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Journal articles on the topic 'Torsion pendulum'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Cong, Linxiao, Jiabin Wang, Jianfei Long, Jianchao Mu, Haoye Deng, and Congfeng Qiao. "Microgravity Decoupling in Torsion Pendulum for Enhanced Micro-Newton Thrust Measurement." Applied Sciences 14, no. 1 (2023): 91. http://dx.doi.org/10.3390/app14010091.

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To enhance the accuracy of micro-Newton thrust measurements via a torsion pendulum, addressing microgravity coupling effects caused by platform tilt and pendulum mass eccentricity is crucial. This study focuses on analyzing and minimizing these effects by alleviating reference surface tilt and calibrating the center of mass during thrust measurements. The study introduced analysis techniques and compensation measures. It first examined the impact of reference tilt and center of mass eccentricity on the stiffness and compliance of the torsion pendulum by reconstructing its dynamic model. Simsca

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2

Pugach, A. F., and D. Olenici. "Observations of Correlated Behavior of Two Light Torsion Balances and a Paraconical Pendulum in Separate Locations during the Solar Eclipse of January 26th, 2009." Advances in Astronomy 2012 (2012): 1–6. http://dx.doi.org/10.1155/2012/263818.

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On January 26th, 2009, simultaneous observations of the reactions of two very light torsion balances (Kiev, Ukraine) and a paraconical pendulum (Suceava, Romania, 440 km away) were performed during a solar eclipse that was not visible at those locations but only in the Indian Ocean. Significant correlation between the behavior of the torsion balances and the pendulum was observed. The conclusion is that a solar eclipse influences the reactions of torsion balances and pendulums, even in areas of the Earth where it is not optically visible.

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3

Zhao, Yan, Baofeng Zhang, Fangfang Han, Huan Tian, Xiao Yu, and Junchao Zhu. "Instantaneous Characteristics of Nonlinear Torsion Pendulum and Its Application in Parameter Estimation of Nonlinear System." Mathematical Problems in Engineering 2018 (2018): 1–10. http://dx.doi.org/10.1155/2018/7858403.

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The nonlinear model of torsion pendulum is presented by considering the nonlinear damping force and nonlinear restoring force. The analytic solution of the nonlinear model is calculated to analyze the relationship between the characteristics of torsion pendulum and the nonlinear factors. The instantaneous characteristics of nonlinear torsion pendulum are analyzed by instantaneous undamped natural frequency and instantaneous damping coefficient. The instantaneous characteristics can be used for the parameter estimation of nonlinear torsion pendulum system. The nonlinear characteristics of the t

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4

O’Connell, James. "Magnetic torsion pendulum." Physics Teacher 38, no. 6 (2000): 377–78. http://dx.doi.org/10.1119/1.1321826.

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5

Bassan, Massimo, Fabrizio De Marchi, Lorenzo Marconi, Giuseppe Pucacco, Ruggero Stanga, and Massimo Visco. "Torsion pendulum revisited." Physics Letters A 377, no. 25-27 (2013): 1555–62. http://dx.doi.org/10.1016/j.physleta.2013.04.017.

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6

Bassan, Massimo, Luciano Di Fiore, Aniello Grado, Yury Minenkov, Enzo Reali, and Giuseppe Pucacco. "Stroboscopic torsion pendulum." European Journal of Physics 41, no. 1 (2019): 015801. http://dx.doi.org/10.1088/1361-6404/ab4c42.

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7

Fahmy, I. R., M. S. Abdul-Wahab, and R. J. Shalash. "Digital torsion pendulum." Polymer Testing 9, no. 2 (1990): 127–35. http://dx.doi.org/10.1016/0142-9418(90)90025-9.

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8

Czerwiński, Ernest, Paweł Olejnik, and Jan Awrejcewicz. "Modeling And Parameter Identification Of Vibrations Of A Double Torsion Pendulum With Friction." Acta Mechanica et Automatica 9, no. 4 (2015): 204–12. http://dx.doi.org/10.1515/ama-2015-0033.

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Abstract The purpose of this paper is to investigate a double torsion pendulum with planar frictional contact. The single torsion pendulum with one-degree-of-freedom is an angular equivalent of the linear harmonic oscillator. The second degree of freedom has been obtained by adding a free body to the inverted single torsion pendulum. The free body’s angular displacement is caused by frictional forces appearing in the interface (contact zone) between the free body and the pendulum column’s head kinematically excited at its base by a mechanism with torsion spiral spring. An experimental station

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9

Willemenot, E., and P. Touboul. "Electrostatically suspended torsion pendulum." Review of Scientific Instruments 71, no. 1 (2000): 310–14. http://dx.doi.org/10.1063/1.1150198.

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10

Chen, Yeqing, Yi Zeng, Haoran Li, Jiye Zhang, and Lieshan Zhang. "Research on the Measurement Technology of Rotational Inertia of Rigid Body Based on the Principles of Monocular Vision and Torsion Pendulum." Sensors 23, no. 10 (2023): 4787. http://dx.doi.org/10.3390/s23104787.

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Damping is an important factor contributing to errors in the measurement of rotational inertia using the torsion pendulum method. Identifying the system damping allows for minimizing the measurement errors of rotational inertia, and accurate continuous sampling of torsional vibration angular displacement is the key to realizing system damping identification. To address this issue, this paper proposes a novel method for measuring the rotational inertia of rigid bodies based on monocular vision and the torsion pendulum method. In this study, a mathematical model of torsional oscillation under a

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11

Iskakov, Zharilkassin. "EXPERIMENTAL STUDY OF DAMPED OSCILLATIONS OF A TORSIONAL PENDULUM." CBU International Conference Proceedings 6 (September 25, 2018): 1089–93. http://dx.doi.org/10.12955/cbup.v6.1299.

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A laboratory work methodic on the experimental study of damping torsion oscillations under educational laboratory conditions was developed in this article. A torsion pendulum, which is usually used for bullet flight speed experimental determination based on angular momentum, mechanical energy conservation laws, and the laws of natural oscillations patterns, was used for this purpose. A torsion pendulum is a rod suspended on a vertically stretched steel wire and capable of performing oscillatory motion in the horizontal plane. Two rectangle shaped bodies are attached at the rod's ends, also two

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12

Newman, Riley, Michael Bantel, Eric Berg, and William Cross. "A measurement of G with a cryogenic torsion pendulum." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2026 (2014): 20140025. http://dx.doi.org/10.1098/rsta.2014.0025.

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A measurement of Newton's gravitational constant G has been made with a cryogenic torsion pendulum operating below 4 K in a dynamic mode in which G is determined from the change in torsional period when a field source mass is moved between two orientations. The source mass was a pair of copper rings that produced an extremely uniform gravitational field gradient, whereas the pendulum was a thin fused silica plate, a combination that minimized the measurement's sensitivity to error in pendulum placement. The measurement was made using an as-drawn CuBe torsion fibre, a heat-treated CuBe fibre, a

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13

Lisowski, Bartłomiej, Clement Retiere, José Pablo Garcia Moreno, and Paweł Olejnik. "Semiempirical identification of nonlinear dynamics of a two-degree-of-freedom real torsion pendulum with a nonuniform planar stick–slip friction and elastic barriers." Nonlinear Dynamics 100, no. 4 (2020): 3215–34. http://dx.doi.org/10.1007/s11071-020-05684-6.

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Abstract The purpose of this study is to identify the nonlinear dynamics of the double torsion pendulum with planar friction and elastic barriers. The original experimental stand consists of a disk-shaped body that rotates freely on top of a forced column with a system of barriers limiting the torsional vibrations of the pendulum bodies that create an nonuniform planar rotational friction contact. Two beam springs form soft barriers modeled by Voigt elements that limit the angular displacement of one of the pendulum bodies—the disk, while the second limiting system, made of a much more rigid b

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14

Shimoda, Tomofumi, Satoru Takano, Ching Pin Ooi, et al. "Torsion-Bar Antenna: A ground-based mid-frequency and low-frequency gravitational wave detector." International Journal of Modern Physics D 29, no. 04 (2019): 1940003. http://dx.doi.org/10.1142/s0218271819400030.

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Expanding the observational frequency of gravitational waves is important for the future of astronomy. Torsion-Bar Antenna (TOBA) is a mid-frequency and low-frequency gravitational wave detector using a torsion pendulum. The low resonant frequency of the rotational mode of the torsion pendulum enables ground-based observations. The overview of TOBA, including the past and present status of the prototype development, is summarized in this paper.

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15

Hou, Yong Jun. "Dynamics Analysis of Vibrating Screen Based on Double Compound Pendulum with Single Motor Driving." Applied Mechanics and Materials 459 (October 2013): 335–41. http://dx.doi.org/10.4028/www.scientific.net/amm.459.335.

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By Lagrange equation, the dynamic equation of vibrating screen based on double compound pendulum with single motor driving was established. With simulation method, dynamic simulating model was built, and influences of pendulum installing position, stiffness of torsion damping spring of pendulum rod, initial installing angle and length of pendulum rod on motion characteristics of vibrating screen was discussed. Research results showed that, by choosing suitable stiffness of torsion damping spring or length of pendulum rod, this kind of vibrating screen may achieve the approximate linear traject

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16

Milotti, Edoardo. "Nonlinear behaviour in a torsion pendulum." European Journal of Physics 22, no. 3 (2001): 239–48. http://dx.doi.org/10.1088/0143-0807/22/3/307.

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17

Sinning, H. R. "Theory of the Collette torsion pendulum." Journal of Physics E: Scientific Instruments 19, no. 10 (1986): 866–70. http://dx.doi.org/10.1088/0022-3735/19/10/021.

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18

Bantel, M. K., and R. D. Newman. "A cryogenic torsion pendulum: progress report." Classical and Quantum Gravity 17, no. 12 (2000): 2313–18. http://dx.doi.org/10.1088/0264-9381/17/12/302.

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19

Newman, R. D., and M. K. Bantel. "On determiningGusing a cryogenic torsion pendulum." Measurement Science and Technology 10, no. 6 (1999): 445–53. http://dx.doi.org/10.1088/0957-0233/10/6/306.

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20

Fan, Xiang-Dong, Qi Liu, Lin-Xia Liu, Vadim Milyukov, and Jun Luo. "Coupled modes of the torsion pendulum." Physics Letters A 372, no. 5 (2008): 547–52. http://dx.doi.org/10.1016/j.physleta.2007.08.020.

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21

Parpia, J., G. W. Morley, P. Vestey, J. Nyéki, B. Cowan, and J. Saunders. "Torsion pendulum studies of thin slabs." Physica B: Condensed Matter 329-333 (May 2003): 133–34. http://dx.doi.org/10.1016/s0921-4526(02)01933-6.

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22

Wang, Shaoxin, Heshan Liu, Lei Dai, et al. "Using DWS Optical Readout to Improve the Sensitivity of Torsion Pendulum." Sensors 23, no. 19 (2023): 8087. http://dx.doi.org/10.3390/s23198087.

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In space gravitational wave detection missions, a drag-free system is used to keep the test mass (TM) free-falling in an ultralow-noise environment. Ground verification experiments should be carried out to clarify the shielding and compensating capabilities of the system for multiple stray force noises. A hybrid apparatus was designed and analyzed based on the traditional torsion pendulum, and a technique for enhancing the sensitivity of the torsion pendulum system by employing the differential wavefront sensing (DWS) optical readout was proposed. The readout resolution experiment was then car

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23

Takano, Satoru, Tomofumi Shimoda, Yuka Oshima, et al. "TOrsion-Bar Antenna: A Ground-Based Detector for Low-Frequency Gravity Gradient Measurement." Galaxies 12, no. 6 (2024): 78. http://dx.doi.org/10.3390/galaxies12060078.

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The Torsion-Bar Antenna (TOBA) is a torsion pendulum-based gravitational detector developed to observe gravitational waves in frequencies between 1 mHz and 10 Hz. The low resonant frequency of the torsion pendulum enables observation in this frequency band on the ground. The final target of TOBA is to observe gravitational waves with a 10 m detector and expand the observation band of gravitational waves. In this paper, an overview of TOBA, including the previous prototype experiments and the current ongoing development, is presented.

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24

Xu, Hao, Qiangbing Mao, Yong Gao, et al. "A newly designed decoupling method for micro-Newton thrust measurement." Review of Scientific Instruments 94, no. 1 (2023): 014504. http://dx.doi.org/10.1063/5.0120130.

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A decoupling method is proposed for micro-Newton thrust measurement with a torsion pendulum. The basic approach is to reduce the influences introduced by the propellant tube and wires of the thruster. A hollow aluminum tube is used to hang the torsion pendulum and is also chosen as the transport pipe for the propellant of the thruster. The electric control box of the thruster is mounted on the pendulum body, which is powered by an externally installed power supply through a liquid metal conductive unit. The control of the electric control box is performed through wireless transmission. With th

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25

Zhang, Peng Fei, Xiao Yan Lei, and Liang Gao. "Vibration Characteristic Comparative Analysis of Standard Wheels and Damped Wheels." Applied Mechanics and Materials 209-211 (October 2012): 2131–37. http://dx.doi.org/10.4028/www.scientific.net/amm.209-211.2131.

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The standard wheel and damped wheel model were established in ANSYS, through modal analysis to study the vibration characteristics of them. The results show that vibration of standard wheel is mainly manifested as torsion pendulum vibration of tread, radial and axial vibration of web and combination vibration of tread and web in frequency of 0～5000Hz.In this frequency range, 0~1000Hz mainly manifested as torsion pendulum vibration of the tread, above 1000Hz, these three have the performance, especially in the web vibration is most active, therefore, Web is the primary noise radiation source in

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26

Hong, Xinguo, and Kunquan Lu. "Viscosity measurement with double‐wire torsion pendulum." Review of Scientific Instruments 66, no. 8 (1995): 4318–25. http://dx.doi.org/10.1063/1.1145321.

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27

Chen, Y. T., and A. Cook. "Thermal noise limitations in torsion pendulum experiments." Classical and Quantum Gravity 7, no. 7 (1990): 1225–39. http://dx.doi.org/10.1088/0264-9381/7/7/018.

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28

Hermida, Élida B., and Leandro J. Cieri. "Extended capabilities of an inverted torsion pendulum." Polymer Testing 25, no. 2 (2006): 276–79. http://dx.doi.org/10.1016/j.polymertesting.2005.09.013.

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29

Zhong-Kun, Hu, Wang Xue-Li, and Luo Jun. "Thermoelastic Correction in the Torsion Pendulum Experiment." Chinese Physics Letters 18, no. 1 (2000): 7–9. http://dx.doi.org/10.1088/0256-307x/18/1/303.

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30

Liang, Zhao, Tu Ying, Gu Bang-Ming, Hu Zhong-Kun, and Luo Jun. "An Abnormal Vibrational Mode of Torsion Pendulum." Chinese Physics Letters 20, no. 8 (2003): 1206–9. http://dx.doi.org/10.1088/0256-307x/20/8/306.

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31

Zhen Xiang, Pan, Imtiyaz Ansari, and G. Pritchard. "Torsion pendulum automation by a single microcomputer." Polymer Testing 5, no. 5 (1985): 321–39. http://dx.doi.org/10.1016/0142-9418(85)90008-x.

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32

YANG, FENG-YU, SHEAU-SHI PAN, JIAN-LIN HUANG, and SHENG-JUI CHEN. "THE MEASUREMENT OF THE PENDULUM DAMPING EFFECT IN SOLID DENSITY SYSTEM." International Journal of Modern Physics: Conference Series 24 (January 2013): 1360025. http://dx.doi.org/10.1142/s2010194513600252.

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The magnetic damping structure was used in measuring the gravitational constant G by torsion balance. The main purpose is to reduce the effect of pendulum vibration modes. This effect can affect the position of torsion balance. When we use the method A mentioned in OIML R111 to measure density, the pendulum vibration modes of the hanging pan will also be found. In this paper, we will try to introduce the magnetic damping structure to be used on the hanging pan and will present the results of density measurement with the magnetic damper used.

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33

Wang, Shaoxin, Zuolei Wang, Dongxu Liu, et al. "Torsion Pendulum Apparatus for Ground Testing of Space Inertial Sensor." Sensors 24, no. 23 (2024): 7816. https://doi.org/10.3390/s24237816.

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The precise movement of the test mass along a geodesic is crucial for gravitational wave detection in space. To maintain this motion, the core payload-inertial sensor incorporates multiple functional units designed to mitigate various sources of stray force noise affecting the test mass. Understanding the limits of these noise sources is essential for enhancing the inertial sensor system design. Additionally, thorough ground-based verification of these functional units is necessary to ensure their reliability for space missions. To address these challenges, we developed a low-frequency torsion

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34

Klaus, Leonard. "Comparison of Two Experiments Based on a Physical and a Torsion Pendulum to Determine the Mass Moment of Inertia Including Measurement Uncertainties." Measurement Science Review 17, no. 1 (2017): 9–18. http://dx.doi.org/10.1515/msr-2017-0002.

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Abstract To determine the mass-moment-of-inertia properties of devices under test with particularly small mass moments of inertia (some 10−4 kg m2), two measurement set-ups based on different measurement principles were developed. One set-up is based on a physical pendulum, the second set-up incorporates a torsion pendulum. Both measurement set-ups and their measurement principles are described in detail, including the chosen data acquisition and analysis. Measurement uncertainty estimations according to the Guide to the Expression of Uncertainty in Measurement (GUM) were carried out for both

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35

Junos, M. Haniff, Nurulasikin Mohd Suhadis, and Mahmud M. Zihad. "Experimental Determination of the Moment of Inertias of USM e-UAV." Applied Mechanics and Materials 465-466 (December 2013): 368–72. http://dx.doi.org/10.4028/www.scientific.net/amm.465-466.368.

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This paper presents the experimental determination of the moment of inertia of USM e-UAV by using pendulum method. Compound pendulum experiment is used to determine the moment of inertia about x and y axes while the moment of inertia about z-axis is determined using bifilar torsion pendulum method. An experimental setup is developed with appropriate dimension to accommodate USM e-UAV. Experimental data are presented and discussed.

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36

ZHOU, Z. B., S. B. QU, H. B. TU, Y. Z. BAI, S. C. WU, and J. LUO. "PROGRESS OF GROUND TEST OF INERTIAL SENSOR FOR ASTROD I." International Journal of Modern Physics D 17, no. 07 (2008): 985–92. http://dx.doi.org/10.1142/s0218271808012644.

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An electrostatically controlled torsion pendulum has been constructed to investigate the performance of the ASTROD I inertial sensor on the ground. The twist motion of the pendulum is monitored by a capacitive transducer and controlled by an electrostatic actuator. The preliminary experimental results show that the torque resolution of the pendulum is 2 × 10-12 N m Hz-1/2 at 3 mHz. Further improvements under consideration for the inertial sensor are discussed.

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37

Ross, M. P., K. Venkateswara, C. A. Hagedorn, et al. "A low-frequency torsion pendulum with interferometric readout." Review of Scientific Instruments 92, no. 5 (2021): 054502. http://dx.doi.org/10.1063/5.0043098.

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38

Marini, Ricardo L., and Eugenio S. Galian. "Torsion Pendulum Investigation of Electromagnetic Inertia Manipulation Thrusting." Journal of Propulsion and Power 26, no. 6 (2010): 1283–90. http://dx.doi.org/10.2514/1.46541.

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39

Xinguo, Hong, and Lu Kunquan. "Torsion Pendulum Method in Viscosity Measurement of Melts." Chinese Physics Letters 12, no. 11 (1995): 641–44. http://dx.doi.org/10.1088/0256-307x/12/11/001.

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40

Hong, Xinguo, and Kunquan Lu. "Viscosity measurement with an improved torsion pendulum method." Journal of Non-Crystalline Solids 250-252 (August 1999): 111–15. http://dx.doi.org/10.1016/s0022-3093(99)00291-4.

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41

Wang, Dian-Hong, Xue-li Wang, Liang Zhao, and Liang-cheng Tu. "Eddy current loss testing in the torsion pendulum." Physics Letters A 290, no. 1-2 (2001): 41–48. http://dx.doi.org/10.1016/s0375-9601(01)00641-7.

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42

Denman, H. H. "Tautochronic bifilar pendulum torsion absorbers for reciprocating engines." Journal of Sound and Vibration 159, no. 2 (1992): 251–77. http://dx.doi.org/10.1016/0022-460x(92)90035-v.

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43

Devos, P., J. Cornelis, F. Servaes, and R. De Batist. "Low temperature torsion pendulum measurements on YBCO superconductors." Journal of Alloys and Compounds 211-212 (September 1994): 276–78. http://dx.doi.org/10.1016/0925-8388(94)90501-0.

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44

Bala, Sandeep. "Torsion pendulum experiment at the International Physics Olympiad." Resonance 5, no. 6 (2000): 76–85. http://dx.doi.org/10.1007/bf02833858.

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45

Ye, Ji Fei, Guang Yu Wang, and Dian Kai Wang. "Measurement of Laser Ablation Micro Impulse Using the Torsion Pendulum Interferometry." Advanced Materials Research 301-303 (July 2011): 1078–82. http://dx.doi.org/10.4028/www.scientific.net/amr.301-303.1078.

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A method is described for measuring the micro impulse induced by the laser ablation. This method is based upon the torsion pendulum interferometry technique. The method measures the micro impulse through the detection of the swinging angle of torsion pendulum. The swinging angle is obtained by the laser differential interferometry. For the 10-4~10-7 magnitude micro-impulse, It could be the important measurement method in the research of micro laser plasma thruster (mLPT). The results of some preliminary experiments are presented with detailed reference to experiment methodology and accuracy. T

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46

Wang, De Min, Jian Zhang, Jian Liu, Tong Zhu, Fang Chao Shao, and Lei Zhong. "Research on Measurement Equipment for Moment of Inertia of Triple Torsion Bars Based on Torsion Pendulum." Applied Mechanics and Materials 851 (August 2016): 286–91. http://dx.doi.org/10.4028/www.scientific.net/amm.851.286.

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In order to increase the measuring range of the moment of inertia, a new measurement equipment with triple torsion bars based on torsion pendulum was designed. The equipment could switch the number of torsion bars from single to double or triple by inserting or extracting two movable pins and implement the function of three different measurement devices. The detailed deducing process for the measuring range of the moment of inertia at various measurement states was given. The results show that the measuring range of the measurement equipment has been significantly improved compared with other

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47

Aguilar-Ibáñez, Carlos Fernando, Oscar Octavio Gutiérrez-Frías, Juan Carlos Martínez-García, Rubén Garrido-Moctezuma, and Bernardo Gómez-González. "Lyapunov-Based PD Linear Control of the Oscillatory Behavior of a Nonlinear Mechanical System: The Inverted Physical Pendulum with Moving Mass Case." Mathematical Problems in Engineering 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/162875.

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This paper concerns active vibration damping of a frictionless physical inverted pendulum with a radially moving mass. The motion of the inverted pendulum is restricted to an admissible set. The proposed Proportional Derivative linear controller damps the inverted pendulum (which is anchored by a torsion spring to keep it in a stable upright position), exerting a force on the radially moving mass. The controller design procedure, which follows a traditional Lyapunov-based approach, tailors the energy behavior of the system described in Euler-Lagrange terms.

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48

Zhao, Yan, Xiao Lin Zhang, Jun Wang, and Wen Yan Tang. "Measurement of Moment of Inertia Based on Torsion Pendulum." Advanced Materials Research 588-589 (November 2012): 964–67. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.964.

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The measurement system based on torsion pendulum is presented to measure the moment of inertia considering the effect of air damping. With the introduction of air-hovered turntable, the influence of friction force is reduced. In order to increase the effect of the air damping, damping paddles are used to increase the area of test object. The pendulum motion of test object can be measured by the displacement sensor. The moment of inertia of test objects can be calculated by the damping ratio and oscillation period. The experimental results show that the relative measurement error of the moment

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49

Tondji, Y., and R. M. Botez. "Semi-empirical estimation and experimental method for determining inertial properties of the Unmanned Aerial System – UAS-S4 of Hydra Technologies." Aeronautical Journal 121, no. 1245 (2017): 1648–82. http://dx.doi.org/10.1017/aer.2017.105.

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ABSTRACTThis article presents a structural analysis of the Unmanned Aerial System UAS-S4 ETHECATL. Mass, centre of gravity position and principal mass moment of inertia are numerically determined and further experimentally verified using the ‘pendulum method’. The numerical estimations are computed through Raymer and DATCOM statistical-empirical methods coupled with mechanical calculations. The mass of the UAS-S4 parts are estimated according to their sizes and the UAS-S4 class, by the means of Raymer statistical equations. The UAS-S4 is also decomposed in several simple geometrical figures wh

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50

Phillips, Peter R. "Test of spatial isotropy using a cryogenic torsion pendulum." Physical Review Letters 59, no. 15 (1987): 1784–87. http://dx.doi.org/10.1103/physrevlett.59.1784.

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