from their light curves

In astronomy,the brightness of a source is typically expressed in terms of magnitude.Conventionally,the magnitude is defined by the logarithm of received flux.This relationship is known as the Pogson formula.For received flux with a small signal to noise ratio（S/N）,however,the formula gives a large magnitude error.We investigate whether the use of Inverse Hyperbolic Sine function（hereafter referred to as the Asinh magnitude）in the modified formulae could allow for an alternative calculation of magnitudes for small S/N flux,and whether the new approach is better for representing the brightness of that region.We study the possibility of increasing the detection level of gravitational microlensing using 40 selected microlensing light curves from the 2013 and 2014 seasons and by using the Asinh magnitude.Photometric data of the selected events are obtained from the Optical Gravitational Lensing Experiment（OGLE）.We found that utilization of the Asinh magnitude makes the events brighter compared to using the logarithmic magnitude,with an average of about 3.42×10^（-2）magnitude and an average in the difference of error between the logarithmic and the Asinh magnitude of about 2.21×10（-2）magnitude.The microlensing events OB140847 and OB140885 are found to have the largest difference values among the selected events.Using a Gaussian fit to find the peak for OB140847 and OB140885,we conclude statistically that the Asinh magnitude gives better mean squared values of the regression and narrower residual histograms than the Pogson magnitude.Based on these results,we also attempt to propose a limit in magnitude value for which use of the Asinh magnitude is optimal with small S/N data.

Solutions of the Dirac Equation with Gravitational plus Exponential Potential

The solutions of the Alhaidari formalism of the Dirac equation for the gravitational plus exponential potential have been presented using the parametric Nikiforov-Uvarov method. The energy eigenvalues and the corresponding unnormalized eigenfunctions are obtained in terms of Laguerre polynomials.

Simulation of the gravitational wave frequency distribution of neutron star-black hole mergers

LIGO-Virgo has observed the gravitational waves(GWs)from the coalescence of binary black hole(BBH)and binary neutron star(BNS)during O1 and O2,and the ones from NS-BH are expected to be hunted in the operating O3 run.The population properties and mass distribution of NS-BH mergers are poorly understood now,thus researchers simulated their chirp mass(M)distribution by a synthetic model,in which the BHs and NSs were inferred by LIGO-Virgo(O1/O2),and obtained the values in the range of 2.1 M_(⊙)<M<7.3 M_(⊙).In this paper,we further simulate the GW frequency(fGW)distribution of NS-BH mergers by the above-stated synthetic model,with a basic binary system model through the Monte Carlo method.Our results predict that the median with 90%credible intervals is 165+475-64 Hz in the case of Schwarzschild BH when the system just before merger,and this GW frequency is expected to increase several times in the merger stage,which is lying in the frequency band of LIGO-Virgo,i.e.,about 15 Hz to a few kHz.Our results provide an important reference for hunting the NS-BH mergers by the on-going O3 run of LIGO-Virgo.

Gravitational Wave Detection Based on Squeeze-and-excitation Shrinkage Networks and Multiple Detector Coherent SNR

Deep learning techniques have been applied to the detection of gravitational wave signals in the past few years.Most existing methods focus on the data obtained by a single detector.However,the signal-to-noise ratio(SNR)of gravitational wave signals in a single detector is pretty low,making it hard for deep neural networks to learn effective features.Therefore,how to use the observation signals obtained by multiple detectors in deep learning methods is a serious issue.We simulate binary neutron star signals from multiple detectors,including the Advanced LIGO and Virgo detectors.We calculate coherent SNR of multiple detectors using a fully coherent allsky search method and obtain the coherent SNR data required for our proposed deep learning method.Inspired by the principle of attention network Squeeze-and-Excitation Networks(SENet)and the soft thresholding shrinkage function,we propose a novel Squeeze-and-Excitation Shrinkage(SES)module to better extract effective features.Then we use this module to establish a gravitational wave squeeze-and-excitation shrinkage network(GWSESNet)detection model.We train and validate the performance of our model on the coherent SNR data set.Our model obtains satisfactory classification accuracy and can excellently complete the task of gravitational wave detection.

Construction of Earth's gravitational field model from CHAMP,GRACE and GOCE data

The basic principle of spectral combination method is discussed,and the general expressions of the spectral weight and spectral combination of the united-processing of various types of gravimetric data are shown.What＇s more,based on degree error RMS of potential coefficients,the detailed expressions of spectral combination formulae and the corresponding spectral weights in the Earth＇s gravitational field model（EGM） determination using GOCE ＋ GRACE and CHAMP ＋ GRACE ＋ GOCE are derived.The fundamental situation that ulux-champ2013 s,tongji-GRACE01,go-cons-gcf-2-tim-r5 constructed respectively by CHAMP,GRACE,GOCE data and go-cons-gcf-2-dir-r5 constructed by syncretic processing of GRACE,GOCE and LAGEOS data are explained briefly,the degree error RMS,cumulative geoid height error and cumulative gravity anomaly error of these models are calculated.A syncretic model constructed from CHAMP,GRACE and GOCE data,which is expressed by champ ＋ grace ＋ goce,is obtained based on spectral combination method.Experimentation results show that the precision of CHAMP data model is the lowest in satellite-only models,so it is not needed in the determination of syncretic models.The GRACE data model can improve the GOCE data model in medium-long wavelength,so the overall precision of syncretic model can be improved.Consequently,as many types of gravimetric data as possible should be combined together in the data processing in order to strengthen the quality and reliability with widening scope and improve the precision and spatial resolution of the computational results.

缔合Legendre函数的快速插值计算及其在六边形网格模型重力异常计算中的应用

鉴于局部区域非等纬度分布点的超高阶次球谐综合计算效率较低,本文深入研究了缔合Legendre函数的插值算法,结合模型重力异常求解的展开式,提出了超高阶模型空间重力异常插值快速计算方法,为了验证本文方法在东西狭长分布的点集更具有应用优势,采用球谐旋转变换技术进一步提升了计算效率。试验结果表明,利用2160阶次EGM2008模型计算日本地区同一高度的30303个非等纬度分布的六边形网格点处模型重力异常,插值快速计算方法相比逐点计算,在误差不超±0.005 mGal水平下,计算耗时从3669.41 s缩减到98.05 s,同时经过球谐旋转变换,将南北狭长的日本区域点集旋转为东西狭长分布,使得上述相应计算内容的耗时进一步由98.05 s缩减到19.06 s,计算效率相比最初方法提速比达到近200倍,有效解决了非等纬度分布点的超高阶模型重力异常快速解算的效率难题,且验证了该方法在东西狭长分布的情况下具有更高的提速比。

基于FEM的引力参考传感器自引力计算与补偿

空间引力波探测太极计划将利用激光干涉的方法,测量两个检验质量之间的距离变化反演引力波信息。在0.1 mHz处,要求检验质量在敏感轴方向的总残余加速度保持在3×10^(-15)m·s^(-2)/√Hz以下。由航天器载荷静引力、热形变和质量波动引起的自引力噪声是检验质量的残余加速度噪声主要来源之一,要求检验质量在敏感轴方向的自引力加速度小于1×10^(-10)m/s^(2),引力梯度小于5×10^(-8)s^(-2)。为了计算检验质量处的自引力大小和引力梯度,针对检验质量与引力源几何形状的不规则性,基于有限元法编写程序计算了引力参考传感器中的引力源作用在检验质量上的线加速度、角加速度和引力梯度。为了缩短计算时间,提出“类自适应”网格划分方法以减小网格数量,并设计了配重以补偿自引力。计算结果显示,经过补偿后的检验质量在敏感轴方向的自引力加速度为9.2377×10^(-12)m/s^(2),引力梯度为-2.5691×10^(-8)s^(-2),满足设计要求。本研究能够为航天器和引力参考传感器的设计与引力补偿提供参考与指导。

The GECAM Real-time Burst Alert System

Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor(GECAM),consisting of two microsatellites,is designed to detect gamma-ray bursts associated with gravitational-wave events.Here,we introduce the real-time burst alert system of GECAM,with the adoption of the BeiDou-3 short message communication service.We present the post-trigger operations,the detailed ground-based analysis,and the performance of the system.In the first year of the in-flight operation,GECAM was triggered by 42 gamma-ray bursts.The GECAM real-time burst alert system has the ability to distribute the alert within~1 minute after being triggered,which enables timely follow-up observations.

Gravitational form factors of the proton from near-threshold vector meson photoproduction

We systematically analyze the quark and gluon gravitational form factors(GFFs)of the proton by connecting the energy-momentum tensor and near-threshold vector meson photoproduction(NTVMP).Specifically,the quark contributions of GFFs are determined by applying global fitting to the cross section of the lightest vector mesonρ0 photoproduction.Combined with the gluon GFFs obtained from heavy quarkonium J/ψphotoproduction data,the complete GFFs are obtained and compared with the experimental results and lattice quantum chromodynamics determinations.In addition,we use the resonance via Padé(RVP)method based on the Schlessinger point method to obtain a model-independent quark D-term distribution through direct analytical continuation of deeply virtual Compton scattering experimental data.If errors are considered,the results obtained with RVP are essentially consistent with those obtained by NTVMP.Moreover,the comprehensive information on GFFs helps to uncover the mass distribution and mechanical properties inside the proton.This study is not only an important basis for delving into the enigmatic properties of the proton,but also has significance for theoretically guiding future JLab and EIC experimental measurements.

共振激励和重力作用下一维水平弦垂直振动驻波理论与实验研究

本文用本征函数展开法和拉普拉斯变换求解了重力作用下水平放置的一端固定、另一端以极小振幅作垂直简谐振动的一维弦的竖向振动波动方程,得出解析解,得到弦(弹性绳)共振形成驻波时的所有本征频率,且本征频率和驻波波腹大小、位置均与重力无关.实验上测量了驻波波腹的数目随共振频率变化的关系,利用理论推导出的波动方程中波速的表达式及测量弹性绳振动时的张力和绳子的长度,算出绳子的质量线密度,与实验值吻合,从另一角度验证了一维弦的横振动所满足的波动方程理论的正确性.