Interactions of Penny-Shaped Cracks in Three-Dimensional Solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is developed in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

Micromechanics Modeling Of Strength For Nanocrystalline Copper

We present a model in this paper for predicting the inverse Hall-Petch phenomenon in nanocrystalline (NC) materials which are assumed to consist of two phases: grain phase of spherical or spheroidal shapes and grain boundary phase. The deformation of the grain phase has an elasto-viscoplastic behavior, which includes dislocation glide mechanism, Coble creep and Nabarro-Herring creep. However the deformation of grain boundary phase is assumed to be the mechanism of grain boundary diffusion. A Hill self-consistent method is used to describe the behavior of nanocrystalline pure copper subjected to uniaxial tension. Finally, the effects of grain size and its distribution, grain shape and strain rate on the yield strength and stress-strain curve of the pure copper are investigated. The obtained results are compared with relevant experimental data in the literature.

Evolution and propagation of density waves on galactic disk .1. General evolution equation of wavelet and discussion of its solution

This paper presents a general self-consistent theory of evolution and propagation of wavelets on the galactic disk. A simplified model for this theory, i. e. the thin transition-layer approximation is proposed.There are three types of solutions to the basic equation governing the evolution of wavelets on the disk: (ⅰ) normal propagating type; (ⅱ) swing type; (ⅲ) general evolving type. The results show that the first two types are applicable to a certain domain on the galactic disk and a certain region of the wave number of wavelets. The third is needed to join the other two types and to yield a coherent total picture of the wave motion. From the present theory, it can be seen that the well-known "swing theory" of the G-L sheet model holds only for a certain class of basic states of galaxies.

Magnetic field configurations of radio jets in the double source of radio galaxy

As an improvement of resolution of observations, more and more radio galaxies with radiojets have been identified and many fine structures in the radio jets yielded. In the presentpaper, the two-dimensional magnetohydrodynamical theory is applied to the analysis of themagnetic field configurations in the radio jefs. Two-dimensional results not only are con-sistent theoretically, but also explain the fine structures of observations. One of the theo-retical models is discussed in detail, and is in good agreement as compared with the observedradio jets of NGC6251. The results of the present paper also show that the magneticfields in the radio jets are mainly longitudinal ones and associate with the double sources ofQSOs if the magnetic field of the central object is stronger; the fields in the radio jets aremainly transverse ones and associate with the double sources of radio galaxies if the fieldof the central object is weaker. The magnetic field has great influence on the morphol-ogy and dynamic process.

The permanence of density waves of galaxy and the numerical investigation of waser mechanism

This paper deals with in detail the permanence of the spiral structure of galaxies andthe characters of waser mechanism. A simplified model of galaxy is adopted. Variousdynamical characters of density waves are studied using numerical calculation method. Theresults verify very well the switch character f waser and the tunnel effect of density wavesat the potential barrier of corotation circle as is shown in a previous work of the author.

Sediment sources and the flood record from Wanghu lake, in the middle reaches of the Yangtze River

A sediment core was collected from the centre of Wanghu Lake, in the Middle Reaches of the Yangtze River. The recent part of the core was dated using a combination of Pb-210 and spheroidal carbonaceous particle (SCP) techniques. Extrapolating this chronology dated the laminated section of the core, between 723 and 881 mm, to the first half of the 18th century and this section was selected for detailed study. The thicknesses of the laminae were measured using reflecting and polarizing microscopes whilst geochemistry was determined by an electron probe. The thickness of the dark layers was found to be positively correlated with titanium concentrations, and negatively correlated with aluminium and potassium concentrations. The thickness of the light layers was found to be negatively correlated with the concentrations of titanium. It is concluded that the dark layers were deposited from the Fushui River, a tributary of the Yangtze River, under periods of normal flow whilst the light Layers were mainly deposited from the Yangtze River itself during flood periods. Documentary evidence for floods occurring in the take catchment corresponded with thick laminations of high titanium concentration. Further, two of the three thickest, light laminations with low titanium concentrations were found to be synchronous with recorded flood dates of the main Yangtze River in its Middle Reaches, but one was synchronous with a local drought. These data suggest that the Lake sediment provides an archive of the relative water levels of the Yangtze and Wanghu including floods of both the main Yangtze River and the local hydrological regime. (c) 2006 Elsevier B.V. All rights reserved.

Simultaneous multiwavelength observations of sagittarius A

We observed Sgr A* using the Very Large Array (VLA) and the Giant Metrewave Radio Telescope (GMRT) at multiple centimeter and millimeter wavelengths on 2003 June 17. The measured flux densities of Sgr A*, together with those obtained from the Submillimeter Array (SMA) and the Keck II 10 m telescope on the same date, are used to construct a simultaneous spectrum of Sgr A* from 90 cm to 3.8 mu m. The simultaneous spectrum shows a spectral break at about 3.6 cm, a possible signature of synchrotron self-absorption of the strong radio outburst that occurred near epoch 2003 July 17. At 90 cm, the flux density of Sgr A* is 0.22 +/- 0.06 Jy, suggesting a sharp decrease in flux density at wavelengths longer than 47 cm. The spectrum at long cm wavelengths appears to be consistent with free-free absorption by a screen of ionized gas with a cutoff similar to 100 cm. This cutoff wavelength appears to be three times longer than that of similar to 30 cm suggested by Davies, Walsh, & Booth based on observations in 1974 and 1975. Our analysis suggests that the flux densities of Sgr A* at wavelengths longer than 30 cm could be attenuated and modulated by stellar winds from massive stars close to Sgr A*.

The radio counter-jet of the QSO 3C 48

We present multi- frequency radio observational results of the quasar 3C 48. The observations were carried out with the Very Large Array ( VLA) at five frequencies, 0.33, 1.5, 4.8, 8.4, and 22.5 GHz, and with the Multi- Element Radio Linked Interferometer Network ( MERLIN) at the two frequencies of 1.6 and 5 GHz. The source shows a one- sided jet to the north within 1", which then extends to the northeast and becomes diffuse. Two bright components ( N2 and N3), containing most of the flux density, are present in the northern jet. The spectral index of the two components is alpha(N2) similar to -0.99 +/- 0.12 and alpha(N3) similar to - 0.84 +/- 0.23 ( S proportional to nu(alpha)). Our images show the presence of an extended structure surrounding component N2, suggestive of strong interaction between the jet and the interstellar medium ( ISM) of the host galaxy. A steep- spectrum component, labelled S, located 0.25 " southwest to the flat- spectrum component which could be the core of 3C 48, is detected at a significance of > 15 sigma. Both the location and the steepness of the spectrum of component S suggest the presence of a counter- jet in 3C 48.

Bending of jets in the QSO NRAO 530

We present radio images of NRAO 530 on scales ranging from pc to kpc. The observations include the EVN at 5 GHz, the VLBA at 1.6, 8.6 and 15 GHz, the MERLIN at 1.6 and 5 GHz, and the VLA at 5, 8.4, 15, 22, and 43 GHz. The VLBI images show a core-jet structure with an oscillating trajectory on a scale of about 30 mas north of the strongest compact component (core). Superluminal motions are detected in five of the jet components with apparent velocities in the range of 13.6 to 25.2c. A new component is detected at 15 GHz with the VLBA observations, which appears to be associated with the outburst in 2002. Significant polarized emission is detected around the core with the VLBA observations at 15 GHz. Rapid variations of the polarization intensity and angle are found between the epochs in 2002 and 2004. On the kpc-scale, a distant component (labelled as WL) located 11 aresec west (PA=-86 degrees) of the core is detected beyond the core-jet structure which extended to several hundreds of mas in the north-west direction (-50 degrees). A significant emission between the core-jet structure and the WL is revealed. A clump of diffuse emission (labelled EL, 12 arcsec long) at PA 70 degrees to the core, is also detected in the VLA observations, suggesting the presence of double lobes in the source. The core component shows a flat spectrum, while the distant components WL and EL have steep spectra. The steep spectra of the distant components and the detection of the arched emission suggest that the distant components are lobes or hot-spots powered by the core of NRAO 530. The morphologies from pc- to kpc-scales and the bending of jets are investigated. The observed radio morphology from pc to kcp appears to favor the model in which precession or wobbling of the nuclear disk drives the helical motion of the radio plasma and produces the S-shaped structure on kpc scale.

ELECTRONIC-STRUCTURES OF THE ALKALI-CONTAINING BUCKMINSTERFULLERENES (A-DELTA-C60) (A=LI,NA,K,RB,CS) AND THE HALOGEN-CONTAINING BUCKMINSTERFULLERENES (H-DELTA-C60) (H=F,CL,BR,I)

The geometrical parameters and electronic structures of C60, (A partial derivative C60) (A = Li, Na, K, Rb, Cs) and (H partial derivative C60) (H = F, Cl, Br, I) have been calculated by the EHMO/ASED (atom superposition and electron delocalization) method. When putting a central atom into the C60 cage, the frontier and subfrontier orbitals of (A partial derivative C60) (A = Li, Na, K, Rb, Cs) and (H partial derivative C60) (H = F, Cl) relative to those of C60 undergo little change and thus, from the viewpoint of charge transfer, A (A = Li, Na, K, Rb, Cs) and H (H = F, Cl) are simply electron donors and acceptors for the C60 cage resPeCtively. Br is an electron acceptor but it does influence the frontier and subfrontier MOs for the C60 cage, and although there is no charge transfer between I and the C60 cage, the frontier and subfrontier MOs for the C60 cage are obviously influenced by I. The stabilities DELTAE(X) (DELTAE(X) = (E(X) + E(C60)) - E(x partial derivative C60)) follow the sequence I < Br < None < Cl < F < Li < Na < K < Rb < Cs while the cage radii r follow the inverse sequence. The stability order and the cage radii order have been explained by means of the (exp-6-1) potential.

中国蔷薇属芹叶组（Rosa Sect. Pimpinellifoliae DC. ex Ser.）的分类学研究

本研究通过我国CDBI、 KUN、PE、SZ等主要标本馆约3, 500份馆藏标本的研究和野外考察相结合，对我国蔷薇属（Rosa L.）芹叶组(Sect. pimpinellifoliae DC. ex Ser.）植物以及相关组的一些种进行了性状特征、形态和微形态的研究，对该组的一些种的形态特征描述进行了补充，同时给出详细的地理和海拔范围分布图。综合花粉以及种子（瘦果）形态的研究结果重新制订了分种检索表，同时，对该组一些形态相近容易混淆的种进行了对比研究，特别对一直存在争议的绢毛复合体（绢毛蔷薇R. sericea Lindl.和峨眉蔷薇R. omeiensis Rolfe）进行了大量宏观形态特征的研究，并用光学显微镜（LM）和扫描电镜(SEM)对二者的花粉及种子形态、微形态进行对比研究和分析，主要研究内容包括： 1. 芹叶组孢粉研究 对芹叶组的10个种及相关的4个组共17个种（18个样品）的植物花粉进行了光镜和扫描电镜观察和比较研究。研究结果表明：蔷薇属植物花粉粒大小为中等偏小，极轴长23.98[21.82(R. graciliflora Rehd. et Wils.)～29.18(R. tsinglingensis Pax. et Hoffm.)] μm，赤道轴长28.65[24.15（R. graciliflora）～34.70(R. davidii Crép.)] μm；花粉属辐射对称等极单花粉，花粉形态赤道面观呈球形到超长球形；极面观为三裂圆形或近圆形,三孔沟，孔缘加厚,具中部突起的桥状盖。花粉外壁纹饰为条纹状，光镜下形态特征相差不大；在电镜下外壁条纹和脊沟内穿孔的形状、大小和频度等特征，常具组至种水平上的可见变异，可作为组至种水平划分的依据。 根据花粉外壁条纹特征及穿孔形状和数目等特征，本研究将这些植物的花粉归为5个类型，并编制了分组检索表。同时，根据条纹状的清晰度，排列方式、条纹形状、穿孔大小及其频度等方面的差异，各有特点，对该组的10个种编制了分种检索表。 2. 芹叶组种子形态研究 应用光学显微镜和扫描电镜对我国蔷薇属芹叶组14个种及相关组5个组共36种植物的种子宏观形态及种皮微形态特征进行了观察研究。结果显示，蔷薇属种子形态多样,形状分别为肾形、卵形或锥形等；种子颜色以淡棕色、褐色以及土黄色为主；种子大小种间相差悬殊，相对体积为（长×宽×厚）36.66（4.79～114.47) mm3。光镜下，种子宏观形态特征具组内一致性，在扫描电镜下种子表面结构特征因种而异，其纹饰以网纹为主，可分为3种类型，即近平滑型、负网纹型和网纹型。研究结果表明，蔷薇属种子表面纹饰与地理分布关系不大,具有组及种内稳定性。其种子形态、大小、表而纹饰类型等特征可作为蔷薇属组及种水平上的分类依据。 结合蔷薇属花粉形态研究结果，得出蔷薇属种皮微形态特征与花粉外壁纹饰特征相吻合，在代表组及种的特征上具相关性的结论。同时根据种子形态、微形态结构特征的组间区别和种间差异编制了分组及芹叶组14个种的分种检索表。 3. 绢毛蔷薇复合体的研究 通过对大量标本的研究、野外观察以及扫描电镜对绢毛蔷薇复合体的花粉形态和种皮表面结构进行研究，通过对小叶、花粉及种子的形态定量分析结果支持Rowley (1959)的观点，将峨眉蔷薇处理为绢毛蔷薇的一个变种。 综上研究结果得出，蔷薇属植物的小叶片数目、花被基数以及花粉及种子形态等性状是较为稳定的，这些特征可很好的作为分类学依据。 The morphology, pollen exine sculpture and seed coat structure of the species of Rosa sect. Pimpinellifoliae and related sections were studied.About 3,500 herbarium specimens at CDBI, KUN, PE, and SZ were examined. Field work in Sichuan and Yunnan were conducted. Revisions of some species were carried out and a new key to species of sect. Pimpinellifoliae was proposed based on morphology, pollen exine sculpture and seed coat structure, Detailed morphological descriptions, geographical distributions and the altitudinal ranges of some taxa are given. The systematics of the species complex, the Rosa sericea complex (R. sericea Lindl. & R. omeiensis Rolfe), was emphasized. This thesis focused on the following three aspects: 1. Pollen morphology of Rosa sect. Pimpinellifoliae The pollen morphology of 18 samples representing 10 species of the Eurasian Rosa sect. Pimpinellifoliae and 7 additional species of related sections was investigated under LM and SEM. The pollen grains are monadic, actinomorphic, equipolar, medium-sized, spheroidal to perprolate in equatorial view, 3-lobed circular or semi-circular in polar view, crassimarginate, pontoperculate, and with striate exine sculpture. The striate sculpture varies among sections and species. The equatorial axis ranges from 17.97 μm (R. sikangensis) to 29.18 μm (R. tsinglingensis) with an average of 23.98 μm in length, while polar axis varies from 24.15 μm (R. gracilifolra) to 34.70 μm (R. davidii) with an average of 28.65 μm in length. The pollens can be divided into five types based on striate sculpture and a key to the sections sampled was proposed accordingly. The pollen morphology of species of sect. Pimpinellifoliae is more homogeneous and different from other sections sampled and did not support the two-series subdivisions in sect. Pimpinellifoliae. A key is also provided based on characers of pollen morphology among species in sect. Pimpinellifoliae. 2. Seed coat structure of Rosa sect. Pimpinellifoliae The seed coat structure of 39 samples representing 14 species of Rosa sect. Pimpinellifoliae and 12 additional species of related sections was investigated under LE and SEM. The seed relative volume (Length × width × thickness) ranges from 4.79 to 114.47 mm3 with an average of 36.66. mm3. The seeds are reniform, ovate or oblong in shape, with orange-brown, light brown or deep brown color. Seed coat sculpture was reticulate or striate-like reticulate. There was no difference in sculpture character of various speices under LM, while three types of seed coat sculpture were identified under SEM and a key to species based on the seed coat sculpture was provided. The three types of seed coat sculpture were nearly smooth, areolate and reticulate. The study of the seed coat sculpture of same species sampled from different populations showed that characters on the seed coat are stable, and thus the size, shape and seed coat sculpture can be used in species level identification. Interestingly, characters in the seed coat sculpture and the pollen morphology in sect. Pimpinellifoliae are consistent at in specific or sectional levels. A key to the 14 species sampled was given based on seed coat sculpture. 3. The study on Rosa sericea complex The Rosa sericea complex contains R. omeiensis and R. sericea. They are morphologically similar to one another and the systematic status of R. omeiensis has been controversial. In this study we examined large numbers of herbarium specimens of R. omeiensis and R. sericea and conducted field observations in the Hengduan Mts.. We also performed SEM study of pollen morphology and seed coat structure of R. omeiensis and R. sericea. We further carried out intensive morphometric study on the leaflet, pollen, and seed morphology. Our results showed that R. omeiensis should be sunk to be a variety of R. sericea, just as Rowley’s treatment in 1959. In conclusion, the features in the number of leaflet and petal, and the morphological character on pollen and seed are relatively stable. Therefore these characters are very useful in taxon delimition.

Cross-correlation between WMAP and 2MASS: non-Gaussianity induced by the SZ effect

We study the non-Gaussianity induced by the Sunyaev-Zel'dovich (SZ) effect in cosmic microwave background (CMB) fluctuation maps. If a CMB map is contaminated by the SZ effect of galaxies or galaxy clusters, the CMB maps should have similar non-Gaussian features to the galaxy and cluster fields. Using the WMAP data and 2MASS galaxy catalogue, we show that the non-Gaussianity of the 2MASS galaxies is imprinted on WMAP maps. The signature of non-Gaussianity can be seen with the fourth-order cross-correlation between the wavelet variables of the WMAP maps and 2MASS clusters. The intensity of the fourth-order non-Gaussian features is found to be consistent with the contamination of the SZ effect of 2MASS galaxies. We also show that this non-Gaussianity can not be seen by the high-order autocorrelation of the WMAP. This is because the SZ signals in the autocorrelations of the WMAP data generally are weaker than the WMAP-2MASS cross-correlations by a factor f(2), which is the ratio between the powers of the SZ-effect map and the CMB fluctuations on the scale considered. Therefore, the ratio of high-order autocorrelations of CMB maps to cross-correlations of the CMB maps and galaxy field would be effective to constrain the powers of the SZ effect on various scales.

Recent progress in the studies of endohedral metallofullerenes

This overview presents the recent progress in the area of endohedral metallofullerenes in the past several years. The important results have been summarized as follows: (1) Many metals including Group 3 metals, most of the lanthanide series elements, and Group 2 metals have been encapsulated into a fullerene cage to form mono-, di-, and trimetallofullerenes by using the arc-evaporation technique. (2) Some endohedral metallofullerenes such as Group 3 metals, most of the lanthanide series elements, Group 2 metals, and some of their isomers have been successfully isolated and purified by a two-step or several-step HPLC technique. By using high-temperature and high-pressure extraction with pyridine, Ln@C-80, Ln@C-82, and Ln2@C-80 for most rare-earth metals have been selectively extracted in high yield (about 1% of the saw soot) from fullerenes and other size metallofullerenes. (3) The endohedral nature of metallofullerenes such as Y@C-82, Sc2@C-84, and Sc@C-82 has been finally confirmed by synchrotron X-ray powder diffraction. The symmetries and the structures of metallofullerenes such as Ca@C-82(III), La-2@C-80(I-h), Sc-2@C-84(D-2d), and Sc-2@C-84(C-s) have been confirmed by NMR measurements. (Lb) The information on the electronic structures and properties of endohedral metallofullerenes has been obtained by various spectrometric means Such as EPR, W-vis-MR, XPS, CV. It is generally accepted that three-electron transfer is favorable when M = Y, La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, Lu but Sc, Eu, Sm, Yb, Tm, Ca, Sr, Ba prefer to donate two electrons to the fullerene cages. (5) Several chemical reactions of endohedral metallofullerenes have been reported in which reagents are disilacyclopropane, digermacyclopropane, diphenyldiazomethane, and trifluoroacetic acid. (6) Mass spectrometry provided the crucial evidence that led to the discovery of metallofullerenes in 1985 and has always played a key role in their identification and characterization, Ion-mobility measurements of gas-phase ions have obtained the information of structures and the formation mechanism of endohedral metallofullerenes. till Theoretical calculations on the endohedral metallofullerenes have made an important contribution to the studies on the symmetry of the cage, the position of metal atom(s) inside the cage, the number of electronic transfer between metal atom(s) and fullerene cage, etc. (C) 2000 Elsevier Science S.A. All rights reserved.

Mass spectral study of extractable La- and Lu-containing fullerenes

Mass spectra of LaxC2n (x = 1,2), well known endohedral metallofullerenes, and Lu2C2n (2n = 76-112), new members of extractable metallofullerenes, were studied. Positive-ion laser desorption/ionization (LDI) and electron impact (EI) mass spectra indicated that lutetium is a special lanthanide that prefers to form dilutetium fullerenes by the are-burning method. However, the signals for Lu2C2n become very weak in negative-ion LDI-MS, this is different from La-2@C-80, which has close relative abundances in positive- and negative-ion MS. The distinction between Lu2C2n and La-2@C-80 in the negative-ion LDI mass spectra may be due to the different structures of La- and Lu-containing fullerenes. (C) 1997 by John Wiley & Sons, Ltd.

特大地震激发地球自由振荡的数值模拟研究

Large earthquakes, such as the Chile earthquake in 1960 and the Sumatra-Andaman earthquake on Dec 26, 2004 in Indonesia, have generated the Earth’s free oscillations. The eigenfrequencies of the Earth’s free oscillations are closely related to the Earth’s internal structures. The conventional methods, which mainly focus on calculating the eigenfrequecies by analytical ways, and the analysis on observations can not easily study the whole processes from earthquake occurrence to the Earth’s free oscillation inspired. Therefore, we try to use numerical method incorporated with large-scale parallel computing to study on the Earth’s free oscillations excited by giant earthquakes. We first give a review of researches and developments of the Earth’s free oscillation, and basical theories under spherical coordinate system. We then give a review of the numerical simulation of seismic wave propagation and basical theories of spectral element method to simulate global seismic wave propagation. As a first step to study the Earth’s free oscillations, we use a finite element method to simulate the propagation of elastic waves and the generation of oscillations of the chime bell of Marquis Yi of Zeng, by striking different parts of the bell, which possesses the oval crosssection. The bronze chime bells of Marquis Yi of Zeng are precious cultural relics of China. The bells have a two-tone acoustic characteristic, i.e., striking different parts of the bell generates different tones. By analysis of the vibration in the bell and the spectrum analysis, we further help the understanding of the mechanism of two-tone acoustic characteristics of the chime bell of Marquis Yi of Zeng. The preliminary calculations have clearly shown that two different modes of oscillation can be generated by striking different parts of the bell, and indicate that finite element numerical simulation of the processes of wave propagation and two-tone generation of the chime bell of Marquis Yi of Zeng is feasible. These analyses provide a new quantitative and visual way to explain the mystery of the two-tone acoustic characteristics. The method suggested by this study can be applied to simulate free oscillations excited by great earthquakes with complex Earth structure. Taking into account of such large-scale structure of the Earth, small-scale low-precision numerical simulation can not simply meet the requirement. The increasing capacity in high-performance parallel computing and progress on fully numerical solutions for seismic wave fields in realistic three-dimensional spherical models, Spectral element method and high-performance parallel computing were incorporated to simulate the seismic wave propagation processes in the Earth’s interior, without the effects of the Earth’s gravitational potential. The numerical simulation shows that, the results of the toroidal modes of our calculation agree well with the theoretical values, although the accuracy of our results is much limited, the calculated peaks are little distorted due to three-dimensional effects. There exist much great differences between our calculated values of spheroidal modes and theoretical values, because we don’t consider the effect the Earth’ gravitation in numerical model, which leads our values are smaller than the theoretical values. When , is much smaller, the effect of the Earth’s gravitation make the periods of spheroidal modes become shorter. However, we now can not consider effects of the Earth’s gravitational potential into the numerical model to simulate the spheroidal oscillations, but those results still demonstrate that, the numerical simulation of the Earth’s free oscillation is very feasible. We make the numerical simulation on processes of the Earth’s free oscillations under spherically symmetric Earth model using different special source mechanisms. The results quantitatively show that Earth’s free oscillations excited by different earthquakes are different, and oscillations at different locations are different for free oscillation excited by the same earthquake. We also explore how the Earth’s medium attenuation will take effects on the Earth’s free oscillations, and take comparisons with the observations. The medium attenuation can make influences on the Earth’s free oscillations, though the effects on lower-frequency fundamental oscillations are weak. At last, taking 2008 Wenchuan earthquake for example, we employ spectral element method incorporated with large-scale parallel computing technology to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. Full 3-D visualization of the numerical results displays the profile of the seismic wave propagation with respect to time. The three-point source, which was proposed by the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture processes than one-point source. Primary results show that those synthetic signals calculated from three-point source agree well with the observations. This can further reveal that the source rupturing process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes. In conclusion, the numerical simulation can not only solve some problems concluding the Earth’s ellipticity and anisotropy, which can be easily solved by conventional methods, but also finally solve the problems concluding topography model and lateral heterogeneity. We will try to find a way to fully implement self-gravitation in spectral element method in future, and do our best to continue researching the Earth’s free oscillations using the numerical simulations to see how the Earth’ lateral heterogeneous will affect the Earth’s free oscillations. These will make it possible to bring modal spectral data increasingly to bear on furthering our understanding of the Earth’s three-dimensional structure.