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    20 May 2019 Volume 38 Issue 5
      
    Application of dimensional analysis in gravitational wave physics
    HE Xiao-kai, CAO Zhou-jian, LIANG Can-bin
    College Physics. 2019, 38(5):  1.  doi:10.16854 /j.cnki.1000-0712.180525
    Abstract ( 1395 )   PDF (193KB) ( 759 )  
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    Fluid mechanics is a physics problem that most books on dimensional analysis explain most.

    However,the dimensional analysis is a powerful and universal analysis method in physics. Taking the application of

    dimensional analysis in gravitational wave physics as an example,this paper makes readers deeply understand the

    universality of the dimensional analysis method. In particular,the total mass of a binary black hole is regarded as an

    uneccential physical parameter in the process of constructing the theoretical template of gravitational wave for the

    binayr black holes system. The reason is rarely mentioned in the usual literature. The method of dimensional

    analysis is used to show that the above conclusions are valid even for the gravitational theory beyond general

    relativity. Therefore,this paper not only clearly expounds the reasons why the above conclusion holds in the

    framework of general relativity,but also provides some guidelines for the establishment of the theoretical template of

    gravitational wave based on the gaviational theory beyond general relativity.

    Three kinds of ordering formulas for vacuum projection operators and their applications
    ZHANG Chun-zao, REN Gang, FAN Hong-yi
    College Physics. 2019, 38(5):  5.  doi:10.16854 /j.cnki.1000-0712.180476
    Abstract ( 1481 )   PDF (167KB) ( 563 )  
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    Three kinds of ordering formulas for the vacuum projector | 0?? 0 | ,i .e.,normally ordered-,antinormally

    ordered- and Weyl ordered-forms,are derived systematically and concisely. It is further deduced that

    many more operator identities play important roles in calculating various physical quantities.

    The spatial and momentum distributions of an ideal anyon gas   in a harmonic potential trap
    YUAN Du-qi
    College Physics. 2019, 38(5):  8.  doi:10.16854 /j.cnki.1000-0712.180355
    Abstract ( 1282 )   PDF (710KB) ( 402 )  
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    By using fractional exclusion statistics,the generalized Fermi energy is obtained for a finite ideal anyon gas in a threedimensional

    spherically symmetric harmonic potential trap,the particle number effect and physical essence of generalized Fermi energy

    and generalized Fermi temperature are revealed. The distributions in the coordinate and momentum spaces for ideal anyon gas at zero

    temperature and finite temperature are derived,respectively,the generalized Fermi sphere and its radius are given. The effects of

    statistical parameters,particle number and temperature on the distributions are studied,and are compared with the spatial distribution

    and momentum distribution of ideal Fermi gas.

    Optical transmission properties of a zero index material plate
    GAO Hua, WEI Guo-guo, LIU Mei-qing, GUO Xiao-tong, WANG Yi-xian, ZHANG Qiang
    College Physics. 2019, 38(5):  15.  doi:10.16854 /j.cnki.1000-0712.180256
    Abstract ( 1285 )   PDF (788KB) ( 474 )  
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    The zero-index material ( ZIM) is a new type of meta-material,which is flourishing in recent years.

    It has unique properties and wide applications,as a result,it is not only active in the frontiers of scientific research

    and also worth being recommended to physics classes. In this paper,the electromagnetic properties inside the ZIMs

    and the transmission characteristics of a ZIM plate are theoretically analyzed by using the classical electrodynamics

    and numerically simulated by using a commercial software. The results show that,as a double ZIM plate, if the

    impedance is matched with that of the free space, its transmittance is independent of the thickness of the plate,the

    value is always maintained at 1; while for a single ZIM plate, its transmittance decreases with the increase of the

    thickness. The reasons for these two special transmission characteristics are further analyzed. These results have a

    guiding significance and reference value for understanding the characteristics of the ZIMs and designing the

    functional devices using the ZIMs.

    Self-inductance of tightly wound ellipsoidal coil
    JIANG Jun-qin
    College Physics. 2019, 38(5):  20.  doi:10.16854 /j.cnki.1000-0712.180406
    Abstract ( 1292 )   PDF (639KB) ( 322 )  
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    Based on the viewpoint of interaction energy of the current element,the integral expression of the self

    -inductance for a tightly wound ellipsoidal coil is derived. By using mathematica 10.3,the integral result for the azimuth

    angle  is expressed as the linear combination of the first and the second kinds of complete elliptic integral,

    and then the self-inductance is numerically investigated. The axis ratio ( c /a) dependence of the self-inductance is

    calculated and discussed. This result shows that when c /a = 1. 7,the self - inductance per unit volume is the

    minimum. Finally,a convenient and practical polynomial interpolation function for self-inductance is given.

    The Hall effect of cylindrical conductor shell
    DU An, ZHU Lin
    College Physics. 2019, 38(5):  24.  doi:10.16854 /j.cnki.1000-0712.180383
    Abstract ( 1473 )   PDF (259KB) ( 472 )  
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    A Hall effect device with coaxial cable structure is proposed. When the central conductor passes

    through the current,the potential difference between the inside and outside surfaces of the conductor shell through

    current is generated. We discuss the dependence of the potential difference on the currents through the central

    conductor and the conductor shell and the sizes of the conductor shell,and find that the maximum value of the Hall

    potential difference appears as the conductor shell is very thin.

    Numerical simulation on Goos-Hänchen shift and its application in optics education
    CAO Zhao-lou
    College Physics. 2019, 38(5):  26.  doi:10.16854 /j.cnki.1000 0712.180537
    Abstract ( 1076 )   PDF (483KB) ( 570 )  
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    In micro - nano optics,Goos-Hänchen( GH) shift is an important phenomenon. Stationary phase

      method is usually utilized to obtain the GH shift,but it is difficult for students to understand the underlying physical

    essence.In this paper,we study the GH shift from a novel perspective.Incident and reflected light field are calculated

    based on angular spectrum theory.GH shift can then be expressed by the spot shift before and after reflection.As the

    stationary phase method can only be applied to the finite-aperture plane wave and Gaussian beam, the incidence of

    Gaussian beam on an epsilon -near - zero material is numerically calculated for comparing with stationary phase

    method.The numerical procedure can be further applied in incidence of an arbitrary beam on an arbitrary material.It

    is shown that numerical results agree well with analytical results when the incident angle is far from the critical angle,

    but near the critical angle, the present numerical results can be used to describe the GH shift of Gaussian beam

    more accurately.The numerical approach can be used in the calculation of GH shift of various light beams.The work

    can be of help to understand the GH shift and the applicable condition of stationary phase method.

    Research and design of a new type of period measuring instrument for trifilar-torsional-pendulum
    SHI Ming-ji, LI Bo-bo, WANG Fei
    College Physics. 2019, 38(5):  30.  doi:10.16854 /j.cnki.1000-0712.180528
    Abstract ( 1462 )   PDF (703KB) ( 405 )  
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    The rotational inertia of complex or heterogeneous rigid body can be measured by trifilar torsional

    pendulum.The torsion pendulum period is an important parameter related to the accuracy of the test. Manual

    counting and stopwatch timing are very laborious and easy to make mistakes.The photoelectric sensor and the measurement

    are easily affected by the yawing or shaking,which will lead to the omission of one period.To this end,a

    new type of trifilar torsional pendulum periodic measuring instrument is proposed,which consists of light source,polarizer,

    detector,photosensitive resistance module,data acquisition system and computer installed with upper computer

    software.The polarization characteristics of light and Marius's law are used to detect the torsion pendulum situation

    of the trifilar torsional pendulum.We can get the period of trifilar torsional pendulum by using the linear fitting

    function of origin data processing software.Using the photoelectric measurement device in the market and the new

    trifilar torsional pendulum period measuring instrument at the same time,a comparative experiment is carried out to

    measure the moment of inertia of the lower plate of trifilar torsional pendulum.The experimental results show that the

    relative error of the existing photoelectric measuring device is 0.83%,and the relative error of the new trifilar torsional

    pendulum period measuring instrument is up to 0.11%, indicating that the accuracy of the new type trifilar

    torsional pendulum periodic measuring instrument is higher than the existing photoelectric measuring device.Because

    the intensity of the transmission light is not affected by the small range swing or sloshing of the trifilar torsional pendulum,

    the new rifilar torsional pendulum periodic measuring instrument has a strong anti-interference ability.Besides,

    the device has the advantages of fast measuring speed, simple operation,convenience,and has certain popularization

    value.

    Production and research of Magnus effect demonstration teaching aids
    LV Zhi-yuan, DU Yun-gang, LI Ke-hong, TIAN Xing-le, CHENG Hao-ke, HU Xiong-wei
    College Physics. 2019, 38(5):  35.  doi:10.16854 /j.cnki.1000-0712.180546
    Abstract ( 1915 )   PDF (1366KB) ( 475 )  
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    Using the Bernoulli principle,a wind-powered car that demonstrates the Magnus effect is produced,

    and the formula of the car's dynamics is theoretically derived.Further, through the actual measurement of the force of

    the car, the empirical formula of the force of the car is obtained.The car has also been improved to make it lighter

    and new demo features have been added.

    Study of the phenomenon of burning candles floating in water
    XUN Zhi-peng, LI Chuan-nan, LIANG Han-pu, ZHOU Yu-han
    College Physics. 2019, 38(5):  39.  doi:10.16854 /j.cnki.1000-0712.180540
    Abstract ( 1713 )   PDF (1382KB) ( 615 )  
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    The mechanism of burning candle in water is investigated theoretically and experimentally.By establishing

    an approximate vertical well structure model, the whole burning process of candles is analyzed theoretically

    from the angle of radiant energy flow.Then the effects of candle length, radius and counterweight on the suspension

    process of candles are investigated experimentally.Finally, the vibration mode of taper is analyzed.

    Design and implementation of digital holographic comprehensive experiment system for teaching
    SHENG Wei
    College Physics. 2019, 38(5):  45.  doi:10.16854 /j.cnki.1000-0712.180393
    Abstract ( 1136 )   PDF (922KB) ( 378 )  
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    The holography is a 3D imaging and measurement technology full of application prospects. In order

    to better assist the experimental teaching of holography,a set of digital holographic comprehensive experimental system

    is designed for teaching. The system consists of computational simulation,optical photography,digital reconstruction

    and measurement. The system adopts optimized holographic optical setup,and is equipped with user -

      friendly algorithm program,which reduces the threshold of digital holographic experiment and makes the experiment

      suitable for non-related major students.

    Construction and theoretical verification of standing wave thermoacoustic refrigerator
    ZHANG Shi-hong, WANG Yin-peng, YAN Qi-qi
    College Physics. 2019, 38(5):  48.  doi:10.16854 /j.cnki.1000-0712.180543
    Abstract ( 1307 )   PDF (976KB) ( 311 )  
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    A prototype of standing wave thermoacoustic refrigerator is designed and constructed based on the

    characteristics of standing wave and the basic theory of heat transfer. Besides,the methods of analyzing thermoacoustic

    effect by pressure acoustics and linear thermoacoustic theory are verified respectively. The results of experiment

    show that the cold side can obtain an ideal cooling of 2.16 K when the speaker driver voltage is 7 V,driving

    frequency is 315 Hz,and dimensionless thermoacoustic stack location is 0. 27; the driving voltage of

    loudspeaker has a positive correlation with the refrigerating capacity in the range of measurement. The experimental

    results are well matched by the prediction of the DeltaEC program and linear thermoacoustic theory when use the

    physical parameter values of the experimental device,which verifies the feasibility of this analysis method.

    Optical wavelength measurement system based on Bragg diffraction
    WANG Zhi-yuan, DONG Xi-jie, LI Li, ZHAO Jin-bo, ZHANG Mao, GU Ting-long
    College Physics. 2019, 38(5):  53.  doi:10.16854 /j.cnki.1000-0712.180472
    Abstract ( 1236 )   PDF (626KB) ( 454 )  
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    By combining with acousto-optic effect and Bragg diffraction of the monochromatic wave,the quantitative

    relation between wavelength of the acoustic wave and the wavelength of the monochromatic wave are deduced.

    Then the unknown monochromatic wavelength is measured by adjusting the acoustic frequency. The scheme is based

    on Bragg diffraction as the theoretical basis. In contrast to different technologies,we use acousto-optic devices with

    the most stable and large acousto-optic factor,and solved the environmental factors on the impact of such experiments

    is too large,cumbersome experimental steps and other issues successful. This program can directly adjust the

    acoustic frequency to achieve a variety of monochromatic wavelength measurement,and wide the measurement range

    of the wavelength of monochromatic.

    Analysis of light intensity distribution for a varied-slid width grating
    CAO Chi-yu, WANG Wen-ling, HUANG An-ping
    College Physics. 2019, 38(5):  57.  doi:10.16854 /j.cnki.1000-0712.180109
    Abstract ( 1653 )   PDF (1804KB) ( 616 )  
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    The regular pattern of the grating diffraction with unequal and cyclic slid width has been analyzed,

    and the corresponding quantitative description of its light intensity distribution has been obtained. By comparing

    with equal-slid-width grating,the diffraction factor within a cycle and interference factor among cycles are applied

    to describe the light intensity distribution of the varied-slid-width grating. Such a light intensity distribution has

    further been simulated by Matlab and the influence of each parameter has been discussed to get a more accurate

    demonstration of the light intensity distribution of the varied-slid-width grating.

    Discussion on the intensity ratio of sodium doublet in sodium atom spectroscopy experiment
    TAN Zhi-yang, CHEN Sen, WU Ping
    College Physics. 2019, 38(5):  63.  doi:10.16854 /j.cnki.1000-0712.180448
    Abstract ( 1733 )   PDF (375KB) ( 1069 )  
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    By analyzing the working mechanism of the low-pressure sodium lamp,it is found that the plasma in

    the low pressure sodium lamp is in non-local thermal equilibrium state. Therefore,this paper uses the corona model

    suitable for non-isothermal plasma to calculate the intensity ratio of sodium doublet in the sodium atom spectroscopy

    experiment. The calculated results agree well with the experimental results,with a five percent error,which gives a

    good explanation for the experimental phenomenon.