Gravitational instability in binary protoplanetary disks new constraints on giant planet fo

LS-DYNA常见问题汇总1.0资料来源：网络和自己的总结yuminhust2005Copyright of original English version owned by relative author. Chinese version owned by /Kevin目录1.Consistent system of units 单位制度 (2)2.Mass Scaling 质量缩放 (4)3.Long run times 长分析时间 (9)4.Quasi-static 准静态 (11)5.Instability 计算不稳定 (14)6.Negative Volume 负体积 (17)7.Energy balance 能量平衡 (20)8.Hourglass control 沙漏控制 (27)9.Damping 阻尼 (32)10.ASCII output for MPP via binout (37)11.Contact Overview 接触概述 (41)12.Contact Soft 1 接触Soft=1 (45)13.LS-DYNA中夹层板(sandwich)的模拟 (47)14. 怎样进行二次开发 (50)1.Consistent system of units 单位制度相信做仿真分析的人第一个需要明确的就是一致单位系统(Consistent Units)。

计算机只认识0&1、只懂得玩数字，它才不管你用的数字的物理意义。

而工程师自己负责单位制的统一，否则计算出来的结果没有意义，不幸的是大多数老师在教有限元数值计算时似乎没有提到这一点。

见下面LS-DYNA FAQ中的定义：Definition of a consistent system of units (required for LS-DYNA):1 force unit = 1 mass unit * 1 acceleration unit1 力单位＝1 质量单位× 1 加速度单位1 acceleration unit = 1 length unit / (1 time unit)^21 加速度单位= 1 长度单位/1 时间单位的平方The following table provides examples of consistent systems of units.As points of reference, the mass density and Young‘s Modulus of steel are provided in each system of units. ―GRA VITY‖ is gravitational acceleration.2.Mass Scaling 质量缩放质量缩放指的是通过增加非物理的质量到结构上从而获得大的显式时间步的技术。

密集颗粒流的本构定律（来源Nature）原作者：Pierre Job, YoeelForterre& Olivier Pouliquen颗粒流的连续流描述在预测自然地理灾害或者设计工业程序中会有很大的帮助。

然而，决定物料在剪切力下如何移动的、干颗粒流的本构方程仍然是有争议的1-10。

一个困难是，颗粒材料可以表现11得像固体（在一个沙堆里），液体（从发射井喷出来的时候）或者是气体（剧烈搅动的时候）。

对于两个极端状态，基于碰撞引起的急流动力学定理12和慢塑性流动的土壤力学13，提出了本构方程。

然而，颗粒像液体一样流动过这样一个过渡的密集状态，仍然没有达成共识，并在过去几十年里激发了很多的研究14。

颗粒状液体的主要特征有：屈服准则（临界切应力下，流动不发生）和流动时对剪切速率的复杂相依性。

这样看来，颗粒材料与粘塑性流体有相似的特征，如宾汉流体。

这里，通过类比、数值计算15，16和实验工作17-19，我们得出了一个新的密集颗粒流的本构关系。

然后，通过在粗糙侧墙间在颗粒堆上的颗粒流试验，产生一个复杂的3D流型模型，验证了我们的三维（3D）模型。

我们所展示的是，在没有任何合适参数的情况下，此模型给出了大量的、关于流型和速度场的预测。

我们的结果支持这个想法，一个简单的粘塑性方案可以大量地捕获颗粒流的性质，并且可以作为一种基本工具应用到地理或工业中模仿更复杂的流动。

我们最近对比了不同的流体位形14，从而加深了对密集颗粒流的理解。

流变学的观点中，最简单的位形见插图1。

对限制于两粗糙平面间法向应力P 下的颗粒材料，在运用剪切力τ给定的剪切速率∙γ下进行剪切。

在参考文献15和16中，对硬颗粒，通过用量纲论证和数值模拟，剪切力显示出与法向应力成比例，用一维函数表示比例系数，叫做惯性数I ： 5.0)//(,)(s P d I P I ργμτ==（1）这里)(I ρ是摩擦系数，d 是颗粒直径，s ρ是颗粒密度。

梗概作文《三体》500字英文回答："Three-Body" is a science fiction novel written by Liu Cixin. It tells the story of humanity's encounter with an alien civilization and the ensuing struggle for survival. The novel is set in both the present day and during the Cultural Revolution in China.The story begins when a Chinese astrophysicist named Ye Wenjie sends a message into space, inviting alien civilizations to come to Earth. Her message is received by an alien civilization called the Trisolarans, who are facing the imminent destruction of their own planet due to gravitational instability. The Trisolarans decide to invade Earth and take over as their new home.The novel explores various themes, including the nature of human civilization, the limits of scientific knowledge, and the potential for human extinction. It also delves intothe moral and ethical dilemmas faced by the characters as they navigate the complex and dangerous world of the Trisolarans.One of the most fascinating aspects of the novel is its depiction of the Trisolarans. They are a highly advanced civilization with technology far beyond that of Earth. However, they also face their own challenges and struggles, which adds depth and complexity to their characters.The novel is filled with suspense and mystery, as the characters try to unravel the secrets of the Trisolarans and find a way to save humanity. It also raises thought-provoking questions about the nature of reality and the potential for life on other planets.Overall, "Three-Body" is a captivating and thought-provoking novel that explores the complexities of human nature and the vastness of the universe. It is a must-read for fans of science fiction and anyone interested in exploring the possibilities of extraterrestrial life.中文回答：《三体》是刘慈欣所著的一部科幻小说。

The Secrets of the Solar SystemThe Solar System has always been a subject of fascination for humans. From the ancient times, people have been observing the movements of celestial bodies and trying to understand the secrets of the universe. With the advancements in technology, we have been able to gather more information about the Solar System. However, there are still many mysteries that remain unsolved. In this article, we will explore some of the secrets of the Solar System.One of the most interesting things about the Solar System is the formation of planets. Scientists believe that the Solar System was formed around 4.6 billion years ago from a cloud of gas and dust. As the cloud collapsed, it formed a rotating disk, which eventually led to the formation of the Sun and the planets. However, the exact process of planet formation is still not fully understood. There are many theories, but none of them can fully explain all the observations. For example, the formation of giant planets like Jupiter is still a mystery. Some scientists believe that they formed by the accretion of solid particles, while others think that they formed through the gravitational instability of the gas disk.Another mystery of the Solar System is the origin of life. Earth is the only planet in the Solar System known to harbor life. However, scientists believe that life could exist on other planets or moons in the Solar System. For example, there is evidence of liquid water on Mars, and some of the moons of Jupiter and Saturn have subsurface oceans. The question is, how did life originate on Earth, and could it have originated elsewhere in the Solar System? There are many theories, but none of them can fully explain the origin of life. Some scientists believe that life originated through a process called abiogenesis, where simple organic molecules combined to form more complex ones, eventually leading to the formation of life. Others think that life could have been brought to Earth by comets or asteroids.The Solar System is also home to some of the most fascinating objects in the universe, such as asteroids, comets, and dwarf planets. These objects can tell us a lot about the history of the Solar System. For example, the study of asteroids can help us understand the formation of the Solar System and the evolution of planets. Comets, on the other hand, canprovide us with information about the early Solar System and the conditions that existed at that time. Dwarf planets, like Pluto, can tell us about the outer reaches of the Solar System and the interactions between the planets and other objects.The study of the Solar System is not just about understanding the past, but also about preparing for the future. One of the biggest threats to life on Earth is the impact of an asteroid or comet. In the past, these impacts have caused mass extinctions, and it is important to understand the risks and develop strategies to mitigate them. Scientists are constantly monitoring the Solar System for objects that could pose a threat to Earth. They are also developing technologies to deflect or destroy these objects if necessary.Finally, the study of the Solar System can also inspire us and expand our horizons. The exploration of space has always been a source of wonder and excitement for humans. The Solar System is a vast and beautiful place, and the more we learn about it, the more we realize how much there is to discover. The exploration of the Solar System has also led to many technological advancements, from the development of new materials to the creation of new propulsion systems. These advancements have the potential to benefit humanity in many ways, from improving our understanding of the universe to improving our quality of life on Earth.In conclusion, the Solar System is a fascinating and mysterious place. From the formation of planets to the search for extraterrestrial life, there are many secrets waiting to be uncovered. The study of the Solar System is not just about understanding the past, but also about preparing for the future and expanding our horizons. As we continue to explore and learn more about the Solar System, we will undoubtedly discover new mysteries and uncover new secrets.。

描写肥胖的短句子唯美英文(篇一)标题：A Collection of Exquisite English Sentences Depicting Obesity (Not Less Than 60)1. The mirror reflected her plump figure, revealing her struggle with obesity.2. Her curves danced and swayed as she moved, a testament to her generous proportions.3. His size overshadowed the room, the embodiment of excess and indulgence.4. She wore her weight with confidence, a queen of ample beauty.5. His belly protruded like a mountXXn, a testament to a life well-fed.6. The stXXrcase groaned under the weight of her corpulent body, echoing her burden.7. The scale's numbers climbed higher and higher, matching the weight of her heart.8. Her double chin served as a reminder of her love for life's culinary pleasures.9. The doorway seemed narrower as he squeezed his rotund frame through it, a dXXly struggle.10. Her body was a canvas pXXnted with layers of flesh, sculpted by her insatiable appetite.11. The sea of adipose tissue swelled beneath her skin, an ocean of self-indulgence.12. Each step she took brought a symphony of creaking joints and heavy breathing.13. His size eclipsed the room, casting darkness upon his once vibrant existence.14. The buttons on his shirt fought a losing battle agXXnst the belly that strXXned agXXnst them.15. The embrace of her body was soft and inviting, a refuge from the harshness of the world.16. His thighs wobbled like gelatin, an embodiment of the instability of his weight.17. She walked with grace despite the extra pounds, defying society's expectations.18. The excess weight clung to his body like a stubborn shadow, unwilling to let go.19. Her laughter shook her heavy frame, a reminder of the joy found in life's indulgences.20. His bulging stomach seemed to have a gravitational pull of its own, attracting attention.21. Her silhouette cast a long shadow, a testament to the immensity of her being.22. The squeeze of a chXXr reminded her of her physical limitations, causing a pang of self-awareness.23. His body radiated warmth, a comforting embrace for those seeking solace.24. The echoes of her footsteps lingered, a reminder of the weight she carried.25. Despite her size, her eyes beamed with kindness, a stark contrast to society's judgment.26. Hugs from her were an enveloping experience, a comforting refuge for weary souls.27. The seams on his clothes strXXned with each breath, testament to an expanding wXXstline.28. She was a masterpiece, beautifully flawed and resilient in a world obsessed with perfection.29. His curves spoke volumes, telling stories of self-discovery and acceptance.30. Her larger-than-life presence filled the room, magnetic and captivating.31. The rolls of fat on his body hid a gentle heart, guarded by layers of protection.32. She reveled in food's comforting embrace, finding solace in every bite.33. His body moved with a graceful momentum, defying expectations with each step.34. She floated through life with a weightless grace, her size an afterthought.35. The weight on her shoulders was metaphorical as well as physical, carrying the burdens of society's judgment.36. He embraced his curves with pride, celebrating the beauty found in every bulge.37. Her smiles were infectious, radiating warmth from a face framed by soft flesh.38. The world saw her body, but she knew her true worth lay beyond the confines of her skin.39. His laughter echoed through the room, shaking the walls and breaking stereotypes.40. She refused to let her weight define her, choosing self-love over societal expectations.41. The abundance of her figure made her presence impossible to ignore, a force to be reckoned with.42. Despite his weight, his spirit soared, unburdened by society's narrow definitions of beauty.43. The scale's numbers were just numbers to her, unable to measure the depth of her soul.44. She moved with a sensuality that defied logic, embracing her curves with every step.45. His weight became a metaphor for a life well-lived, marked by indulgence and joy.46. She carried the weight of the world on her body, an embodiment of resilience and strength.47. The softness of her body was a comfort to those who sought solace in her embrace.48. His size was a representation of his insatiable appetite for life, never settling for less.49. She wore her weight with pride, a walking rebellion agXXnst societal norms.50. The mountXXns of flesh on his body held hidden treasures of compassion and understanding.51. Her laughter rippled through the XXr, a melody composed of joy and self-acceptance.52. The shadows cast by her ample figure were a testament to the depth of her being.53. His body was a protector, offering warmth and comfort to those lucky enough to be close.54. She moved with a grace that belied her size, defying gravity with every step.55. The folds of her skin were maps of her journey, telling stories of growth and resilience.56. His heart was as big as his stomach, overflowing with love and compassion.57. The pressure on her joints was a reminder of the weight she carried, both physically and emotionally.58. She lived life unapologetically, embracing her body's curves and defying societal expectations.59. His round face told the tale of laughter and joy shared with loved ones.60. She blossomed like a rose, her full figure a testament to her vibrant spirit.这些唯美的英文句子描绘了肥胖的身体，展现了其中的美丽和复杂性。

See discussions, stats, and author profiles for this publication at: https:///publication/295135098 Observation of Gravitational Waves from a Binary Black Hole MergerARTICLE in PHYSICAL REVIEW LETTERS · FEBRUARY 2016Impact Factor: 7.51READS2182 AUTHORS, INCLUDING:B. C. BarishCalifornia Institute of Technology 389 PUBLICATIONS 6,264 CITATIONSSEE PROFILE Kent BlackburnCalifornia Institute of Technology 329 PUBLICATIONS 6,872 CITATIONSSEE PROFILERijuparna Chakraborty66 PUBLICATIONS 247 CITATIONSSEE PROFILEW.P. KellsCalifornia Institute of Technology265 PUBLICATIONS 5,620 CITATIONSSEE PROFILEObservation of Gravitational Waves from a Binary Black Hole MergerB.P.Abbott et al.*(LIGO Scientific Collaboration and Virgo Collaboration)(Received21January2016;published11February2016)On September14,2015at09:50:45UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal.The signal sweeps upwards in frequency from35to250Hz with a peak gravitational-wave strain of1.0×10−21.It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole.The signal was observed with a matched-filter signal-to-noise ratio of24and a false alarm rate estimated to be less than1event per203000years,equivalent to a significance greaterthan5.1σ.The source lies at a luminosity distance of410þ160−180Mpc corresponding to a redshift z¼0.09þ0.03−0.04.In the source frame,the initial black hole masses are36þ5−4M⊙and29þ4−4M⊙,and the final black hole mass is62þ4−4M⊙,with3.0þ0.5−0.5M⊙c2radiated in gravitational waves.All uncertainties define90%credible intervals.These observations demonstrate the existence of binary stellar-mass black hole systems.This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.DOI:10.1103/PhysRevLett.116.061102I.INTRODUCTIONIn1916,the year after the final formulation of the field equations of general relativity,Albert Einstein predicted the existence of gravitational waves.He found that the linearized weak-field equations had wave solutions: transverse waves of spatial strain that travel at the speed of light,generated by time variations of the mass quadrupole moment of the source[1,2].Einstein understood that gravitational-wave amplitudes would be remarkably small;moreover,until the Chapel Hill conference in 1957there was significant debate about the physical reality of gravitational waves[3].Also in1916,Schwarzschild published a solution for the field equations[4]that was later understood to describe a black hole[5,6],and in1963Kerr generalized the solution to rotating black holes[7].Starting in the1970s theoretical work led to the understanding of black hole quasinormal modes[8–10],and in the1990s higher-order post-Newtonian calculations[11]preceded extensive analytical studies of relativistic two-body dynamics[12,13].These advances,together with numerical relativity breakthroughs in the past decade[14–16],have enabled modeling of binary black hole mergers and accurate predictions of their gravitational waveforms.While numerous black hole candidates have now been identified through electromag-netic observations[17–19],black hole mergers have not previously been observed.The discovery of the binary pulsar system PSR B1913þ16 by Hulse and Taylor[20]and subsequent observations of its energy loss by Taylor and Weisberg[21]demonstrated the existence of gravitational waves.This discovery, along with emerging astrophysical understanding[22], led to the recognition that direct observations of the amplitude and phase of gravitational waves would enable studies of additional relativistic systems and provide new tests of general relativity,especially in the dynamic strong-field regime.Experiments to detect gravitational waves began with Weber and his resonant mass detectors in the1960s[23], followed by an international network of cryogenic reso-nant detectors[24].Interferometric detectors were first suggested in the early1960s[25]and the1970s[26].A study of the noise and performance of such detectors[27], and further concepts to improve them[28],led to proposals for long-baseline broadband laser interferome-ters with the potential for significantly increased sensi-tivity[29–32].By the early2000s,a set of initial detectors was completed,including TAMA300in Japan,GEO600 in Germany,the Laser Interferometer Gravitational-Wave Observatory(LIGO)in the United States,and Virgo in binations of these detectors made joint obser-vations from2002through2011,setting upper limits on a variety of gravitational-wave sources while evolving into a global network.In2015,Advanced LIGO became the first of a significantly more sensitive network of advanced detectors to begin observations[33–36].A century after the fundamental predictions of Einstein and Schwarzschild,we report the first direct detection of gravitational waves and the first direct observation of a binary black hole system merging to form a single black hole.Our observations provide unique access to the*Full author list given at the end of the article.Published by the American Physical Society under the terms of the Creative Commons Attribution3.0License.Further distri-bution of this work must maintain attribution to the author(s)and the published article’s title,journal citation,and DOI.properties of space-time in the strong-field,high-velocity regime and confirm predictions of general relativity for the nonlinear dynamics of highly disturbed black holes.II.OBSERVATIONOn September14,2015at09:50:45UTC,the LIGO Hanford,W A,and Livingston,LA,observatories detected the coincident signal GW150914shown in Fig.1.The initial detection was made by low-latency searches for generic gravitational-wave transients[41]and was reported within three minutes of data acquisition[43].Subsequently, matched-filter analyses that use relativistic models of com-pact binary waveforms[44]recovered GW150914as the most significant event from each detector for the observa-tions reported here.Occurring within the10-msintersite FIG.1.The gravitational-wave event GW150914observed by the LIGO Hanford(H1,left column panels)and Livingston(L1,rightcolumn panels)detectors.Times are shown relative to September14,2015at09:50:45UTC.For visualization,all time series are filtered with a35–350Hz bandpass filter to suppress large fluctuations outside the detectors’most sensitive frequency band,and band-reject filters to remove the strong instrumental spectral lines seen in the Fig.3spectra.Top row,left:H1strain.Top row,right:L1strain.GW150914arrived first at L1and6.9þ0.5−0.4ms later at H1;for a visual comparison,the H1data are also shown,shifted in time by this amount and inverted(to account for the detectors’relative orientations).Second row:Gravitational-wave strain projected onto each detector in the35–350Hz band.Solid lines show a numerical relativity waveform for a system with parameters consistent with those recovered from GW150914[37,38]confirmed to99.9%by an independent calculation based on[15].Shaded areas show90%credible regions for two independent waveform reconstructions.One(dark gray)models the signal using binary black hole template waveforms [39].The other(light gray)does not use an astrophysical model,but instead calculates the strain signal as a linear combination of sine-Gaussian wavelets[40,41].These reconstructions have a94%overlap,as shown in[39].Third row:Residuals after subtracting the filtered numerical relativity waveform from the filtered detector time series.Bottom row:A time-frequency representation[42]of the strain data,showing the signal frequency increasing over time.propagation time,the events have a combined signal-to-noise ratio(SNR)of24[45].Only the LIGO detectors were observing at the time of GW150914.The Virgo detector was being upgraded, and GEO600,though not sufficiently sensitive to detect this event,was operating but not in observational mode.With only two detectors the source position is primarily determined by the relative arrival time and localized to an area of approximately600deg2(90% credible region)[39,46].The basic features of GW150914point to it being produced by the coalescence of two black holes—i.e., their orbital inspiral and merger,and subsequent final black hole ringdown.Over0.2s,the signal increases in frequency and amplitude in about8cycles from35to150Hz,where the amplitude reaches a maximum.The most plausible explanation for this evolution is the inspiral of two orbiting masses,m1and m2,due to gravitational-wave emission.At the lower frequencies,such evolution is characterized by the chirp mass[11]M¼ðm1m2Þ3=5121=5¼c3G596π−8=3f−11=3_f3=5;where f and_f are the observed frequency and its time derivative and G and c are the gravitational constant and speed of light.Estimating f and_f from the data in Fig.1, we obtain a chirp mass of M≃30M⊙,implying that the total mass M¼m1þm2is≳70M⊙in the detector frame. This bounds the sum of the Schwarzschild radii of thebinary components to2GM=c2≳210km.To reach an orbital frequency of75Hz(half the gravitational-wave frequency)the objects must have been very close and very compact;equal Newtonian point masses orbiting at this frequency would be only≃350km apart.A pair of neutron stars,while compact,would not have the required mass,while a black hole neutron star binary with the deduced chirp mass would have a very large total mass, and would thus merge at much lower frequency.This leaves black holes as the only known objects compact enough to reach an orbital frequency of75Hz without contact.Furthermore,the decay of the waveform after it peaks is consistent with the damped oscillations of a black hole relaxing to a final stationary Kerr configuration. Below,we present a general-relativistic analysis of GW150914;Fig.2shows the calculated waveform using the resulting source parameters.III.DETECTORSGravitational-wave astronomy exploits multiple,widely separated detectors to distinguish gravitational waves from local instrumental and environmental noise,to provide source sky localization,and to measure wave polarizations. The LIGO sites each operate a single Advanced LIGO detector[33],a modified Michelson interferometer(see Fig.3)that measures gravitational-wave strain as a differ-ence in length of its orthogonal arms.Each arm is formed by two mirrors,acting as test masses,separated by L x¼L y¼L¼4km.A passing gravitational wave effec-tively alters the arm lengths such that the measured difference isΔLðtÞ¼δL x−δL y¼hðtÞL,where h is the gravitational-wave strain amplitude projected onto the detector.This differential length variation alters the phase difference between the two light fields returning to the beam splitter,transmitting an optical signal proportional to the gravitational-wave strain to the output photodetector. To achieve sufficient sensitivity to measure gravitational waves,the detectors include several enhancements to the basic Michelson interferometer.First,each arm contains a resonant optical cavity,formed by its two test mass mirrors, that multiplies the effect of a gravitational wave on the light phase by a factor of300[48].Second,a partially trans-missive power-recycling mirror at the input provides addi-tional resonant buildup of the laser light in the interferometer as a whole[49,50]:20W of laser input is increased to700W incident on the beam splitter,which is further increased to 100kW circulating in each arm cavity.Third,a partially transmissive signal-recycling mirror at the outputoptimizes FIG. 2.Top:Estimated gravitational-wave strain amplitude from GW150914projected onto H1.This shows the full bandwidth of the waveforms,without the filtering used for Fig.1. The inset images show numerical relativity models of the black hole horizons as the black holes coalesce.Bottom:The Keplerian effective black hole separation in units of Schwarzschild radii (R S¼2GM=c2)and the effective relative velocity given by the post-Newtonian parameter v=c¼ðGMπf=c3Þ1=3,where f is the gravitational-wave frequency calculated with numerical relativity and M is the total mass(value from Table I).the gravitational-wave signal extraction by broadening the bandwidth of the arm cavities [51,52].The interferometer is illuminated with a 1064-nm wavelength Nd:Y AG laser,stabilized in amplitude,frequency,and beam geometry [53,54].The gravitational-wave signal is extracted at the output port using a homodyne readout [55].These interferometry techniques are designed to maxi-mize the conversion of strain to optical signal,thereby minimizing the impact of photon shot noise (the principal noise at high frequencies).High strain sensitivity also requires that the test masses have low displacement noise,which is achieved by isolating them from seismic noise (low frequencies)and designing them to have low thermal noise (intermediate frequencies).Each test mass is suspended as the final stage of a quadruple-pendulum system [56],supported by an active seismic isolation platform [57].These systems collectively provide more than 10orders of magnitude of isolation from ground motion for frequen-cies above 10Hz.Thermal noise is minimized by using low-mechanical-loss materials in the test masses and their suspensions:the test masses are 40-kg fused silica substrates with low-loss dielectric optical coatings [58,59],and are suspended with fused silica fibers from the stage above [60].To minimize additional noise sources,all components other than the laser source are mounted on vibration isolation stages in ultrahigh vacuum.To reduce optical phase fluctuations caused by Rayleigh scattering,the pressure in the 1.2-m diameter tubes containing the arm-cavity beams is maintained below 1μPa.Servo controls are used to hold the arm cavities on resonance [61]and maintain proper alignment of the optical components [62].The detector output is calibrated in strain by measuring its response to test mass motion induced by photon pressure from a modulated calibration laser beam [63].The calibration is established to an uncertainty (1σ)of less than 10%in amplitude and 10degrees in phase,and is continuously monitored with calibration laser excitations at selected frequencies.Two alternative methods are used to validate the absolute calibration,one referenced to the main laser wavelength and the other to a radio-frequencyoscillator(a)FIG.3.Simplified diagram of an Advanced LIGO detector (not to scale).A gravitational wave propagating orthogonally to the detector plane and linearly polarized parallel to the 4-km optical cavities will have the effect of lengthening one 4-km arm and shortening the other during one half-cycle of the wave;these length changes are reversed during the other half-cycle.The output photodetector records these differential cavity length variations.While a detector ’s directional response is maximal for this case,it is still significant for most other angles of incidence or polarizations (gravitational waves propagate freely through the Earth).Inset (a):Location and orientation of the LIGO detectors at Hanford,WA (H1)and Livingston,LA (L1).Inset (b):The instrument noise for each detector near the time of the signal detection;this is an amplitude spectral density,expressed in terms of equivalent gravitational-wave strain amplitude.The sensitivity is limited by photon shot noise at frequencies above 150Hz,and by a superposition of other noise sources at lower frequencies [47].Narrow-band features include calibration lines (33–38,330,and 1080Hz),vibrational modes of suspension fibers (500Hz and harmonics),and 60Hz electric power grid harmonics.[64].Additionally,the detector response to gravitational waves is tested by injecting simulated waveforms with the calibration laser.To monitor environmental disturbances and their influ-ence on the detectors,each observatory site is equipped with an array of sensors:seismometers,accelerometers, microphones,magnetometers,radio receivers,weather sensors,ac-power line monitors,and a cosmic-ray detector [65].Another∼105channels record the interferometer’s operating point and the state of the control systems.Data collection is synchronized to Global Positioning System (GPS)time to better than10μs[66].Timing accuracy is verified with an atomic clock and a secondary GPS receiver at each observatory site.In their most sensitive band,100–300Hz,the current LIGO detectors are3to5times more sensitive to strain than initial LIGO[67];at lower frequencies,the improvement is even greater,with more than ten times better sensitivity below60Hz.Because the detectors respond proportionally to gravitational-wave amplitude,at low redshift the volume of space to which they are sensitive increases as the cube of strain sensitivity.For binary black holes with masses similar to GW150914,the space-time volume surveyed by the observations reported here surpasses previous obser-vations by an order of magnitude[68].IV.DETECTOR VALIDATIONBoth detectors were in steady state operation for several hours around GW150914.All performance measures,in particular their average sensitivity and transient noise behavior,were typical of the full analysis period[69,70]. Exhaustive investigations of instrumental and environ-mental disturbances were performed,giving no evidence to suggest that GW150914could be an instrumental artifact [69].The detectors’susceptibility to environmental disturb-ances was quantified by measuring their response to spe-cially generated magnetic,radio-frequency,acoustic,and vibration excitations.These tests indicated that any external disturbance large enough to have caused the observed signal would have been clearly recorded by the array of environ-mental sensors.None of the environmental sensors recorded any disturbances that evolved in time and frequency like GW150914,and all environmental fluctuations during the second that contained GW150914were too small to account for more than6%of its strain amplitude.Special care was taken to search for long-range correlated disturbances that might produce nearly simultaneous signals at the two sites. No significant disturbances were found.The detector strain data exhibit non-Gaussian noise transients that arise from a variety of instrumental mecha-nisms.Many have distinct signatures,visible in auxiliary data channels that are not sensitive to gravitational waves; such instrumental transients are removed from our analyses [69].Any instrumental transients that remain in the data are accounted for in the estimated detector backgrounds described below.There is no evidence for instrumental transients that are temporally correlated between the two detectors.V.SEARCHESWe present the analysis of16days of coincident observations between the two LIGO detectors from September12to October20,2015.This is a subset of the data from Advanced LIGO’s first observational period that ended on January12,2016.GW150914is confidently detected by two different types of searches.One aims to recover signals from the coalescence of compact objects,using optimal matched filtering with waveforms predicted by general relativity. The other search targets a broad range of generic transient signals,with minimal assumptions about waveforms.These searches use independent methods,and their response to detector noise consists of different,uncorrelated,events. However,strong signals from binary black hole mergers are expected to be detected by both searches.Each search identifies candidate events that are detected at both observatories consistent with the intersite propa-gation time.Events are assigned a detection-statistic value that ranks their likelihood of being a gravitational-wave signal.The significance of a candidate event is determined by the search background—the rate at which detector noise produces events with a detection-statistic value equal to or higher than the candidate event.Estimating this back-ground is challenging for two reasons:the detector noise is nonstationary and non-Gaussian,so its properties must be empirically determined;and it is not possible to shield the detector from gravitational waves to directly measure a signal-free background.The specific procedure used to estimate the background is slightly different for the two searches,but both use a time-shift technique:the time stamps of one detector’s data are artificially shifted by an offset that is large compared to the intersite propagation time,and a new set of events is produced based on this time-shifted data set.For instrumental noise that is uncor-related between detectors this is an effective way to estimate the background.In this process a gravitational-wave signal in one detector may coincide with time-shifted noise transients in the other detector,thereby contributing to the background estimate.This leads to an overestimate of the noise background and therefore to a more conservative assessment of the significance of candidate events.The characteristics of non-Gaussian noise vary between different time-frequency regions.This means that the search backgrounds are not uniform across the space of signals being searched.To maximize sensitivity and provide a better estimate of event significance,the searches sort both their background estimates and their event candidates into differ-ent classes according to their time-frequency morphology. The significance of a candidate event is measured against the background of its class.To account for having searchedmultiple classes,this significance is decreased by a trials factor equal to the number of classes [71].A.Generic transient searchDesigned to operate without a specific waveform model,this search identifies coincident excess power in time-frequency representations of the detector strain data [43,72],for signal frequencies up to 1kHz and durations up to a few seconds.The search reconstructs signal waveforms consistent with a common gravitational-wave signal in both detectors using a multidetector maximum likelihood method.Each event is ranked according to the detection statistic ηc ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2E c =ð1þE n =E c Þp ,where E c is the dimensionless coherent signal energy obtained by cross-correlating the two reconstructed waveforms,and E n is the dimensionless residual noise energy after the reconstructed signal is subtracted from the data.The statistic ηc thus quantifies the SNR of the event and the consistency of the data between the two detectors.Based on their time-frequency morphology,the events are divided into three mutually exclusive search classes,as described in [41]:events with time-frequency morphology of known populations of noise transients (class C1),events with frequency that increases with time (class C3),and all remaining events (class C2).Detected with ηc ¼20.0,GW150914is the strongest event of the entire search.Consistent with its coalescence signal signature,it is found in the search class C3of events with increasing time-frequency evolution.Measured on a background equivalent to over 67400years of data and including a trials factor of 3to account for the search classes,its false alarm rate is lower than 1in 22500years.This corresponds to a probability <2×10−6of observing one or more noise events as strong as GW150914during the analysis time,equivalent to 4.6σ.The left panel of Fig.4shows the C3class results and background.The selection criteria that define the search class C3reduce the background by introducing a constraint on the signal morphology.In order to illustrate the significance of GW150914against a background of events with arbitrary shapes,we also show the results of a search that uses the same set of events as the one described above but without this constraint.Specifically,we use only two search classes:the C1class and the union of C2and C3classes (C 2þC 3).In this two-class search the GW150914event is found in the C 2þC 3class.The left panel of Fig.4shows the C 2þC 3class results and background.In the background of this class there are four events with ηc ≥32.1,yielding a false alarm rate for GW150914of 1in 8400years.This corresponds to a false alarm probability of 5×10−6equivalent to 4.4σ.FIG.4.Search results from the generic transient search (left)and the binary coalescence search (right).These histograms show the number of candidate events (orange markers)and the mean number of background events (black lines)in the search class where GW150914was found as a function of the search detection statistic and with a bin width of 0.2.The scales on the top give the significance of an event in Gaussian standard deviations based on the corresponding noise background.The significance of GW150914is greater than 5.1σand 4.6σfor the binary coalescence and the generic transient searches,respectively.Left:Along with the primary search (C3)we also show the results (blue markers)and background (green curve)for an alternative search that treats events independently of their frequency evolution (C 2þC 3).The classes C2and C3are defined in the text.Right:The tail in the black-line background of the binary coalescence search is due to random coincidences of GW150914in one detector with noise in the other detector.(This type of event is practically absent in the generic transient search background because they do not pass the time-frequency consistency requirements used in that search.)The purple curve is the background excluding those coincidences,which is used to assess the significance of the second strongest event.For robustness and validation,we also use other generic transient search algorithms[41].A different search[73]and a parameter estimation follow-up[74]detected GW150914 with consistent significance and signal parameters.B.Binary coalescence searchThis search targets gravitational-wave emission from binary systems with individual masses from1to99M⊙, total mass less than100M⊙,and dimensionless spins up to 0.99[44].To model systems with total mass larger than 4M⊙,we use the effective-one-body formalism[75],whichcombines results from the post-Newtonian approach [11,76]with results from black hole perturbation theory and numerical relativity.The waveform model[77,78]assumes that the spins of the merging objects are alignedwith the orbital angular momentum,but the resultingtemplates can,nonetheless,effectively recover systemswith misaligned spins in the parameter region ofGW150914[44].Approximately250000template wave-forms are used to cover this parameter space.The search calculates the matched-filter signal-to-noiseratioρðtÞfor each template in each detector and identifiesmaxima ofρðtÞwith respect to the time of arrival of the signal[79–81].For each maximum we calculate a chi-squared statisticχ2r to test whether the data in several differentfrequency bands are consistent with the matching template [82].Values ofχ2r near unity indicate that the signal is consistent with a coalescence.Ifχ2r is greater than unity,ρðtÞis reweighted asˆρ¼ρ=f½1þðχ2rÞ3 =2g1=6[83,84].The final step enforces coincidence between detectors by selectingevent pairs that occur within a15-ms window and come fromthe same template.The15-ms window is determined by the10-ms intersite propagation time plus5ms for uncertainty inarrival time of weak signals.We rank coincident events basedon the quadrature sumˆρc of theˆρfrom both detectors[45]. To produce background data for this search the SNR maxima of one detector are time shifted and a new set of coincident events is computed.Repeating this procedure ∼107times produces a noise background analysis time equivalent to608000years.To account for the search background noise varying acrossthe target signal space,candidate and background events aredivided into three search classes based on template length.The right panel of Fig.4shows the background for thesearch class of GW150914.The GW150914detection-statistic value ofˆρc¼23.6is larger than any background event,so only an upper bound can be placed on its false alarm rate.Across the three search classes this bound is1in 203000years.This translates to a false alarm probability <2×10−7,corresponding to5.1σ.A second,independent matched-filter analysis that uses adifferent method for estimating the significance of itsevents[85,86],also detected GW150914with identicalsignal parameters and consistent significance.When an event is confidently identified as a real gravitational-wave signal,as for GW150914,the back-ground used to determine the significance of other events is reestimated without the contribution of this event.This is the background distribution shown as a purple line in the right panel of Fig.4.Based on this,the second most significant event has a false alarm rate of1per2.3years and corresponding Poissonian false alarm probability of0.02. Waveform analysis of this event indicates that if it is astrophysical in origin it is also a binary black hole merger[44].VI.SOURCE DISCUSSIONThe matched-filter search is optimized for detecting signals,but it provides only approximate estimates of the source parameters.To refine them we use general relativity-based models[77,78,87,88],some of which include spin precession,and for each model perform a coherent Bayesian analysis to derive posterior distributions of the source parameters[89].The initial and final masses, final spin,distance,and redshift of the source are shown in Table I.The spin of the primary black hole is constrained to be<0.7(90%credible interval)indicating it is not maximally spinning,while the spin of the secondary is only weakly constrained.These source parameters are discussed in detail in[39].The parameter uncertainties include statistical errors and systematic errors from averaging the results of different waveform models.Using the fits to numerical simulations of binary black hole mergers in[92,93],we provide estimates of the mass and spin of the final black hole,the total energy radiated in gravitational waves,and the peak gravitational-wave luminosity[39].The estimated total energy radiated in gravitational waves is3.0þ0.5−0.5M⊙c2.The system reached apeak gravitational-wave luminosity of3.6þ0.5−0.4×1056erg=s,equivalent to200þ30−20M⊙c2=s.Several analyses have been performed to determine whether or not GW150914is consistent with a binary black hole system in general relativity[94].A first TABLE I.Source parameters for GW150914.We report median values with90%credible intervals that include statistical errors,and systematic errors from averaging the results of different waveform models.Masses are given in the source frame;to convert to the detector frame multiply by(1þz) [90].The source redshift assumes standard cosmology[91]. Primary black hole mass36þ5−4M⊙Secondary black hole mass29þ4−4M⊙Final black hole mass62þ4−4M⊙Final black hole spin0.67þ0.05−0.07 Luminosity distance410þ160−180MpcSource redshift z0.09þ0.03−0.04。

行星形成演化模型推断及行星系统结构分析引言行星是宇宙中存在的体量较大的天体，围绕星体进行周期性运动。

行星的形成与演化一直是天文学领域的研究热点，科学家通过建立各种模型来推断行星的形成演化过程，并对行星系统的结构进行分析。

本文将探讨行星形成演化模型的推断方法，并对行星系统的结构进行分析。

行星形成演化模型推断行星形成指的是星际物质在尘埃和气体云中逐渐聚集，并在重力的作用下形成行星的过程。

科学家通过观测和模拟实验，提出了几种不同的行星形成模型。

1.核心凝聚模型（Core Accretion Model）核心凝聚模型是目前被广泛接受的行星形成模型之一。

根据该模型，行星形成是通过尘埃和气体云逐渐聚集形成一个核心，并进一步通过吸积周围的气体来增长。

核心凝聚模型解释了为何重力吸积能够起到关键的作用。

这个模型解释了为什么质量较小的太阳系行星如地球等，会由一个金属核心和一个由气体组成的大气层构成。

2.不稳定星际云塌缩模型（Gravitational Instability Model）不稳定星际云塌缩模型是另一种广泛被讨论的行星形成模型。

该模型认为星际云的不稳定性导致了局部区域的塌缩，从而形成行星。

与核心凝聚模型不同的是，不稳定星际云塌缩模型不需要较长时间的演化过程，行星形成可以在短时间内完成。

3.太阳局域磁场建模（Solar Nebula Magnetohydrodynamic Modeling）太阳局域磁场建模是一种基于磁流体动力学的行星形成模型。

该模型认为，磁场在星云中的存在将会对星云的演化和行星的形成产生重要的影响。

太阳局域磁场建模提供了解释行星形成过程中的角动量转移以及对行星系统结构的影响的机制。

行星系统结构分析行星系统的结构研究是推断行星形成过程中各个参数的重要一环。

通过对不同行星系统的观测和分析，科学家们对行星系统的结构有了更深入的认识。

1.行星系统的轨道结构行星系统的轨道结构取决于行星的质量、角动量和其所处的环境。

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有效应力⒀Eigenfunction 特征函数⑸Eigenvalue 特征值⑸electrolyte 电解液，电解质⒀electrostatic 静电的，静电学的⒀embankment 堤防，路堤⒅encapsulate 囊括⑼Enclose 放入封套，围绕⑶encompass 包围，包括⑼epoxy 环氧的⑼Epoxy-coated 环氧涂层的⑼Equilibrium 平衡，均衡⑹Equilibrium 平衡，平静⑸Euler-Bernoulli beam equation 欧拉-贝努利梁公式⑶excitation 激动，激励⒃expansion joint 伸缩缝⒄FFacede 正面的⑴facet （多面体的）面，刻面，小平面⒀feat 技艺，功绩⑻feldspar 长石⒀felt 毡，毡制品⑼Fixture 固定设备⑹Flexibility 柔性，适应性，机动性⑶Flexural rigidity 弯曲刚度⑸Flexural 曲折的，弯曲的⑸Flexural 弯曲的⑹flow net 流网⒀foil 箔，金属薄片⑼footing 基脚，基础⒁⒂⒃⒄⒅Force or flexibility method 力法⑶Framework 构架，框架⑴Framework 构架，框架⑷Frictional 摩擦的，摩擦力的⑹Ggabion 篾筐⒂galvanize 电镀，通电流于⑼geophysical engineering 地球物理⒀geophysical 地球物理学的⒀geosynthetic 地工合成物⒂geotechnical engineering 岩土工程⒀geotechnical 土工技术的⒃Girder 大梁，钢桁的支架⑶Girder 大梁⑷Glass transition 玻璃化转变⑵global positioning system （GPS）全球定位系统⑿Gravitational 地心吸力，引力作用⑶gunter‘s chain 甘特氏测链⑿gusset 节点板⒄Gyration 旋回，回转，旋转⑸HHabitat（动植物的）生活环境，产地，栖息地⑴Hard bid 竞标⑻Harmonic 和谐的，融洽的⑸help out 帮助……解决困难⒁Hinge 铰，铰链⑹Hip 屋脊⑷hold back 抑制，阻碍⒂Hot dip galvanise 热镀⑼hot-rolled 热轧⑾Hydrate 氢氧化物水化⑴Iimmiscible 不能混合的，不融合的⒀impact 冲击，影响⑻implant 灌输植入⒄in effect 事实上⒁Inclement 险恶的，严酷的，严寒的⑴incorporate 合并的，一体化的⑼indeterminate 不确定的⑾Indeterminate 模糊的，不确定的⑸Infrastructure 下部构造，基础设施⑻infrastructure 下部构造，基础设施⒃inplace 就地的，现场的⑽Instability 不稳定（性）⑸Intensive property 强度性质，广延性质⑵Intercept 截取，拦截⑵internal friction 内摩擦⒂interparticle 粒子⒀invar 因钢，镍铁合金⑿Jjig 夹具⑽Joist 托梁，棱条⑷Joist 托梁，小梁⑶juncture 接合点⒁Kkernel 核心，要点⒁Kiln（砖，石灰等）窑，烧窑⑴Kiln-fired material 窑烧制材料⑴kinematice 运动学的，运动学上的⒃Llandscape 风景，景观，美化⒂laser scanner 激光扫描器⑿lateral 横向的，侧面的，侧向的⒂lattice 格子，格构⒄Leeward 在下风方向的⑹limit state 极限状态⑾line 衬里，衬砌物⒅Linearize 使线性化⑸litigation 起诉，诉讼⑻Live load 活载⑹logistics 后勤，后勤学⑻Longitudinal 经度的，纵向的⑹Mmagnesium 镁⒀Malleable 有延展性的，可锻的⑴masonry 石工术，石建筑或砖建筑⒂Matrix stiffness method 矩阵刚度法⑶Matrix 矩阵⑶Method of virtual work 虚功法⑶microscopic 显微镜的⑼mineralogy 矿物学⒀Modulus 模数，模量⑵Moment distribution method 弯矩分配法⑶Moment 片刻，瞬间，力矩⑶mortarless 无灰泥的⒂mulch 覆盖，覆盖物⒅Multistory 多层楼的⑺multitasking 多（重）任务处理⑻NNeck 颈缩⑵negligible 可以忽略的⒁neutral axis 中性轴⑾Node 节点⑷Nomadic 游牧的，游牧生活的⑴nominal 名义上的⑾nondestructive 非破坏性的⑽nonstructural 非结构的⒁Oobstruction 阻塞，妨碍，障碍物⒄Offset strain 残余变形应变，条件应变⑵Offset 偏移量，抵销，弥补，抵销，偏移⑵Orthogonal 直角的，正交的⑹outfall 河口，排水口⒅over-deck truss bridge 下承式桁架桥⒄overlap （与……）交迭，重叠⑽overload 使超载，超过负荷⑾overrun 超限，超支⑻oversight 失察，监管，疏忽⑻overturn 倾覆，推翻⒁overwhelmingly 压倒性地，不可抵抗地⒀Pparallelism 平行，对应，类似⑽partial safety factor 分项安全系数⑽Particle size 粒径⒅Pascal 帕斯卡⑵passivate 使钝化⑼Passivating film 钝化膜⑼paymaster 发薪人员⑻penetrate 穿透，渗透⑼phase 阶段，相⒀pier 码头，桥墩⒄Pin 钉，栓，销⑸Pinned connection 铰结⑺Pinned support 铰支⑸Pitch truss 坡顶桁架⑷Pitch 斜度，倾斜⑷Planar truss 平面桁架⑷Planar 平面的⑷plastic hinge 塑性铰⑾plasticity index 塑性指标⒅plastification 增塑作用，塑化⑾Plumbing 管道设备，水暖设备⑴Polymer 聚合体，聚合物⑵Ponding 蓄水，坑洼⑹pore water pressure 空隙水压力⒀porosity 多孔性，孔隙率⒀potassium 钾⒀precast 预浇制⑼precipitate 沉淀物，使沉淀⒀predesignate 预先指示⑾predicable 可推断的，可肯定的⑾prerequisite 先决条件⑽prescribe 指示，规定⑽prescriptive说明性的，规定的⒃Prestressed concrete beam 预应力混凝土梁⑶proceeding 行动，会议录⑻Proportional 比例的，成比例的⑸proximity 接近，亲近⒁publicly 公然地，公开地⒃QQuonset 匡西特活动房屋⑴RRadius of gyration 回转半径⑸Rafter 椽⑷random variable 随机变量⑾random 随意，随机⑾Real property 不动产⑻Reassemble 重新召集，重新装配⑵Rebar 钢筋⑴Recoverable 可重获的，可恢复的⑵refinery 精炼厂，炼油厂⑼rehabilitation 复原⒅Reinforced concrete 钢筋混凝土⑴reinstatement 恢复⒅remold 改造，改铸⒀renovation 革新⑻repeatability 可重复性，再现性⑽reproducibility 重复能力，再现行⑽response spectrum 反应谱⒃Restraint 抑制，约束⑹resultant 合成的，合力⒁retaining wall 挡土墙⒂reticle 十字线，刻线⑿Reversal 颠倒，倒转，反向⑵right-of-way 道路用地⒅Rigid joint 刚结点⑺Rigidity 坚硬，刚性，刚度⑸roadstead 锚地，停泊处⒅robotic 机器人的，像机器人的⑿Roller 滚筒⑹Rotational 转动的，轮流的⑹roughen 变粗糙⑼Rupture 破裂，断裂⑵SSagging 下垂，松垂，垂度⑶sampling 取样⑽Sandcrete block 细石混凝土砌块⑴Sandcrete 细骨料混凝土⑴schematically 示意性地⑾Scheme 设计，方案⑺sealant 密封剂⑼Segment 段，节，片段⑴segmental 部分的，分割的⒂seismic performance ratio 耐震性能比⒃seismic performance 耐震性能⒃seismic 地震的⒃Semi-rigid 半刚性的⑺serviceability 有用性，适用性⑾setback 退步，顿挫⒂settlement 沉降，解决⒁shape factor 形状系数⑾Shear 剪，剪切⑶sheen 光辉，光泽⑼Side sway 侧移⑺simultaneously 同时地⒂sinkage 下沉⒄Skyscraper 摩天楼，高耸的烟囱⑴Slenderness ratio 长细比⑸Slenderness 苗条，细长⑸Slope deflection method 转角位移法⑶soil nailed wall 土钉墙⒂soluble 可溶的，可溶解的⒀Speciality 特性，专业⑴specimen 标本，样本，试件⑽Specimen 标本，样品，试件⑵stake out 用桩号标出⒅Statically determinate 静定的⑶Statically determine 静定的⑹Statically indeterminate 超静定的⑹stockpile 积蓄，库存⒅story performance rating 楼层性能分级⒃Stout 结实的，矮胖的⑶Straightforward 坦率的，直接了当的⑺strap footing 连梁基础⒁Strength 力量，强度⑸Stress 应力⑸⑹⑺⑻⑼⑽⑾⑿⒀⒁⒂⒃⒄⒅Strut 支柱，压杆⑹subset 子集⒃substructure 基础，下部结构⒄Superposition 重叠，迭加⑹superstructure 上部构造，上部结构⒄suspension bridge 悬索桥⒄Symmetric 相称性的，均衡的⑹Symmetry 对称，匀称⑶Synthetic 合成的，人造的，综合的⑴Ttaut （绳子）拉紧的，整洁的，紧张的⑿Teepee 印第安人的圆锥形帐篷⑴tender 投标⑻Tensile 可拉长的，张力的，拉力的⑵Tension 张力，拉力⑶terrestrial 陆地的⑿Tetrahedron 四面体⑷the American congress on surveying and mapping（ACSM）美国测绘协会⑿theodolite 经纬仪⑿Three-dimensional framework 三维框架⑷tie-back anchor 背拉锚，地锚⒂Titanium 钛⑴total station 全站仪⑿transient 短暂的，瞬时的⒃traumatize 使受损伤⒃treated timber 防腐处理木材⒂Triangulate 分成三角形，对……作三角测量⑺triangulation 三角测量（法）⑿triaxial 三轴的，三维的，空间的⑽trigonometry 三角法、三角学⑿tripod 三脚架⑿Trivial solution 平凡解⑸Trivial 价值不高的，微不足道的⑸Truncate 截去（圆锥等的）尖端⑷Truncated truss 截顶桁架⑷Truss 桁架⑷tsunami 海啸⒃Two-dimensional 二维的⑹UUltimate strength 极限强度⑵Unbraced frame 无支持框架⑺Unbraced 无支撑的⑺uncertainty 无常，不确定性⑾unconfined 无限制的，无约束的⑽understrength 力量不足的，人员不足的⑾unfactored 未乘系数的⒁uniaxial 单轴的⑽Unidirectional 单向的，单向性的⑶Unknown 位置的，未知数⑹Unsightly 不悦目的，难看的⑶untensioned 未拉紧的，松弛的⒂Vvariability 可变性⑾variable 变数，可变物⑾ventilate 使通风⑼Vernier 游标尺，游标⑿viaduct 高架桥⒄vinyl 乙烯基，含乙烯基的化合物⒂virtual 虚的，虚拟的⒃Wwaterway 水路，航道⒅Web 腹板⑺Web 网，梁腹⑷Weld connection 焊接⑺well-being 按实状态⒃Wide-flange beam 宽翼缘工字钢⑶Windward 迎风，上风⑹wrong iron 熟铁⒄YYield strength 屈服强度⑵Yurt 蒙古包⑴。