Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green’s function method for neutron-rich Ca,Ni,Zr,and Sn isotopes

The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.

Study on Characteristics of 3-D Translating-Pulsating Source Green Function of Deep-Water Havelock Form and Its Fast Integration Method

The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.

Synthesis of accelerations of the 1976 Tangshan earthquake(M_S 7.8)in near-and far-field by using semi-empirical method

In this paper a heterogeneous fault model of the Tangshan earthquake is suggested, which consists of two southern sub faults striking N30°E and two northern sub faults striking N50°E. Total length of the main shock fault is 114 km and seismic moment is about 1.4×10 20 N·m. The epicentre of the main shock is located at the southern part, near the intersection of the two bands. Accelerations of two aftershocks ( M L 5.5, M S 6.9 ) were used as empirical Green's functions to synthesize the accelerations of the main shock in near and far field. A method that small events and main shock are considered not satisfying the similarity relationship in the improved empirical Green's function is also applied in this paper. Peak values, duration and response spectra of synthesized accelerations in far field are in agreement with the observed records. The synthesized results in near field are also in agreement with the epicentral intensity distribution of the main shock. The results show that the peak acceleration of Tangshan earthquake in epicentral region exceeds 1.1 g. It is consistent with the peak accelerations recorded in some large earthquakes occurred in recent years.

Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems

In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.

In-plane dynamic Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method

Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green＇s function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.

基于经验格林函数法的2021年M_(S)6.4漾濞地震近场强震动模拟

由于震中附近强震台分布不均,文中联合使用近场2个国家强震动观测台网的强震台和7个云南地震预警台网烈度台的强震记录,采用经验格林函数法构建了特性化震源模型,并利用此模型对近场强震动进行了模拟。结果表明:烈度台的记录可与强震台的记录联合,共同作为强震动模拟的对象,但应注意区分二者的有效频带;在0.20~30.0Hz频带,在53YBX台处的NS分量上,模拟结果的伪加速度反应谱较好地再现了0.1s处的峰值,在EW分量上,合成的速度波形虽然幅值较低,但较好地再现了速度脉冲波段;在53DLY台处的合成波形较好地再现了约2s的长周期地震动;在0.50~30.0Hz频带,合成波形和反应谱与信噪比较高的烈度台的记录较为一致。文中确定的用于模拟强震动的特性化震源模型由一个强震动生成域构成,其面积和相应的短周期范围内加速度震源谱的水平段幅值与地震矩的关系均遵循经验标度律。

利用视震源时间函数反演尼泊尔M_S8.1地震破裂过程

以2015年4月26日MS7.1余震为经验格林函数事件,利用全国和全球的宽频带记录提取了2015年4月25日尼泊尔MS8.1地震的P波视震源时间函数和Rayleigh波视震源时间函数,并通过联合反演这些视震源时间函数获得了这次地震的时空破裂过程图像.无论是P波视震源时间函数还是Rayleigh波视震源时间函数都呈现出很强的方位依赖性,表明震源断层具有相当的尺度且破裂朝东南方向扩展.时空破裂过程图像清楚地证实了这一特征,并更清晰地显示,破裂几乎是纯粹的单侧破裂,从破裂起始点开始,沿断层面向东南方向扩展~100km,同时沿断层面向深部扩展~80km,形成~125°的破裂优势方向和~5.8m的最大位错.地震的破裂时间历史相对简单,呈非间断性扩展,持续时间约50s.

泸定地震大渡河区域灾害调查及格林函数库应用可行性探讨

2022年9月5日,四川省甘孜州泸定县发生M_(S)6.8地震,造成了较为严重的人员伤亡.震后中国地震局地球物理研究所科考队对泸定M_(S)6.8地震中大渡河干流上的几座梯级水电站和极震区等附近区域进行了灾害调查.调查结果表明梯级电站在本次地震中受影响较小,不影响正常运转.地震发生后,我们也采用经验格林函数方法并考虑震源参数的不确定性特征,对震区的石棉擦罗地区(位置①)、大渡河流域兴康高速特大桥区域(位置②)、历史地震古滑坡—摩岗岭附近区域(位置③)等三个典型位置合理范围的地震动加速度时程进行了快速估计.初步结果表明:位置①和③建筑物存在被本次地震破坏的可能性;位置②桥梁受地震破坏的可能性较小.最后,结合本次灾害调查结果、工程自建地震监测台网、典型位置地震动快速估计的结果,本文对重点工程区域建设基于实际小震波形的格林函数数据库应用前景的可行性进行了探讨.

沉积层序对谷地场地地震反应的影响-SH波入射

采用一种多域间接边界元方法,求解了层状半空间中多层沉积谷地对平面SH波的放大效应问题。该方法将含有多层沉积的层状半空间分解为开口层状半无限空间域和多个沉积层闭合域,进而通过求解层状半空间中斜线均布荷载动力格林函数来模拟开口域内的散射波场,通过求解全空间中均布荷载动力格林函数来模拟各闭合域的散射波场。方法充分发挥半空间格林函数和全空间格林函数在构造开口半无限空间域和闭合域内散射波场方面的优势,具有灵活性强和精度高的优点。文中验证了方法的正确性,并以正常沉积、软夹层沉积和逆序沉积为例进行了数值计算分析,研究了沉积层序对谷地附近地面运动的影响。数值结果表明,沉积层逆序排列时,低波速层对中高频地震动均有很好的"隔震"效果;沉积层序对地面运动的固有频率和卓越频率均有着显著的影响;沉积序列的改变会导致沉积动力特性的改变,进而会影响到沉积谷地与层状场地的动力相互作用机制。

用余震作为经验格林函数从GDSN长周期波形资料中提取1999年集集地震的震源时间函数

1999年 9月 2 0日 17h 4 7minUTC(北京时间 9月 2 1日 0 1h 4 7min)中国台湾省南投县集集镇发生MW7.6地震 ,随后又发生许多中强余震 .我们从这些余震中选择了MW6 .1和MW6 .2两次余震分别作为经验格林函数 ,并从包括IRIS ,GEOSCOPE和CDSN在内的全球数字地震台网的长周期波形资料中提取了主震的震源时间函数 .对于发生在 9月 2 2日的MW6 .1余震 ,有 2 6个台站的 78条记录的 97对震相清晰可用 ;对于发生在 9月 2 5日的MW6 .2余震 ,有 2 4个台站的 72条记录的 81对震相清晰可用 .对于每个台站 ,从P和S两种震相中提取震源时间函数 ,分别称之为P波震源时间函数和S波震源时间函数 .这样 ,利用两次余震从长周期波形资料中共提取了 178个震源时间函数 .从这些震源时间函数可以看到 ,除在特殊方位的几个震源时间函数由于主震和余震的震源机制的差别引起较大的畸变外 ,大多数台站的震源时间函数都具有相似性 ;同时 ,其形状随方位发生一定程度的变化 .这两种特征都是对所提取的震源时间函数的稳定性和可靠性的客观反映 .通过分析确认 ,这次地震由两次子事件构成 ,总持续时间约 2 6s .第二次事件比第一次事件晚大约 7s ,第一次事件的矩释放率比第二次事件大 15 % .

2013年四川芦山M_S7.0地震强地面运动模拟

运用经验格林函数法模拟2013年4月20日芦山MS7.0地震的近场强地面运动.在拟合过程中,首先参考前人远场反演结果给出的滑动量分布特征和主震波形的包络线特征,确定强震动生成区的大致范围和数量;然后利用Somerville等提出的地震矩与凹凸体面积的经验关系式确定强震动生成区细小划分的初值,继而利用遗传优化算法确定以上二者的最优值及其它震源参数.将数值模拟波形与实际地震观测记录在时间域和频率域分别进行比较,结果显示,在所选取的30个观测台站中,多数台站的数值模拟结果与实际观测结果符合得很好,特别是大于1Hz的高频部分.断层面上有两个强震动生成区,其位置与前人反演的滑动量集中分布区相一致,而且强震动生成区规模比Somerville等获得的标度率估计值要小.

Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space

Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green＇s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green＇s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.

A fast integration method for translating-pulsating source Green＇s function in Bessho form

The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.

Precise determination of focal parameters for July 20, 1995 M_L=4.1 earthquake sequence in the Huailai basin

On July 20, 1995 an M_L= 4.1 earthquake occurred in Huailai basin, northwest of Beijing, with epicenter coordinates 40.326°N, 115.448°E and focal depth 5.5 km. Following the main shock, microseismicity sharply increased in the basin. This earthquake sequence was recorded by Sino-European Cooperative Huailai Digital Seismograph Network (HDSN) and the hypocenters were precisely located. Using 8 aftershocks as empirical Green(s function (EGF) we calculated the source time function (STF) of the ML=4.1 event respectively, and by superposing these results, we obtained the average time function which has better signal to noise ratio. The final result shows that the ML=4.1 earthquake consisted of two events, one of which was stronger, the other was weaker, STFs from each station demonstrate an obvious (seismic Doppler effect(. Through a trial-and-error method, the following results were drawn: for the 1st event, the rupture length is 0.44 km, rupture velocity is 4.0 km/s, while for the 2nd event those parameters are 0.25 km, 3.0 km/s, the two events ruptured in the direction of 140° and 90° respectively (measured from the strike of the fault, anticlockwise positive), the two events were separated by 0.57 km in space, and 0.09 s in time. Using single EGF, we also retrieved the source time function of other 13 events with ML(2.1 in the Huailai earthquake sequence. These results were reached: each of the 13 events consisted of single event, with the duration of the source time functions ranging between 0.05～0.16 s. Using far-field ground displacement measurement method, the scalar seismic moment, stress drop and rupture radii of 25 events with 0.95(ML(4.1 were obtained. The trend that scalar seismic moment and stress drop increase with magnitude was obvious. In the magnitude range 0.9(ML(2.4, the obtained radii show no correlativity with magnitude, we tend to believe, in such small magnitude range, precise measurement for radii of such small events is beyond the data used in this study.

Statistical Average of Spin Operators for Calculation of Three-Component Magnetization （II）： Solution of Equation

In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green＇s function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.

Simulation of strong earthquake characteristics of a scenario earthquake(M_(S)7.5)based on the enlightenment of 2022 M_(S)6.9 earthquake in Menyuan

The Menyuan area is an important transportation hub in the Hexi Corridor.The Menyuan M_(S)6.9 earthquake that occurred on January 8,2022 had a major impact on the local infrastructure and transportation of this region.Due to the high possibility of similar strong earthquakes occurring in this area in the future,preliminary assessment of the seismic intensity characteristics of destructive earthquakes in this region is essential for effective disaster control.This paper uses the empirical Green′s function(EGF)method as a numerical simulation tool to predict the ground motion intensity of Datong Autonomous County under the action of the scenario earthquake(M_(S)7.5).Seismic records of aftershocks of the 2016 Menyuan M_(S)6.4 earthquake were used as Green’s functions for this simulation.The uncertainties associated with various source parameters were considered,and 36possible earthquake scenarios were simulated to obtain 72 sets of horizontal ground motions in Datong County.The obtained peak ground acceleration(PGA)vs.time histories of the horizontal ground motion were screened using the attenuation relationships provided by the fifth-edition of China’s Seismic Ground Motion Parameter Zoning Map and the NGA-West2dataset.Ultimately,32 possible acceleration-time histories were selected for further analysis.The screened PGA values ranged from 78.8 to 153 cm/s^(2).The uncertainty associated with the initial rupture point was found to greatly affect the results of the earthquake simulation.The average acceleration spectrum of the selected acceleration-time history exceeded the expected spectrum of a intermediate earthquake,which means that buildings in Datong County might sustain some damage should the scenario earthquake occur.This research can provide reliable ground motion input for urban earthquake damage simulation and seismic design in Datong County.Growing the dataset of small earthquakes recorded in this region will facilitate the large-scale simulation of ground motions under different earthquake scenarios.

Theoretical Investigation of Exchange Bias in Compensated Cases

The exchange bias （EB） of the ferromagnetic （FM）/antiferromagnetic （AFM） bilayers in a compensated case is studied by use of the many-body Green＇s function method of quantum statistical theory. The so-called compensated case is that there is no net magnetization on the AFM side of the interface. Our conclusion is that the EB in this case is primarily from the asymmetry of the interracial exchange coupling strengths between the FM and the two sublattices of the AFM. The effects of the layer thickness, temperature and the interracial coupling strength oi2 the exchange bias HE are investigated. The dependence of HE on the FM layer thickness and temperature is qualitatively in agreement with experimental results. HE is nearly inversely proportional to FM thickness. When temperature varies, both HE and He decrease with temperature increasing. The anisotropy of the FM layer only slightly influence He, but does not influence HE.

半无限长导线端面Green函数严格形式的一个新推导

为得到半无限长理想导线端面上的单体Green函数,应用介观问题中求解Green函数常用的代数迭代方法,利用端面处的自洽关系,推导出任意截面的半无限长链端面上Green函数的严格形式.该结果克服了多数文献中通常采用的直接积分法计算而忽略虚纵向波矢态的贡献,具有更强的严格性和更广的适用范围.