On the Amplitude of Burst Oscillations in 4U 1636-54 Evidence for Nuclear Powered Pulsars

a r X i v :a s t r o -p h /9803119v 1 10 M a r 1998

On the Amplitude of Burst Oscillations in

4U 1636-54:Evidence for Nuclear Powered Pulsars

Tod E.Strohmayer 1,William Zhang 3,Jean H.Swank 3,Nicholas E.White 3

Laboratory for High Energy Astrophysics

Goddard Space Flight Center

Greenbelt,MD 20771

Iosif Lapidus 2

Univeristy of Sussex,England

ABSTRACT

We present a study of 581Hz oscillations observed during a thermonuclear X-ray burst from the low mass X-ray binary (LMXB)4U 1636-54with the Rossi X-ray Timing Explorer (RXTE).This is the ?rst X-ray burst to exhibit both millisecond oscillations during the rising phase as well as photospheric radius expansion.We measure an oscillation amplitude within 0.1s of the onset of this burst of 75±17%,that is,almost the entire thermal burst ?ux is modulated near onset.The spectral evolution during the rising phase of this burst suggests that the X-ray emitting area on the neutron star was increasing,similar to the behavior of bursts from 4U 1728-34with 363Hz oscillations reported recently.We argue that the combination of large pulsed amplitudes near burst onset and the spectral evidence for localized emission during the rise strongly supports rotational modulation as the mechanism for the oscillations.We discuss how theoretical interpretation of spin modulation amplitudes,pulse pro?les and pulse phase spectroscopy can provide constraints on the masses and radii of neutron stars.We also discuss the implications of these ?ndings for the beat frequency models of kHz X-ray variability in LMXB.

Subject headings:X-rays:bursts -stars:individual (4U 1636-54)stars:neutron -stars:rotation

1.Introduction

Large amplitude millisecond oscillations have now been observed during thermonuclear X-ray bursts from six low mass X-ray binary(LMXB) systems with the Rossi X-ray Timing Explorer (RXTE)(see Strohmayer,Zhang&Swank1997; Smith,Morgan&Bradt1997,Zhang et al.1996; Swank et al.1997;and Strohmayer et al.1997). The thermonuclear instability which triggers an X-ray burst burns in a few seconds the nuclear fuel which has been accumulated on the neutron star surface over several hours.This>103dif-ference between the accumulation and burning timescales means that it is extremely unlikely that the conditions required to trigger the insta-bility will be achieved simultaneously over the entire stellar surface.This realization,?rst em-phasized by Joss(1978),led to the study of lat-eral propagation of the burning instability over the neutron star surface(see Fryxell&Woosley 1982,Nozakura,Ikeuchi&Fujimoto1984,and Bildsten1995).The subsecond risetimes of ther-monuclear X-ray bursts suggests that convection plays an important role in the physics of the burning front propagation,especially in the low accretion rate regime which leads to large igni-tion columns(see Bildsten(1998)for a review of thermonuclear burning on neutron stars).Bild-sten(1995)has shown that pure helium burn-ing on neutron star surfaces is in general inho-mogeneous,displaying a range of behavior which depends on the local accretion rate.Low accre-tion rates lead to convectively combustible accre-tion columns and standard type I bursts,while high accretion rates lead to slower,nonconvective propagation which may be manifested in hour long?ares.These studies emphasize that the physics of thermonuclear burning is necessarily a multi-dimensional problem and that localized burning is to be expected,especially at the onset of bursts.

There is now good evidence that the oscilla-tions seen during the rising phase of bursts from 4U1728-34are produced by spin modulation of such a localized thermonuclear hotspot on the surface of the neutron star,and that the ob-served oscillation frequency is a direct measure of the neutron star spin frequency(see Strohmayer, Zhang&Swank1997).These observations pro-vide the most compelling evidence to date that neutron stars in LMXB are rotating with near millisecond periods.

In this Letter we present new burst data from the LMXB4U1636-54which provides further ev-idence in support of the spin modulation hypoth-esis for the millisecond burst oscillations.We present data from a thermonuclear burst from 4U1636-54which reveals a strong transient os-cillation during the burst rise at1.723ms with an initial amplitude of75±17%.We also discuss the implications of these?ndings for the spin mod-ulation interpretation and how they can be used to place constraints on the mass and radius of neutron stars.Finally,we discuss some implica-tions of our observations for the current theories of kilohertz quasiperiodic oscillations(QPO)in LMXB.

2.Observations and data description

Zhang et al.(1996)reported the discovery of 581Hz oscillations during several thermonuclear X-ray bursts from4U1636-54.Here we focus on a single burst detected from this source with RXTE at22:39:22UTC on December28,1996. This burst is unique in that it reveals strong os-cillations at581Hz prior to the onset of photo-spheric radius expansion.Oscillations are not de-tected during the photospheric expansion phase, but reappear with much weaker amplitude after photospheric touchdown in a manner very sim-ilar to that reported for bursts from4U1728-34 and KS1731-26(Strohmayer et al.1997;and Smith,Morgan,&Bradt1997).

For this burst we obtained event mode data with125μs(1/8192s)time resolution and64 spectral channels across the2-100keV PCA

bandpass.This data mode employs a pair of data bu?ers which are alternately read out after a se-lectable accumulation interval.Each bu?er can store≈16,000events.In the case that the source countrate is high enough to?ll the bu?er before the end of an accumulation interval gaps in the data can occur.For the event data shown here we did have short gaps when the burst?ux was high,but telemetry constraints preclude selecting a shorter accumulation interval.For these bursts we also had125μs,2-90keV binnned timing data which does not su?er from gaps.

3.Oscillations during the rise of a radius

expansion burst

At the time of the burst in question the persis-tent countrate from4U1636-54in the total PCA bandpass was about2100cts/sec.4U1636-54is classi?ed as an atoll source and it was in the so called banana branch during these observa-tions(see Hasinger&van der Klis1989).We will present more detailed analysis of the accre-tion driven?ux and properties of all the X-ray bursts observed in a subsequent paper.Figure 1shows the2-90keV PCA lightcurve(top) and the hardness ratio(6-18keV)/(2-6keV) at1/16s resolution for this burst.The drop in the hardness ratio at about1.5s is a clear in-dication of photospheric radius expansion.This burst had a peak?ux in the2-60keV band of 7.2×10?8ergs cm?2s?1and a?uence in the same band of3.9×10?7ergs cm?2.At the sys-tem’s probable distance of6.5kpc(see Lawrence et al.1983)these correspond to3.6×1038ergs s?1and2.0×1039ergs.We used the2-90keV, 125μs binned data to compute a dynamic power spectrum by calculating power spectra from2s of data every1/8s through the burst.Since the data overlap in this analysis the individual power spectra are not independent,however,this procedure provides a straightforward way to in-vestigate the time evolution of the oscillations. The resulting dynamic power spectrum is pre-sented in?gure2,which shows contours of con-stant power spectral amplitude along with the burst pro?le superposed.This analysis reveals the presence of strong oscillations at about580 Hz on the rising edge of the burst as well as os-cillations after photospheric touchdown at a fre-quency about1Hz higher.As we discuss below, the oscillations during the rise are transient,last-ing about0.25s,this introduces a characteristic width to the peak in the power spectrum which results in the broader distribution in frequency of the power spectral contours near the burst rise. We emphasize that the contours centered near 580.5Hz at about2s are not indicative of a real drop in the oscillation frequency at the burst on-set.However,the change in frequency from burst rise to post-peak is real and is not caused by?-nite sampling time e?ects or the transient nature of the oscillations.This trend for the oscilla-tion frequency to increase with time during some bursts has now been reported in all sources with millisecond burst oscillations except KS1731-26, from which only a single burst with oscillations has so far been detected(see Strohmayer et al. 1997;Smith,Morgan,&Bradt1997).

To further characterize the oscillations seen during the rising phase we performed an epoch folding period search on the rising interval.Fig-ure3shows the lightcurve of the burst,focusing on the rising portion.The interval used for this analysis is denoted by the dashed lines in?gure 3.The epoch folding reveals a strong oscillation at1.723ms.We folded the data on this period to determine the pulse pro?le and amplitude.The resulting pulse pro?le is shown in?gure4a.We ?t a model with a constant countrate plus a si-nusoid,A+B sin(2πt/P+φ),to the pulse pro?le and?nd an amplitude B/A=30±4%with an acceptable?t.Since there is no evidence that the persistent?ux component is oscillating at the frequency observed during the burst,to de-termine the pulsed amplitude we?rst subtracted from the folded lightcurve the average persistent countrate calculated from a20s interval prior to the burst.We note that there are no detectable

oscillations during the interval when the drop in hardness ratio at about1.5s(see?gure1)in-dicates the onset of photospheric radius expan-sion.This is consistent with the idea that the expansion of the photosphere destroys the co-herent oscillations,probably both by scattering away the amplitude as well as changing the fre-quency quickly via the expansion of the surface layers.After photospheric touchdown(see?gure 1at about3.5s)the oscillations are again de-tected,but with slightly higher frequency and a much lower amplitude of about5.7%in the2-60keV bandpass.

The presence of large amplitude oscillations very near the onset of this burst is similar to the behavior of bursts from4U1728-34reported by Strohmayer,Zhang&Swank(1997).We found even higher oscillation amplitudes by folding a 62ms interval close to the onset of the burst. The folded interval is denoted by the solid verti-cal lines in?gure3.The background subtracted folded lightcurve obtained from this62ms in-terval is shown in?gure4b.We again?t the sinusoidal model to this lightcurve and found an amplitude of75±17%for this interval.This is easily the largest amplitude of the581Hz os-cillation seen during this burst.Such a large amplitude–almost the entire thermal burst?ux is modulated–only about0.1s after the onset of the burst is strong evidence that we are seeing a rotationally modulated,thermonuclear hotspot.

Strohmayer,Zhang&Swank(1997)reported spectral evidence for an increasing X-ray emit-ting area during burst rise using bursts from 4U1728-34observed with RXTE.We performed similar spectral analysis in order to determine whether the same process is plausible for this burst as an explanation for the strong oscillations seen during the https://www.sodocs.net/doc/6416745391.html,ing the125μs,64channel data we accumulated spectra through the burst on either0.0625,0.125,0.25or0.5s intervals depending on the countrate.We also accumu-lated a20s interval just prior to the burst for use as a background estimate.We?t the back-ground subtracted spectra to a blackbody model to determine temperatures and?uxes as a func-tion of time through the burst.We created a

plot of F1/4

bol

/kT BB versus F bol,where F bol is the bolometric?ux and kT BB is the blackbody tem-perature in keV.For a true blackbody the quan-

tity F1/4

bol

/kT BB∝A1/4/d1/2,where A is the X-ray emitting area and d is the distance to the source.We found results very similar to those reported by Strohmayer,Zhang&Swank(1997)

for bursts from4U1728-34,that is,F1/4

bol

/kT BB increases during the rise.This is strong evidence for an expanding X-ray emission region and thus supports the spin modulation hypothesis in this burst from4U1636-54.We emphasize that this result suggests an increase in the X-ray emitting area prior to the onset of photospheric radius ex-pansion.The onset of photospheric radius expan-sion is re?ected in the drop in hardness ratio at about1.5s in?gure1.It also corresponds to an increase in the emitting surface area,but it is caused by radial expansion of the photosphere due to radiation forces and not the lateral propa-gation of the burning instability.The blackbody spectral analysis indicates that the inferred emit-ting areas were approximately the same both im-mediately before and after the photospheric ra-dius expansion.This result combined with the large di?erence in oscillation amplitudes before and after photospheric expansion suggests that the thermonuclear?ash covered the entire sur-face of the neutron star.

4.Discussion

If the millisecond oscillations seen during bursts are in fact due to spin modulation,then de-tailed study and modelling of the oscillation am-plitudes,pulse pro?les and spectral variability with pulse phase during X-ray bursts can provide a wealth of information on the mass and radius of the neutron star.For example,the maximum modulation amplitude that can be obtained from a hotspot of a given angular size on a rotating

neutron star is set by the strength of general rel-ativistic light bending.For the case that rotation is not rapid enough to substantially distort the exterior spacetime from the Schwarzchild space-time,and this is the case even for spin periods of a few milliseconds(Lamb&Miller1995),then the maximum amplitude depends only on the compactness of the neutron star,that is,the ratio of stellar mass to radius GM/c2R.Stars which are more compact produce lower amplitudes due to?attening of the pulse by light bending(see Pechenick,Ftaclas&Cohen1983;Strohmayer 1992;and Miller&Lamb1997).Since the intrin-sic rotational modulation amplitude can only be decreased by other e?ects such as photon scat-tering(see Miller,Lamb&Psaltis1997;Brain-erd&Lamb1987;and Kyla?s&Phinney1989) or the viewing geometry of the spot,the maxi-mum observed oscillation amplitude represents a lower limit to the intrinsic amplitude.Thus an observed amplitude can be used to place an up-per limit on the compactness of the neutron star, that is,if the star were more compact than some limit it would not be able to produce a modula-tion amplitude as large as that observed.

In principle,stellar rotation will also play a role in the observed properties of spin modula-tion pulsations.For example,assuming the os-cillation frequency of581Hz represents the spin frequency of the neutron star in4U1636-54,then for a10km radius neutron star the spin velocity is v spin/c=2πνspin R≈0.12at the rotational equator.The motion of the hotspot produces a Doppler shift of magnitude?E/E≈v spin/c= 0.12,thus the observed spectrum is a function of pulse phase(see Chen&Shaham1989).Mea-surement of a pulse phase dependent Doppler shift in the X-ray spectrum would provide addi-tional evidence supporting the spin modulation model and would also provide a means of con-straining the neutron star radius.The rotation-ally induced velocity also produces an aberra-tion which results in asymmetric pulses,thus the pulse shapes also contain information on the spin velocity and therefore the stellar radius(Chen& Shaham1989).The component of the spin veloc-ity along the line of site is proportional to cosθ, whereθis the lattitude of the hotspot measured with respect to the rotational equator.The mod-ulation amplitude also depends on the lattitude of the hotspot,as spots near the rotational poles produce smaller amplitudes than those at the equator.Thus we expect a correlation between the observed oscillation amplitude and the size of any pulse phase dependent Doppler shift.Dec-tection of such a correlation in a sample of bursts would de?nitively con?rm the rotational modula-tion model in our opinion.We will present calcu-lations of mass-radius constraints for4U1636-54and4U1728-34including the e?ects of light bending,rotation and angle dependent emission, based on the observed properties of burst oscil-lations as well as spectroscopy of Eddington lim-ited bursts in a subsequent paper.

Several models for the kilohertz QPO seen in 13LMXB systems(see van der Klis1997for a re-cent review)invoke some sort of beat-frequency interpretation for the twin kHz peaks seen in many of the sources(see Miller,Lamb&Psaltis 1997;Strohmayer et al.1996).So far only in4U1728-34does the frequency di?erence be-tween the twin kHz peaks match the frequency observed during X-ray bursts(see Strohmayer et al.1996).In two other sources(KS1731-26and 4U1636-54)the separation of the twin kHz peaks is closer to1/2the frequency of oscillations ob-served during bursts(see Wijnands&van der Klis1997;and Zhang et al.1996).For exam-ple,Wijnands et al.(1997)report a frequency di?erence for the twin kHz QPO in4U1636-54of 276±10Hz.The e?ort to reconcile these observa-tions with a beat-frequency interpretation has led to speculation that the oscillation frequency ob-served during bursts may sometimes be twice the spin frequency of the star,although in4U1636-54the di?erence frequency appears to be a bit less than1/2the burst oscillation frequency,and in some Z sources the frequency di?erence is not

constant(van der Klis et al.1997).If this sce-nario is correct it implies the existence of two antipodal spots on the neutron star surface dur-ing X-ray bursts.In addition to the daunting requirement of initiating the thermonuclear?ash nearly simultaneously on opposite sides of the neutron star,the observation of large oscillation amplitudes shortly after burst onset in4U1636-54places severe constraints on the two hotspot scenario.To see this one can ask the following question.What maximum amplitude can be pro-duced by a star with antipodal hotspots?For two antipodal spots light bending strongly con-strains the amplitudes that can be achieved(see Pechenick,Ftaclas&Cohen1983).Calculations using the Schwarzchild spacetime and isotropic emission from the stellar surface indicate that even a neutron star with an implausibly small compactness of M/R=0.1,recall that rotational modulation amplitude increases with decreasing compactness,can only achieve a maximum am-plitude of about30%,whereas we measured an amplitude of75%from the burst described here. We note that with M/R=0.1a1.4M sun neu-tron star would have a radius of21km.This is far sti?er than any neutron star equation of state that we are familiar with.Rapid rotation could in principle modify this result,but at the mod-est inferred spin period of290.5Hz for the two spots to produce the observed581Hz frequency one would still require implausibly large neutron star radii to make a signi?cant rotational correc-tion to the amplitude.Another process which can increase the amplitude is beaming of radia-tion at the stellar surface.For example,to the extent that electron scattering is the dominant opacity process in neutron star atmospheres then one should expect a speci?c intensity distribu-tion which approximates that from a grey atmo-sphere.Such a distribution is proportional to cosδ+2/3,whereδis the angle from the nor-mal to the stellar surface(see Mihalas1978),so this will modestly increase the rotational mod-ulation amplitude.In addition,it is likely that the emergent spectrum will also be a weak func-tion ofδ(Miller&Lamb1997).With more de-tailed modelling of the emission from hotspots of ?nite size it will be possible to place strong con-straints on the antipodal hotspot interpretation for the burst oscillations.Finally,if further anal-ysis such as pulse phase spectroscopy continues to support the interpretation of the burst oscilla-tion frequency as the neutron star spin frequency in4U1636-54,then kHz QPO frequency separa-tions near1/2the spin frequency would suggest that the beat frequency interpretation may be untenable.

We thank Lars Bildsten,Andrew Cumming, Keith Jahoda,and John Wang for helpful dis-cussions.We thank the anonymous referee for helping us improve the manuscript.T.S.ac-knowledges the High Energy Astrophysics Pro-gram under USRA in the Laboratory for High Energy Astrophysics(LHEA)at NASA’s God-dard Space Flight Center.

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5.Figure Captions

Figure1:2-90keV lightcurve and hardness ratio plot for the burst.The hardness ratio is de?ned as the ratio of counts in the6-18keV range to that in the2-6keV range.The drop in hardness ratio at about1.5s indicates the beginning of the radius expansion phase.The dashed vertical lines denote the time interval used in the epoch folding analysis.

Figure2:Representation of the dynamic power spectrum for the burst shown in?gure1.The contours are levels of constant power spectral am-plitude.The power spectra were calculated from 2s intervals with the center of each succesive in-terval shifted by1/8s.The countrate pro?le of burst1is also shown.The burst pro?le is aligned to the center of each data interval used to calcu-late the power spectra.

Figure3:Lightcurve of the burst focusing on the rise.The interval denoted by dashed lines is that used for the folding analysis shown in?gure4a, while the solid vertical lines denote the62.5ms interval used for the folding analysis displayed in ?gure4b.

Figure4:(a)Folded,background subtracted lightcurve using the0.25second interval denoted with dashed vertcal lines in?gure3.The best ?tting sinusoidal model is also shown.The aver-age amplitude during this interval was30±4%.

(b)The same results are shown for the62.5ms interval shown in?gure3.For this interval the amplitude was75±17%.

Fig.1.—Figure1

Fig.2.—Figure2

Fig.3.—Figure3

Fig.4.—Figure4a

Fig.5.—Figure4b

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几种常用的医学超声设备

几种常用的医学超声设 备 -CAL-FENGHAI-(2020YEAR-YICAI)_JINGBIAN

A型超声诊断仪（amplitude） A型显示是一种最基本的显示方式，示波管上的横坐标表示超声波的传播时间，即探测深度；纵坐标则表示回波脉冲的幅度（amplitude），故称为A型。用A型诊断仪可以测量人体内各器官的位置、尺寸和组织的声学特性，并用于疾病诊断。 M型超声诊断仪（motion） 它在A型超声诊断仪基础上发展来的一种最基本的超声诊断设备。 显像管上的亮度表示回波幅度，由A型回波幅度加到显像管Z轴亮度调制极上所控制；其纵轴表示超声脉冲的传播时间，即探测深度；显像管水平偏转板加一慢时间扫描电压。这样在做人体探查时，就构成一幅各回波目标的活动曲线图。 其在检查心脏时具有一系列优点，如对心血管各个部分大小、厚度、瓣膜运动的测量，以及研究心脏的各部分运动与心电图、心音图及脉搏之间的关系等，所以也称超声心动仪。 此外它还可以研究其他各运动界面的情况，并通过与慢时间扫描同步移动探头，做一些简单的人体断层图。 B型超声诊断仪（brightness） 其也称B型超声切面显像仪。它用回波脉冲的幅度调制显示器亮度，而显示器的横轴和纵轴则与声速扫描的位置一一对应，从而形成一幅亮度调制的超声切面图像。 D型超声多普勒诊断仪 它利用超声波传播过程中与应用目标之间的相对运动所产生的多普勒效应来探测运动目标，主要包括多普勒血流测量和血流成像两种。 目前的彩色血流成像（color flow imaging CFI）则是在实时B型超声图像中，以伪彩色表示心脏或血管中的血液流动。它是利用多次脉冲回波相关处理技术来取得血流运动信息，故常称为彩色多普勒血流成像（color Doppler flow imaging, CDFI）。 经颅多普勒（transcranial Doppler，TCD）诊断仪应用低频多普勒超声，通过颞部、枕部、框部及颈部等透声窗，可以显示颅内脑动脉的血流动力学状况。 C型和F型超声成像设备 它是在B型超声诊断仪的基础上发展起来的，主要用来获取与声束方向垂直或呈一定夹角的平面和曲线上的回波信息并成像。透射式C型成像类似普通X射线成像，反映了声束路径上所有组织总的超声特性，可分别利用总的超声衰减和传播时间进行C型成像。C型和F型扫描成像能提供一些B型超声成像不能获得的信息。 超声外科设备 超声外科学是继超声治疗和诊断之后出现的一个医用超声领域。它用较强的超声波粉碎眼部、肾部的病变组织并排出，如超声乳化白内障摘除等，以达到实施超声外科手术的目的。其优点是降低患者痛苦，缩短手术时间。

英语造句

一般过去式 时间状语：yesterday just now (刚刚) the day before three days ag0 a week ago in 1880 last month last year 1. I was in the classroom yesterday. I was not in the classroom yesterday. Were you in the classroom yesterday. 2. They went to see the film the day before. Did they go to see the film the day before. They did go to see the film the day before. 3. The man beat his wife yesterday. The man didn’t beat his wife yesterday. 4. I was a high student three years ago. 5. She became a teacher in 2009. 6. They began to study english a week ago 7. My mother brought a book from Canada last year. 8.My parents build a house to me four years ago . 9.He was husband ago. She was a cooker last mouth. My father was in the Xinjiang half a year ago. 10.My grandfather was a famer six years ago. 11.He burned in 1991

ABAQUS中的幅值曲线

ABAQUS幅值曲线 在ABAQUS中，通过使用幅值曲线，可以描述边界条件和载荷等模型参数随时间或频率（稳态动力分析）的变化。在Load功能模块和Interaction功能模块中都可以定义幅值曲线，方法：Tools->Amplitude。 ABAQUS中可以定义11种幅值曲线，分别是表格幅型值曲线、等间距型幅值曲线、周期型幅值曲线、调制型幅值曲线、衰减型幅值曲线、依赖于解的幅值曲线、平滑分析步幅值曲线、激励器幅值曲线、谱幅值曲线、用户自定义幅值曲线以及PSD定义幅值曲线。此外，还有一种默认的Ramp幅值曲线。 下边就重点介绍一下一些比较常用的幅值曲线。 1.默认Ramp幅值曲线 该曲线属于一种线性过渡型的幅值曲线，它的含义是从一个分析步的初始状态线性过渡到这个分析步的结束状态。定义时只需确定每个分析步载荷值即可。

2.表格型幅值曲线(tabular) 定义表格型幅值曲线时，只需给出每个时间点上对应的幅值。在分析过程中，ABAQUS 会自动在各个数据点之间进行线性插值。 3.等间距型幅值曲线(Equally spaced) 这种曲线以固定时间间隔给出幅值大小，ABAQUS在每个时间间隔内进行线性插值。定义该类曲线时应给出时间间隔和初始时刻（或最小频率值），默认的初始时刻为0。 4.周期型幅值曲线(Periodic) 如果某个量是周期变化的，就可以使用周期型幅值曲线。周期型幅值曲线用傅里叶(Fourier)级数表示，其表达式为： 式中：N为傅里叶级数项的个数；为圆频率(circular frequency)；t0为起始时刻(starting

time)；A0为初始幅值(initial amplitude)；An为cos项的系数；Bn为sin项的系数。 5.调制型幅值曲线(Modulated) 曲线定义公式为： 6.衰减型幅值曲线(Decay) 曲线定义公式为： 7.依赖于解的幅值曲线(Solution dependent) 这种曲线基于一种独立的求解变量来计算幅值。 8.平滑分析步幅值曲线(Smooth step) ABAQUS/Standard和ABAQUS/Explicit都可以根据平滑分析步数据定义幅值。 9.激励器幅值曲线(Actuator) 10.谱幅值曲线(Spectrum) 在响应谱分析中定义谱幅值曲线，通过确定谱值，频率，相关阻尼来确定。

4.Amplitude Shift Keying (ASK)

RF Simulation Demo: Amplitude Shift Keying 3 评级 | 2.67 out of 5 打印 概览 This step-by-step demo is designed to examine the Amplitude Shift Keying (ASK) digital modulation scheme. Fundamentally, digital modulation requires changing characteristics of the carrier wave over time. Each change results in a sine wave with a different phase, amplitude, or frequency than before. As a result, different “states” of the sine wave are referred to as symbols which represent some digital bit pattern. In this exercise, we will construct a LabVIEW VI that transmits and receives a digital bit stream in software using ASK. 下载 文件名: simple_ask_transceiver.vi 要求: View Background Below is a plot that shows the transmitted signal for 8-ASK. Here the amplitude level of the carrier signal represents 3-bits of digital data. Zero amplitude represents 000 , and the highest amplitude represents 111. The other levels are at intervals between. Programming Open “simple_ask_transceiver.vi” and inspect the front panel. It allows the user to choose the number of symbols that will be used (M-ASK), pulse shaping filter, symbol rate, and carrier rate. Additionally, there is a control for the amount of simulated channel noise in this system. There is a Tab Control which shows graphs of the raw and modulated

学生造句--Unit 1

●I wonder if it’s because I have been at school for so long that I’ve grown so crazy about going home. ●It is because she wasn’t well that she fell far behind her classmates this semester. ●I can well remember that there was a time when I took it for granted that friends should do everything for me. ●In order to make a difference to society, they spent almost all of their spare time in raising money for the charity. ●It’s no pleasure eating at school any longer because the food is not so tasty as that at home. ●He happened to be hit by a new idea when he was walking along the riverbank. ●I wonder if I can cope with stressful situations in life independently. ●It is because I take things for granted that I make so many mistakes. ●The treasure is so rare that a growing number of people are looking for it. ●He picks on the weak mn in order that we may pay attention to him. ●It’s no pleasure being disturbed whena I settle down to my work. ●I can well remember that when I was a child, I always made mistakes on purpose for fun. ●It’s no pleasure accompany her hanging out on the street on such a rainy day. ●I can well remember that there was a time when I threw my whole self into study in order to live up to my parents’ expectation and enter my dream university. ●I can well remember that she stuck with me all the time and helped me regain my confidence during my tough time five years ago. ●It is because he makes it a priority to study that he always gets good grades. ●I wonder if we should abandon this idea because there is no point in doing so. ●I wonder if it was because I ate ice-cream that I had an upset student this morning. ●It is because she refused to die that she became incredibly successful. ●She is so considerate that many of us turn to her for comfort. ●I can well remember that once I underestimated the power of words and hurt my friend. ●He works extremely hard in order to live up to his expectations. ●I happened to see a butterfly settle on the beautiful flower. ●It’s no pleasure making fun of others. ●It was the first time in the new semester that I had burned the midnight oil to study. ●It’s no pleasure taking everything into account when you long to have the relaxing life. ●I wonder if it was because he abandoned himself to despair that he was killed in a car accident when he was driving. ●Jack is always picking on younger children in order to show off his power. ●It is because he always burns the midnight oil that he oversleeps sometimes. ●I happened to find some pictures to do with my grandfather when I was going through the drawer. ●It was because I didn’t dare look at the failure face to face that I failed again. ●I tell my friend that failure is not scary in order that she can rebound from failure. ●I throw my whole self to study in order to pass the final exam. ●It was the first time that I had made a speech in public and enjoyed the thunder of applause. ●Alice happened to be on the street when a UFO landed right in front of her. ●It was the first time that I had kept myself open and talked sincerely with my parents. ●It was a beautiful sunny day. The weather was so comfortable that I settled myself into the

[P]ABAQUS梯形荷载定义(线性荷载)

1 梯形荷载定义 Magnitude的作用即相当于函数distribution的放大/缩小系数。 例如，梯形荷载函数为P=-100*Y+200， 则左图中设定的荷载最终效果为P=1*(-100*X+200)， 即magnitude × amplitude 2 网络帖子 2.1 magnitude和amplitude各自有什么意义-讨论帖 magnitude是大小，amplitude是幅值，举例子，maginitude是100，amplitude假如是你表里的情况，那么就是在0的时候位移为0（0乘以100）, 0.5的时候位移就为100乘以100, 1的时候是0乘以100,1.5的时候是-100乘以100

2.2荷载大小计算magnitude*amplitude*distribute讨论 如题目 1:magnitude：是指你指定的荷载大小假如为1000。 2:amplitude：幅值表式magnitude随时间的变化，若设定amplitude是线性的（0,0 1,5）也即0时刻幅值为0，结束时刻幅值为5，当前分析步的time peroid为1，进行到一半的时候 amplitude=2.5，(幅值曲线可以自定)。 3:distribute：是指荷载随空间变化，如果选择的是analytical fields 的话并且Expression是：2*X+3*Y。那么对于表面上一点坐标为（10,10,2）的话，那么distribute=2*10+3*10=50. 所以在时间为0.5时刻，表面(定义的surface traction所在的表面）上点的坐标是（10,10,2），那么这个时刻该位置上的荷载是magnitude*amplitude*distribute=1000*2.5*50=125000.（方向没考虑）所以呢，以毫米为长度单位的时候，一定要注意distribute中计算出来的空间坐标函数值，这个值一般比较大（因为单位是毫米），再乘以荷载值，结果会很大的，容易荷载放大。 以上个人的理解有不对的地方请指正! Hansha amplitude 不是时间，它是对应某个时间的幅值的大小。就用你的例子，“如果是默认的ramp的，当前分析步的time peroid为1，进行到一半的时候amplitude=0.5”，这只是一个特例，即：0, 0, 1, 1. 其实你自己也下意识地没把amplitue当时间，要不你怎么没说“当前分析步的amplitude peroid为1”呢？amplitude完全可以设成另外的值，譬如：0， 0， 1， 2. 这样当时间步为0.5时，amplitude为1. 对于distribute，要注意的是那个expression对不对，是不是单位一致。至于最后计算出来的函数值，该如何注意？ 语句的通顺，也要注意一下：“amplitude：是当前增量步所在当前分析步所在时间”，是不是读起来有点别扭？还有错别字，最好改过来。 觉得我有点过于较真了吧？实话相告，这就是做有限元做出来的。就这样，还往往会出错。

英语句子结构和造句

高中英语~词性~句子成分~语法构成 第一章节：英语句子中的词性 1.名词：n. 名词是指事物的名称，在句子中主要作主语.宾语.表语.同位语。 2.形容词;adj. 形容词是指对名词进行修饰~限定~描述~的成份，主要作定语.表语.。形容词在汉语中是（的）.其标志是: ous. Al .ful .ive。. 3.动词：vt. 动词是指主语发出的一个动作，一般用来作谓语。 4.副词：adv. 副词是指表示动作发生的地点. 时间. 条件. 方式. 原因. 目的. 结果.伴随让步. 一般用来修饰动词. 形容词。副词在汉语中是（地）.其标志是：ly。 5.代词：pron. 代词是指用来代替名词的词，名词所能担任的作用，代词也同样.代词主要用来作主语. 宾语. 表语. 同位语。 6.介词：prep.介词是指表示动词和名次关系的词，例如：in on at of about with for to。其特征：

介词后的动词要用—ing形式。介词加代词时，代词要用宾格。例如：give up her（him）这种形式是正确的，而give up she（he）这种形式是错误的。 7.冠词：冠词是指修饰名词，表名词泛指或特指。冠词有a an the 。 8.叹词：叹词表示一种语气。例如：OH. Ya 等 9.连词：连词是指连接两个并列的成分，这两个并列的成分可以是两个词也可以是两个句子。例如：and but or so 。 10.数词：数词是指表示数量关系词，一般分为基数词和序数词 第二章节：英语句子成分 主语：动作的发出者，一般放在动词前或句首。由名词. 代词. 数词. 不定时. 动名词. 或从句充当。 谓语：指主语发出来的动作，只能由动词充当，一般紧跟在主语后面。 宾语：指动作的承受着，一般由代词. 名词. 数词. 不定时. 动名词. 或从句充当. 介词后面的成分也叫介词宾语。 定语：只对名词起限定修饰的成分，一般由形容

超声专业术语

超声专业术语 超声成像ultrasonic imaging 实时成像real－time imaging 灰阶显示gray scale display 彩阶显示color scale display 经颅多普勒transcranial doppler 彩色多普勒血流显像color doppler flow imaging 彩色血流造影color flow angiography 彩色多普勒能量图color doppler energy 彩色能量图color power angio 超声内镜ultrasound endoscope 超声导管ultrasound catheter 血管内超声intravascular ultrasound 血管内超声显像intravascular ultrasonic imaging 管腔内超声显像intraluminal ultrasonic imaging 腔内超声显像endoluminal sonography 心内超声显像intracardiac ultrasonic imaging 内镜超声扫描endoscopic ultrasonography 内镜超声技术endosonography 膀胱镜超声技术cystosonography 阴道镜超声技术vaginosonography 经阴道彩色多普勒显像transvaginal color doppler imaging 经直肠超声扫描transrectal ultrasonography 直肠镜超声（技术）rectosonography 经尿道扫查transurethral scanning 介入性超声interventional ultrasound 术中超声监视intraoperative ultrasonic monitoring 超声引导经皮肝穿刺胆管造影ultrasound guided percutaneous transhepatic cholangiography 超声引导经皮穿刺注射乙醇US guided percutaneous alcohol injection 超声引导经皮胆囊胆汁引流US guided percutaneous gallbladder bile drainage 超声引导经皮抽吸US guided percutaneous aspiration 超声引导胎儿组织活检US guided fetal tissue biopsy 超声引导经皮肝穿刺门静脉造影US guided percutaneous transhepatic portography 三维显示three dimensional display 三维图像重建3D image reconstruction 组织特性成像tissue specific imaging 动态成像dynamic imaging 数字成像digital image 血管显像angiography 声像图法echography sonography声像图sonogram echogram 多用途探头multipurpose scanner

六级单词解析造句记忆MNO

M A: Has the case been closed yet? B: No, the magistrate still needs to decide the outcome. magistrate n.地方行政官，地方法官，治安官 A: I am unable to read the small print in the book. B: It seems you need to magnify it. magnify vt.１．放大，扩大；２．夸大，夸张 A: That was a terrible storm. B: Indeed, but it is too early to determine the magnitude of the damage. magnitude n.１．重要性，重大；２．巨大，广大 A: A young fair maiden like you shouldn’t be single. B: That is because I am a young fair independent maiden. maiden n.少女，年轻姑娘，未婚女子 a.首次的，初次的 A: You look majestic sitting on that high chair. B: Yes, I am pretending to be the king! majestic a.雄伟的，壮丽的，庄严的，高贵的 A: Please cook me dinner now. B: Yes, your majesty, I’m at your service. majesty n.１．［Ｍ－］陛下（对帝王，王后的尊称）；２．雄伟，壮丽，庄严 A: Doctor, I traveled to Africa and I think I caught malaria. B: Did you take any medicine as a precaution? malaria n.疟疾 A: I hate you! B: Why are you so full of malice? malice n.恶意，怨恨 A: I’m afraid that the test results have come back and your lump is malignant. B: That means it’s serious, doesn’t it, doctor? malignant a.１．恶性的，致命的；２．恶意的，恶毒的 A: I’m going shopping in the mall this afternoon, want to join me? B: No, thanks, I have plans already. mall n.（由许多商店组成的）购物中心 A: That child looks very unhealthy. B: Yes, he does not have enough to eat. He is suffering from malnutrition.

base on的例句

意见应以事实为根据. 3 来自辞典例句 192. The bombers swooped ( down ) onthe air base. 轰炸机 突袭 空军基地. 来自辞典例句 193. He mounted their engines on a rubber base. 他把他们的发动机装在一个橡胶垫座上. 14 来自辞典例句 194. The column stands on a narrow base. 柱子竖立在狭窄的地基上. 14 来自辞典例句 195. When one stretched it, it looked like grey flakes on the carvas base. 你要是把它摊直, 看上去就象好一些灰色的粉片落在帆布底子上. 18 来自辞典例句 196. Economic growth and human well - being depend on the natural resource base that supports all living systems. 经济增长和人类的福利依赖于支持所有生命系统的自然资源. 12 1 来自辞典例句 197. The base was just a smudge onthe untouched hundred - mile coast of Manila Bay. 那基地只是马尼拉湾一百英里长安然无恙的海岸线上一个硝烟滚滚的污点. 6 来自辞典例句 198. You can't base an operation on the presumption that miracles are going to happen. 你不能把行动计划建筑在可能出现奇迹的假想基础上.

abaqus学习总结

接触的分析步骤及注意事项： 1.如何提取安装文件里的例子 C:\SIMULIA\6.11-1\samples\job_archive 在命令符中输入：abaqus fetch job=ws_solver_seal.py 然后将会出现解压出的seal的路径，找到路径将其复制到工作目录。然后点击file—run scrip…..将文件打开即可 2.模型导入之后，不同的部分显示不同颜色，点击右上侧 ，点击下拉菜单的Part instances。选择其他选项可以显 示不同情况。 3.如何建立面， （1）双击右侧 surface， 选中面—根据颜色选取面的方向对于实体不会有此问题） 其中Magenta为红色，Yellow为黄色， Individually是单个选取，按住shift键可以连续选取；

By angle是通过角度选取，后面是输入角度，有时候该方法很好用。 （2）各个实体模型（instance）的显示与隐藏 有时候选取面或其他操作的时候为了选取面方便，需要只显示其中一个实体，点击下图的A键 使下图中出现下拉菜单 选中instance，即实体 然后选中图中要操作的实体，再点击下图 4.刚体建立参考点（constraint） 双击interaction下的constraints，如下图所示：选择rigid body（刚体）

Continue之后得到如下菜单： 其中body为整个实体，pin指的是销节点，tie指的是捆绑节点，analytical surface是解析面。Reference point是刚体的参考点，可以点击后面的箭头在图中选择参考点，注意：如果将后面的adjust point to center of mass at start of analysis选中则选择的是刚体质心位置！ 销节点与捆绑节点的区别：

英语造句大全

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ABAQUS中的幅值曲线

A B A Q U S中的幅值曲线 Document serial number【NL89WT-NY98YT-NC8CB-NNUUT-NUT108】

ABAQUS幅值曲线 在ABAQUS中，通过使用幅值曲线，可以描述边界条件和载荷等模型参数随时间或频率（稳态动力分析）的变化。在Load功能模块和Interaction功能模块中都可以定义幅值曲线，方法：Tools->Amplitude。 ABAQUS中可以定义11种幅值曲线，分别是表格幅型值曲线、等间距型幅值曲线、周期型幅值曲线、调制型幅值曲线、衰减型幅值曲线、依赖于解的幅值曲线、平滑分析步幅值曲线、激励器幅值曲线、谱幅值曲线、用户自定义幅值曲线以及PSD定义幅值曲线。此外，还有一种默认的Ramp幅值曲线。 下边就重点介绍一下一些比较常用的幅值曲线。 1.默认Ramp幅值曲线 该曲线属于一种线性过渡型的幅值曲线，它的含义是从一个分析步的初始状态线性过渡到这个分析步的结束状态。定义时只需确定每个分析步载荷值即可。 2.表格型幅值曲线(tabular) 定义表格型幅值曲线时，只需给出每个时间点上对应的幅值。在分析过程中，ABAQUS 会自动在各个数据点之间进行线性插值。 3.等间距型幅值曲线(Equally spaced) 这种曲线以固定时间间隔给出幅值大小，ABAQUS在每个时间间隔内进行线性插值。定义该类曲线时应给出时间间隔和初始时刻（或最小频率值），默认的初始时刻为0。 4.周期型幅值曲线(Periodic) 如果某个量是周期变化的，就可以使用周期型幅值曲线。周期型幅值曲线用傅里叶(Fourier)级数表示，其表达式为： 式中：N为傅里叶级数项的个数；为圆频率(circular frequency)；t0为起始时刻(starting time)；A0为初始幅值(initial amplitude)；An为cos项的系数；Bn为sin项的系数。 5.调制型幅值曲线(Modulated) 曲线定义公式为： 6.衰减型幅值曲线(Decay) 曲线定义公式为： 7.依赖于解的幅值曲线(Solution dependent) 这种曲线基于一种独立的求解变量来计算幅值。 8.平滑分析步幅值曲线(Smooth step) ABAQUS/Standard和ABAQUS/Explicit都可以根据平滑分析步数据定义幅值。 9.激励器幅值曲线(Actuator) 10.谱幅值曲线(Spectrum) 在响应谱分析中定义谱幅值曲线，通过确定谱值，频率，相关阻尼来确定。

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主语+谓语 1. 理解主谓结构 1) The students arrived. The students arrived at the park. 2) They are listening. They are listening to the music. 3) The disaster happened. 2．体会状语的位置 1) Tom always works hard. 2) Sometimes I go to the park at weekends.. 3) The girl cries very often. 4) We seldom come here. The disaster happened to the poor family. 3. 多个状语的排列次序 1) He works. 2) He works hard. 3) He always works hard. 4) He always works hard in the company. 5) He always works hard in the company recently. 6) He always works hard in the company recently because he wants to get promoted. 4. 写作常用不及物动词 1. ache My head aches. I’m aching all over. 2. agree agree with sb. about sth. agree to do sth. 3. apologize to sb. for sth. 4. appear (at the meeting, on the screen) 5. arrive at / in 6. belong to 7. chat with sb. about sth. 8. come (to …) 9. cry 10. dance 11. depend on /upon 12. die 13. fall 14. go to … 15. graduate from 16. … happen 17. laugh 18. listen to... 19. live 20. rise 21. sit 22. smile 23. swim 24. stay (at home / in a hotel) 25. work 26. wait for 汉译英： 1.昨天我去了电影院。 2.我能用英语跟外国人自由交谈。 3.晚上7点我们到达了机场。 4.暑假就要到了。 5.现在很多老人独自居住。 6.老师同意了。 7.刚才发生了一场车祸。 8.课上我们应该认真听讲。9. 我们的态度很重要。 10. 能否成功取决于你的态度。 11. 能取得多大进步取决于你付出多少努力。 12. 这个木桶能盛多少水取决于最短的一块板子的长度。