Three-dimensional P-wave velocity structure of the crust beneath Hainan Island and its adjacent regions,China

Using over 3 500 first P arrival times recorded by nine digital seismic stations from Hainan Digital Seismic Net-work during 1999～2005,a 3-D P-wave velocity model of the crust under Hainan Island and adjacent regions has been determined. The results show that the pattern of velocity anomalies in the shallower upper crust is somewhat associated with the surface geological tectonics in the region. A relative low-velocity anomaly appears north of the Wangwu-Wenjiao fault zone and a relative high-velocity anomaly appears south of the Wangwu-Wenjiao fault zone,corresponding to the depressed areas in north Hainan Island,where many volcanoes are frequently active and geothermal values are relatively higher,and the uplifted and stable regions in central and south of the Hainan Is-land. In the middle and lower crust velocities are relatively lower in east Hainan than those in west Hainan,possi-bly suggesting the existence of the upwelling of hot materials from the mantle in east Hainan. The pattern of veloc-ity anomalies also indicates that NW faults,i.e.,the Puqian-Qinglan fault,may be shallower,while the E-W Wangwu-Wenjiao fault may be deeper,which perhaps extends down to Moho depth or deeper.

Three-dimensional crustal P-wave velocity structure in the Yangbi and Eryuan earthquake regions, Yunnan, China

A magnitude 5.5 earthquakes occurred in Eryuan County,Dali Bai Autonomous Prefecture,Yunnan Province,China,on March 3.And a magnitude 5.0 earthquake occurred in the same place on April 17,2013,i.e.,45 days later.Then,on May 21,2021,multiple earthquakes,one with magnitude 6.4 and several at 5.0 or above,occurred in Yangbi County,Dali Bai Autonomous Prefecture,Yunnan Province,China.All of these occurred in the Weixi-QiaohouWeishan fault zone.In this study,1,874 seismic events in Yangbi and Eryuan counties were identified by automatic micro-seismic identification technology and the first arrivals were picked up manually.Following this,a total of 11,968 direct P-wave absolute arrivals and 73,987 high-quality Pwave relative arrivals were collected for joint inversion via the double difference tomography method.This was done to obtain the regional three-dimensional fine crustal P-wave velocity structure.The results show that the travel time residuals before and after inversion decreased from the initial–0.1–0.1 s to–0.06–0.06 s.The upper crust in the study area,which exhibited a low-velocity anomaly,corresponded to the basin region;this indicated that the low-velocity anomaly in the shallow part of the study area was affected by the basin.Results also showed some correlation between the distribution of the earthquakes and velocity structure,as there was a lowvelocity body Lv1 with a wide distribution at depths ranging from 15–20 km in the Yangbi and Eryuan earthquake regions.In addition,earthquakes occurred predominantly in the highlow velocity abnormal transition zone.The low-velocity body in the middle and lower crust may be prone to concentrating upper crustal stress,thus leading to the occurrence of earthquakes.

Three-dimensional P velocity structure in Beijing area

A detail three-dimensional P wave velocity structure of Beijing, Tianjin and Tangshan area (BTT area) was deter-mined by inverting local earthquake data. In total 16 048 P wave first arrival times from 16048 shallow and mid-depth crustal earthquakes, which occurred in and around the BTT area from 1992 to 1999 were used. The first arrival times are recorded by Northern China United Telemetry Seismic Network and Yanqing-Huailai Digital Seismic Network. Hypocentral parameters of 1 132 earthquakes with magnitude ML=1.7~6.2 and the three-dimensional P wave velocity structure were obtained simultaneously. The inversion result reveals the com-plicated lateral heterogeneity of P wave velocity structure around BTT area. The tomographic images obtained are also found to explain other seismological observations well.

Velocity-Free MS/AE Source Location Method for Three-Dimensional Hole-Containing Structures

Microseismic/acoustic emission(MS/AE)source localization method is crucial for predicting and controlling of potentially dangerous sources of complex structures.However,the locating errors induced by both the irregular structure and pre-measured velocity are poorly understood in existing methods.To meet the high-accuracy locating requirements in complex three-dimensional hole-containing structures,a velocity-free MS/AE source location method is developed in this paper.It avoids manual repetitive training by using equidistant grid points to search the path,which introduces A*search algorithm and uses grid points to accommodate complex structures with irregular holes.It also takes advantage of the velocity-free source location method.To verify the validity of the proposed method,lead-breaking tests were performed on a cubic concrete test specimen with a size of 10 cm10 cm10 cm.It was cut out into a cylindrical empty space with a size of/6cm10 cm.Based on the arrivals,the classical Geiger method and the proposed method are used to locate lead-breaking sources.Results show that the locating error of the proposed method is 1.20 cm,which is less than 2.02 cm of the Geiger method.Hence,the proposed method can effectively locate sources in the complex three-dimensional structure with holes and achieve higher precision requirements.

Three-Dimensional Wind Field Retrieved from Dual-Doppler Radar Based on a Variational Method:Refinement of Vertical Velocity Estimates

In this paper,a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps.First,the horizontal wind field is simultaneously recovered through minimizing a cost function defined as a radial observation term with the standard conjugate gradient method,avoiding a weighting parameter specification step.Compared with conventional dual-Doppler wind synthesis approaches,this variational method minimizes errors caused by interpolation from radar observation to analysis grid in the iterative solution process,which is one of the main sources of errors.Then,through the accelerated Liebmann method,the vertical velocity is further reestimated as an extra step by solving the Poisson equation with impermeable conditions imposed at the ground and near the tropopause.The Poisson equation defined by the second derivative of the vertical velocity is derived from the mass continuity equation.Compared with the method proposed by O’Brien,this method is less sensitive to the uncertainty of the boundary conditions and has better stability and reliability.Furthermore,the method proposed in this paper is applied to Doppler radar observation of a squall line process.It is shown that the retrieved vertical wind profile agrees well with the vertical profile obtained with the velocity–azimuth display(VAD)method,and the retrieved radial velocity as well as the analyzed positive and negative velocity centers and horizontal wind shear of the squall line are in accord with radar observations.There is a good correspondence between the divergence field of the derived wind field and the vertical velocity.And,the horizontal and vertical circulations within and around the squall line,as well as strong updrafts,the associated downdrafts,and associated rear inflow of the bow echo,are analyzed well.It is worth mentioning that the variational method in this paper can be applied to simultaneously synthesize the three-dimensional wind field from multiple-Doppler radar observations.

Three-dimensional seismic velocity tomography of the upper crust in Tengchong volcanic area, Yunnan Province

Based on data collected by deep seismic sounding carried out in 1999, a three-dimensional P wave velocity structure is determined with tomographic inversion. The tomographic result shows that there is a P wave low velocity zone (LVZ) in the upper crust beneath the Tengchong volcanic area. The LVZ is in the depth of 7~8 km and may be a smgma chamber or a partial melting body. The result also shows that the LVZ is in the northeastern side of the Rehai hydrothermal field, which is located in another LVZ near the surface. The shallow LVZ may represent a well-developed fracture zone. The strong hydrothermal activity in Rehai area can attribute to the existence of fractures between two LVZs. These fractures are the channels for going upwards of the deep hot fluid.

Three-dimensional high-resolution velocity structure imaging and seismicity study of Yangbi Ms6.4 earthquake

In this study,based on the body wave arrival data of 5506 earthquakes recorded by 32 fi xed stations and 94 temporary stations in Yangbi and surrounding areas,the source parameters of Yangbi Ms6.4 earthquake sequence and three-dimensional(3-D)fi ne Vp,Vs,and Vp/Vs were inverted by using the consistency-constrained double-diff erence tomography method.The results showed that the focal depth after relocation was mostly in the range of 3–10 km,evidently nearly horizontally distributed,and concentrated in the weak area of the high-velocity body or at the side of the high-low-velocity body transition zone toward the high-velocity body,showing a good corresponding relationship with the velocity structure.The velocity structure in the Yangbi area has remarkably uneven characteristics.The seismic activity area is dominated by high-velocity bodies prone to brittle fracture near the surface.As the depth increases,low-velocity anomalies appear.A signifi cant diff erence was observed in the wave velocity ratio between the upper and lower sides of the seismically dense strip.Based on the focal mechanism of the Yangbi Ms6.4 earthquake and the fine 3-D velocity structure,this article concludes that the Yangbi Ms6.4 earthquake was caused by a strong regional tectonic stress concentrated in the relatively weak area by hard high-velocity bodies on the northwest sides.The Ms5.6 foreshock broke the inherent balance of regional stress and promoted the occurrence of the Yangbi Ms6.4 mainshock.Afterward,the stress was adjusted to a new equilibrium state through a large number of aftershocks,forming a foreshock–mainshock–aftershock type of seismic activity model.Based on the activity law of the Yangbi Ms6.4 earthquake sequence and characteristics of the 3D velocity structure distribution,this paper speculates that the seismogenic structure of the Yangbi earthquake was possibly a northwest strike-slip buried fault with a depth of 3–10 km on the southwest side of the Weixi–Qiaohou fault.

Three-Dimensional P-Wave Velocity Structure of the Crust of North China

Since the Xingtai （邢台） earthquake in 1966, China Earthquake Administration has carried out a survey campaign along more than thirty deep seismic sounding （DSS） profiles altogether about twenty thousand kilometers long in North China to study the velocity structure of the crust and the upper mantle in this region, and has obtained a great number of research findings. However, these researches have not provided a 3D velocity structure model of the crust of North China and cannot provide seismic evidence for the study of the deep tectonic characteristics of the crust of the whole region. Hence, based on the information from the published data of the DSS profiles, we have chosen 14 profiles to obtain a 3D velocity structure model of North China using the vectorization function of the GIS software （Arc/Info） and the Kriging data gridding method. With this velocity structure model, we have drawn the following conclusions： （1） The P-wave velocity of the uppermost crust of North China changes dramatically, exhibiting a complicated velocity structure in plane view. It can be divided into three velocity zones mainly trending towards north-west. In the research area, the lowest-velocity zones lie in the Haihe （海河） plain and Bohai （渤海） Bay. Although the geological structure of the sedimentary overburden in the study area is somewhat inherited by the upper crust, there are still several differences between them. （2） Generally, the P-wave velocity of the crust increases with depth in the study area, but there still exists local velocity reversion. In the east, low-velocity anomalies of the Haihe plain gradually disappear with increasing depth, and the Shanxi （山西） graben in the west is mainly characterized by relatively low velocity anomalies. Bounded by the Taihang （太行） Mountains, the eastern and western parts differ in structural trend of stratum above the crystalline basement. The structural trend of the Huanghuaihai （黄淮海） block in the east is mainly north-east, while that of the Shanxi block and the eastern edge of the Ordos block is mainly north-west. （3） According to the morphological features of Moho, the crust of the study area can be divided into six blocks. In the Shanxi block, Moho apppears like a nearly south-north trending depression belt with a large crustal thickness. In the southern edge of the Inner Mongolia block and the south of the Yanshan （燕山） block,the Moho exhibits a feature of fold belt, trending nearly towards east-west. In the eastern edge of the Ordos block, the structure of Moho is relatively complex, presenting a pattern of fold trending nearly towards north-west with alternating convexes and concaves. Beneath the Huanghuaihai block, the middle and northern parts of the North China rift zone, the Moho is the shallowest in the entire region, with alternating uplifts and depressions in its shape. For the anteclise zone in the west of Shandong （山东） Province, the Moho is discontinuous for the fault depression extending in the north-west direction along Zaozhuang （枣庄） -Qufu （曲阜）.

Three-dimensional mixed convection stagnation-point fow past a vertical surface with second-order slip velocity

This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.

Three-dimensional P-wave Velocity Structure Modelling of the Middle and Lower Reaches of the Yangtze River Metallogenic Belt: Crustal Architecture and Metallogenic Implications

In this study,we compiled and analyzed 69310 P-wave travel-time data from 6639 earthquake events.These events(M≥2.0)occurred from 1980 s to June 2019 and were recorded at 319 seismic stations(Chinese Earthquake Networks Center)in the study area.We adopted the double-difference seismic tomographic method(tomo DD)to invert the 3-D P-wave velocity structure and constrain the crust-upper mantle architecture of the Middle and Lower Reaches of the Yangtze River Metallogenic Belt(MLYB).A 1-D initial model extracted from wide-angle seismic profiles was used in the seismic tomography,which greatly reduced the inversion residual.Our results indicate that reliable velocity structure of th e uppermost mantle can be obtained when Pn is involved in the tomography.Our results show that:(1)the pattern of the uppermost mantle velocity structure corresponds well with the geological partitioning:a nearly E-W-trending low-velocity zone is present beneath the Dabie Orogen,in contrast to the mainly NE-trending low-velocity anomalies beneath the Jiangnan Orogen.They suggest the presence of thickened lower crust beneath the orogens in the study area.In contrast,the Yangtze and Cathaysia blocks are characterized by relatively high-velocity anomalies;(2)both the ultra-high-pressure(UHP)metamorphic rocks in the Dabie Orogen and the low-pressure metamorphic rocks in the Zhangbaling dome are characterized by high-velocity anomalies.The upper crust in the Dabie Orogen is characterized by a low-velocity belt,sandwiched between two high velocity zones in a horizontal direction,with discontinuous low-velocity layers in the middle crust.The keel of the Dabie Orogen is mainly preserved beneath its northern section.We infer that the lower crustal delamination may have mainly occurred in the southern Dabie Orogen,which caused the mantle upwelling responsible for the formation of the granitic magmas emplaced in the middle crust as the low-velocity layers observed there.Continuous deep-level compression likely squeezed the granitic magma upward to intrude the upper crustal UHP metamorphic rocks,forming the'sandwich'velocity structure there;(3)high-velocity updoming is widespread in the crust-mantle transition zone beneath the MLYB.From the Anqing-Guichi ore field northeastward to the Luzong,Tongling,Ningwu and Ningzhen orefields,high-velocity anomalies in the crust-mantle transition zone increase rapidly in size and are widely distributed.The updoming also exists in the crust-mantle transition zone beneath the Jiurui and Edongnan orefields,but the high-velocity anomalies are mainly stellate distributed.The updoming high-velocity zone beneath the MLYB generally extends from the crust-mantle transition zone to the middle crust,different from the velocity structure in the upper crust.The upper crust beneath the Early Cretaceous extension-related Luzong and Ningwu volcanic basins is characterized by high velocity zones,in contrast to the low velocity anomalies beneath the Late Jurassic to Early Cretaceous compression-related Tongling ore field.The MLYB may have undergone a compressive-to-extensional transition during the Yanshanian(Jurassic-Cretaceous)period,during which extensive magmatism occurred.The near mantle-crustal boundary updoming was likely caused by asthenospheric underplating at the base of the lower crust.The magmas may have ascended through major crustal faults,undergoing AFC(assimilation and fractional crystallization)processes,became emplaced in the fault-bounded basins or Paleozoic sequences,eventually forming the many Cu-Fe polymetallic deposits there.

Three-dimensional velocity structure and tectonic characteristics of earthquake area in Yibin

In this study,on the basis of absolute first-arrival times of 84756 P-and S-waves from 6085 earthquakes recorded at 56 fixed stations in Yibin and surrounding areas in China from January 2009 to January 2019,focal parameters and three-dimensional(3 D)body-wave high-resolution velocity structures at depths of 0–30 km were retrieved by double-difference tomography.Results show that there is a good correspondence between the spatial distribution of the relocated earthquakes and velocity structures,which were concentrated mainly in the high-velocity-anomaly region or edge of high-velocity region.Velocity structure of P-and S-waves in the Yibin area clearly shows lateral inhomogeneity.The distribution characteristics of the P-and S-waves near the surface are closely related to the geomorphology and geologic structure.The low-velocity anomaly appears at the depth of 15–25 km,which is affected by the lower crust current.The Junlian–Gongxian and Gongxian–Changning earthquake areas,which are the two most earthquake-prone areas in the Yibin region,clearly differ in earthquake distribution and tectonic characteristics.We analyzed the structural characteristics of the Junlian–Gongxian and Gongxian–Changning earthquake areas on the basis of the 3 D bodywave velocity structures in the Yibin region.We found that although most seismicity in the Yibin area is caused by fluid injection,the spatial position of seismicity is controlled by the velocity structures of the middle and upper crust and local geologic structure.Fine-scale 3 D velocity structures in the Yibin area provide important local reference information for further understanding the crustal medium,seismogenic structure,and seismicity.

Aerodynamic unstable critical wind velocity for three-dimensionalopen cable-membrane structures

The aerodynamic unstable critical wind velocity for three-dimensional open cable-membrane structures is investigated. The geometric nonlinearity is introduced into the dynamic equilibrium equations of structures. The disturbances on the structural surface caused by the air flow are simulated by a vortex layer with infinite thickness in the structures. The unsteady Bernoulli equation and the circulation theorem are applied in order to express the aerodynamic pressure as the function of the vortex density. The vortex density is then obtained with the vortex lattice method considering the coupling boundary condition. From the analytical expressions of the unstable critical wind velocities, numerical results and some useful conclusions are obtained. It is found that the initial curvature of open cable-membrane structures has clear influence on the critical wind velocities of the structures.

Three-Dimensional Velocity Distribution Measurement Using Ultrasonic Velocity Profiler with Developed Transducer

This study describes an ultrasonic velocity profiler that uses a new ultrasonic array transducer with unique 5-element configuration, with all five elements acting as transmitters and four elements as receivers. The receivers are designed to reduce the amount of uncertainty. As the fluid moves through this setup, four Doppler frequencies are obtained. The multi-dimensional velocity information along the measurement line can be reconstructed. The transducer has a compact geometry suitable for a wide range of applications, including narrow flow areas. The transducer’s basic frequency and sound pressure are selected and evaluated to be compatible with the application. First, to confirm the measurement ability, the measurement of the developed system in two-dimensional flow is validated by comparing it to the theoretical data. The uncertainty of measurement was within 15%. Second, the three-dimensional measurement in turbulent and swirling flow is proved experimentally to check the applicability of the proposed technique.

A three-dimensional Eulerian method for the numerical simulation of high-velocity impact problems

In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.

A Three-Dimensional Velocity-Map Imaging Setup Designed for Crossed Ion-Molecule Scattering Studies

In this study,we report the design and simulation of an electrostatic ion lens system consisting of 22 round metal plates.The opening of the extractor plate is covered withmetal mesh,which is for shielding the interaction region of the lens system from the high DC voltages applied to all other plates than the repeller and extractor plates.The Simion simulation shows that both velocity-mapping and time focusing can be achieved simultaneously when appropriate voltages are applied to each of the plates.This makes the ion lens system be able to focus large ionic volumes in all three dimensions,which is an essential requirement for crossed ion-molecule scattering studies.A three-dimensional ion velocity measurement system with multi-hit and potential multi-mass capability is built,which consists of a microchannel plate(MCP),a P47 phosphor screen,a CMOS camera,a fast photomultiplier tube(PMT),and a high-speed digitizer.The two velocity components perpendicular to the flight axis are measured by the CMOS camera,and the time-of-flight,from which the velocity component along the flight axis can be deduced,is measured by the PMT.A Labview program is written to combine the two measurements for building the full three-dimensional ion velocity in real time on a frame-by-frame basis.The multi-hit capability comes from the fact that multiple ions from the camera and PMT in the same frame can be correlated with each other based on their various intensities.We demonstrate this by using the photodissociation of CH31 at 304 nm.

Three-Dimensional Shear Wave Velocity Structure of the Northeastern Brazilian Lithosphere

A large number of Rayleigh wave dispersion curves recorded at twenty three seismic stations was used to investigate the 3-D shear wave velocity structure of the northeastern Brazilian lithosphere. A simple procedure to generate a three-dimensional image of Mohorovicic;discontinuity was applied in northeastern Brazil and the Moho 3-D image was in agreement with several isolated crustal thicknesses obtained with different geophysical methods. A detailed 3-D S wave velocity model is proposed for the region. In the crust, our model is more realist than CRUST2.0 global model, because it shows more details either laterally or in depth than global model, i.e., clear lateral variation and gradual increase of S wave velocity in depth. Down to 100 km depth, the 3-D S wave velocity model in northeastern Brazil is dominated by low velocities and this is consistent either with heat flow measurements or with measurements of the flexural strength of the lithosphere developed in the South American continent. Our 3-D S wave velocity model was also used to obtain the lithosphere thickness in each cell of the northeastern Brazil and the results were consistent with global studies about the Lithosphere-Asthenosphere Boundary worldwide.

Three-dimensional crustal velocity structure and activity characteristics of the Madoi Ms7.4 earthquake in 2021

In this paper,using natural earthquake P-wave arrival time data recorded by the seismic network in the surrounding area of Madoi,the three-dimensional fine P-wave crustal velocity structure at depths above 60 km in the epicenter of the Madoi Ms7.4 earthquake was inverted using the double-difference seismic tomography method.On the basis of the relocation of the source of the aftershock sequence,we summarized the strip-shaped distribution characteristics along the strike of the Jiangcuo fault,revealing the significant heterogeneity of the crustal velocity structure in the source area.Research has found that most of the Madoi Ms7.4 aftershocks were located in the weak area of the high-speed anomaly in the upper crust.The focal depth changed with the velocity structure,showing obvious fluctuation and segmentation characteristics.There was a good correspondence between the spatial distribution and the velocity structure.The high-velocity bodies of the upper crust in the hypocenter area provided a medium environment for earthquake rupture,the low-velocity bodies of the middle crust formed the deep material,and the migration channel and the undulating shape of the high-speed body in the lower crust corroborated the strong pushing action in the region.The results confirmed that under the continuous promotion of tectonic stress in the Madoi area,the high-speed body of the Jiangcuo fault blocked the migration of weak materials in the middle crust.When the stress accumulation exceeded the limit,the Madoi Ms7.4 earthquake occurred.Meanwhile,the nonuniform velocity structure near the fault plane determined the location of the main shock and the spatiotemporal distribution of the aftershock sequence.

用Velocity Verlet积分器改进HMC抽样方法

Hamilton Monte Carlo (HMC)方法是一种常用的快速抽样方法.在对哈密顿方程进行抽样时,HMC方法使用Leapfrog积分器,这可能造成方程的位置及动量的迭代值在时间上不同步,其产生的误差会降低抽样效率及抽样结果的稳定性.为此,本文提出了IHMC(Improved HMC)方法,该方法用Velocity Verlet积分器替代Leapfrog积分器,每次迭代时都计算两变量在同一时刻的值.为验证方法的效果,本文进行了两个实验,一个是将该方法应用于非对称随机波动率模型(RASV模型)的参数估计,另一个是将方法应用于方差伽马分布的抽样,结果显示:IHMC方法比HMC方法的效率更高、结果更稳定.

A theory for three-dimensional response of micropolar plates

Through combined applications of the transfer-matrix method and asymptotic expansion technique,we formulate a theory to predict the three-dimensional response of micropolar plates.No ad hoc assumptions regarding through-thickness assumptions of the field variables are made,and the governing equations are two-dimensional,with the displacements and microrotations of the mid-plane as the unknowns.Once the deformation of the mid-plane is solved,a three-dimensional micropolar elastic field within the plate is generated,which is exact up to the second order except in the boundary region close to the plate edge.As an illustrative example,the bending of a clamped infinitely long plate caused by a uniformly distributed transverse force is analyzed and discussed in detail.

Oxygen tension modulates cell function in an in vitro three-dimensional glioblastoma tumor model

Hypoxia is a typical feature of the tumor microenvironment,one of the most critical factors affecting cell behavior and tumor progression.However,the lack of tumor models able to precisely emulate natural brain tumor tissue has impeded the study of the effects of hypoxia on the progression and growth of tumor cells.This study reports a three-dimensional(3D)brain tumor model obtained by encapsulating U87MG(U87)cells in a hydrogel containing type I collagen.It also documents the effect of various oxygen concentrations(1%,7%,and 21%)in the culture environment on U87 cell morphology,proliferation,viability,cell cycle,apoptosis rate,and migration.Finally,it compares two-dimensional(2D)and 3D cultures.For comparison purposes,cells cultured in flat culture dishes were used as the control(2D model).Cells cultured in the 3D model proliferated more slowly but had a higher apoptosis rate and proportion of cells in the resting phase(G0 phase)/gap I phase(G1 phase)than those cultured in the 2D model.Besides,the two models yielded significantly different cell morphologies.Finally,hypoxia(e.g.,1%O2)affected cell morphology,slowed cell growth,reduced cell viability,and increased the apoptosis rate in the 3D model.These results indicate that the constructed 3D model is effective for investigating the effects of biological and chemical factors on cell morphology and function,and can be more representative of the tumor microenvironment than 2D culture systems.The developed 3D glioblastoma tumor model is equally applicable to other studies in pharmacology and pathology.