• Title/Summary/Keyword: M-harmonic function

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Geomagnetic Field Distribution in the Korean Peninsula by Spherical Harmonic Analysis (구면조화해석(球面調和解析)에 의(依)한 한반도내(韓半島內)의 지구자기장(地球磁氣場)의 분포(分布)에 관(關)한 연구(硏究))

  • Min, Kyung Duck;Lee, Sunhee
    • Economic and Environmental Geology
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    • v.12 no.2
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    • pp.95-104
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    • 1979
  • The position of any point on the earth's surface can be. represented in the spherical coordinates by surface spherical harmonics. Since geomagnetic field is a function of position on the earth, it can be also expressed by spherical harmonic analysis as spherical harmonics of trigonometric series of $a_m({\theta})$ cos $m{\phi}$ and $b_m({\theta})$ sin $m{\phi}$. Coefficients of surface spherical harmonics, $a_m({\theta})$ and $b_m({\theta})$, can be drawn from the components of the geomagnetic field, declination and inclination, and vice versa. In this paper, components of geomagnetic field, declination and inclination in the Korean peninsula are obtained by spherical harmonic analysis using the Gauss coefficients calculated from the world-wide magnetic charts of 1960. These components correspond to the values of normal geomagnetic field having no disturbances of subsurface mass, structure, and so on. The vertical and total components offer the zero level for the interpretation of geomagnetic data obtained by magnetic measurement in the Korean peninsula. Using this zero level, magnetic anomaly map is obtained from the data of airborne magnetic. prospecting carried out during 1958 to 1960. The conclusions of this study are as follows; (1) The intensity of horizontal component of normal geomagnetic field in Korean peninsula ranges from $2{\times}10^4$ gammas to $2.45{\times}10^4$ gammas. It decreases about 500 with the increment of $1^{\circ}$ in latitude. Along the same. latitude, it increases 250 gammas with the increment of $1^{\circ}$ in longitude. (2) Intensity of vertical component ranges from $3.85{\times}10^4$ gammas to $5.15{\times}10^4$ gammas. It increases. about 1000 gammas with the increment of $1^{\circ}$ in latitude. Along the same latitude, it decreases. 150~240 gammas with the increment of $1^{\circ}$ in longitude. Decreasing rate is considerably larger in higher latitude than in lower latitude. (3) Total intensity ranges from $4.55{\times}10^4$ gammas to $5.15{\times}10^4$ gammas. It increases 600~700 gammas with the increament of $1^{\circ}$ in latitude. Along the same latitude, it decreases 10~90 gammas. with the increment of $1^{\circ}$ in longitude. Decreasing rate is considerably larger in higher latitude as the case of vertical component. (4) The declination ranges from $-3.8^{\circ}$ to $-11.5^{\circ}$. It increases $0.6^{\circ}$ with the increment of $1^{\circ}$ in latitude. Along the same latutude, it increases $0.6^{\circ}$ with the increment of l O in longitude. Unlike the cases of vertical and total component, the rate of change is considerably larger in lower latitude than in higher latitude. (5) The inclination ranges from $57.8^{\circ}$ to $66.8^{\circ}$. It increases about $1^{\circ}$ with 'the increment of $1^{\circ}$ in latitude Along the same latitude, it dereases $0.4^{\circ}$ with the increment of $1^{\circ}$ in longitude. (6) The Boundaries of 5 anomaly zones classified on the basis of the trend and shape of anomaly curves correspond to the geologic boundaries. (7) The trend of anomaly curves in each anomaly zone is closely related to the geologic structure developed in the corresponding zone. That is, it relates to the fault in the 3rd zone, the intrusion. of granite in the 1st and 5th zones, and mountains in the 2nd and 4th zones.

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Study on the Dynamic Torsional Instability of a Thin Beam (비틀림 하중을 받는 얇은 빔의 동적 불안정성에 관한 연구)

  • 박진선;주재만;박철희
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1995.10a
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    • pp.185-190
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    • 1995
  • In recent years, many researcher have been interested in the stability of a thin beam. Among them, Pai and Nayfeh[1] had investigated the nonplanar motion of the cantilever beam under lateral base excitation and chaotic motion, but this study is associated with internal resonance, i.e. one to one resonance. Also Cusumano[2] had made an experiment on a thin beam, called Elastica, under bending loads. In this experiment, he had shown that there exists out-of-plane motion, involving the bending and the torsional mode. Pak et al.[3] verified the validity of Cusumano's experimental works theoretically and defined the existence of Non-Local Mode(NLM), which is came out due to the instability of torsional mode and the corresponding aspect of motions by using the Normal Modes. Lee[4] studied on a thin beam under bending loads and investigated the routes to chaos by using forcing amplitude as a control parameter. In this paper, we are interested in the motion of a thin beam under torsional loads. Here the form of force based on the natural forcing function is used. Consequently, it is found that small torsional loads result in instability and in case that the forcing amplitude is increasing gradually, the motion appears in the form of dynamic double potential well, finally leads to complex motion. This phenomenon is investigated through the poincare map and time response. We also check that Harmonic Balance Method(H.B.M.) is a suitable tool to calculate the bifurcated modes.

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Optical and Mechanical Characteristics of NF System and NF Gap Control (근접장 광학계의 광학적 및 기계적 특성 분석과 근접장 간격제어)

  • Oh, Hyeong-Ryeol;Lee, Jun-Hee;Gweon, Dae-Gab;Kim, Soo-Kyung
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2000.06a
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    • pp.1528-1532
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    • 2000
  • The conventional optics and near field optics are compared numerically in the view points of the spot size and propagation characteristics. The decaying characteristics of near field light require the optics to access the object within several tens of nanometers. Therefore the gap control is one of the main issues in the near field optics area. In this paper the gap control is done by using the shear force of the NF(Near Field) probe and the characteristics are examined. The probe is modeled as a 2'nd order mass-spring-damper system driven by a harmonic force. The primary cause of the decrease in vibration amplitude is due to the damping force - shear force - between the surface and the probe. Using the model, damping constant and resonance frequency of the probe is calculated as a function of probe-sample distance. Detecting the amplitude and phase shift of the NF probe attached to the high Q-factor piezoelectric tuning fork, we can control the position of the NF probe about 0 to 50nm above the sample. The feedback signal to regulate the probe-sample distance can be used independently for surface topography imaging. 3-D view of the shear force image of a testing sample with the period of $1{\mu}m$ will be shown.

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Evaluating High-Degree-and-Order Gravitational Harmonics and its Application to the State Predictions of a Lunar Orbiting Satellite

  • Song, Young-Joo;Kim, Bang-Yeop
    • Journal of Astronomy and Space Sciences
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    • v.32 no.3
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    • pp.247-256
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    • 2015
  • In this work, an efficient method with which to evaluate the high-degree-and-order gravitational harmonics of the non-sphericity of a central body is described and applied to state predictions of a lunar orbiter. Unlike the work of Song et al. (2010), which used a conventional computation method to process gravitational harmonic coefficients, the current work adapted a well-known recursion formula that directly uses fully normalized associated Legendre functions to compute the acceleration due to the non-sphericity of the moon. With the formulated algorithms, the states of a lunar orbiting satellite are predicted and its performance is validated in comparisons with solutions obtained from STK/Astrogator. The predicted differences in the orbital states between STK/Astrogator and the current work all remain at a position of less than 1 m with velocity accuracy levels of less than 1 mm/s, even with different orbital inclinations. The effectiveness of the current algorithm, in terms of both the computation time and the degree of accuracy degradation, is also shown in comparisons with results obtained from earlier work. It is expected that the proposed algorithm can be used as a foundation for the development of an operational flight dynamics subsystem for future lunar exploration missions by Korea. It can also be used to analyze missions which require very close operations to the moon.

Laser Patterning of Indium Tin Oxide for Flat Panel Display (평판디스플레이를 위한 Indium Tin Oxide의 레이저 페터닝)

  • Ahn, Min-young;Lee, Kyoung-cheol;Lee, Cheon
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2000.07a
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    • pp.340-343
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    • 2000
  • ITO(Indium Tin Oxide) films for transparent electrodes of FPD(Flat Panel Display) were patterned in atmosphere using laser. A pulse type(repetition rate of 10 Hz) Q-switched Nd:YAG laser which can generate the fundamental wavelength at 1064 nm or its harmonics(532, 266 nm) was used for Patterning of the ITO film. In case of using the second harmonic(532 nm) of Nd:YAG laser, the ITO film(thickness of 20 nm) was removed clearly with a laser fluence of 5.2 J/$\textrm{cm}^2$ and a beam scan speed of 200${\mu}{\textrm}{m}$/s. But the glass substrate was damaged when the laser fluence was over 5.2 J/$\textrm{cm}^2$. We discussed the etching mechanism of the ITO film using Nd:YAG laser with observation of the etching characteristics including a depths and widths of ITO films as a function of laser fluence using SEM(Scanning Electron Microscopy) and surface profiler($\alpha$-step 500).

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Analysis of the MODIS-Based Vegetation Phenology Using the HANTS Algorithm (HANTS 알고리즘을 이용한 MODIS 영상기반의 식물계절 분석)

  • Choi, Chul-Hyun;Jung, Sung-Gwan
    • Journal of the Korean Association of Geographic Information Studies
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    • v.17 no.3
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    • pp.20-38
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    • 2014
  • Vegetation phenology is the most important indicator of ecosystem response to climate change. Therefore it is necessary to continuously monitor forest phenology. This paper analyzes the phenological characteristics of forests in South Korea using the MODIS vegetation index with error from clouds or other sources removed using the HANTS algorithm. After using the HANTS algorithm to reduce the noise of the satellite-based vegetation index data, we were able to confirm that phenological transition dates varied strongly with altitudinal gradients. The dates of the start of the growing season, end of the growing season and the length of the growing season were estimated to vary by +0.71day/100m, -1.33day/100m and -2.04day/100m in needleleaf forests, +1.50day/100m, -1.54day/100m and -3.04day/100m in broadleaf forests, +1.39day/100m, -2.04day/100m and -3.43day/100m in mixed forests. We found a linear pattern of variation in response to altitudinal gradients that was related to air temperature. We also found that broadleaf forests are more sensitive to temperature changes compared to needleleaf forests.

Analytical and experimental investigation of stepped piezoelectric energy harvester

  • Deepesh, Upadrashta;Li, Xiangyang;Yang, Yaowen
    • Smart Structures and Systems
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    • v.26 no.6
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    • pp.681-692
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    • 2020
  • Conventional Piezoelectric Energy Harvesters (CPEH) have been extensively studied for maximizing their electrical output through material selection, geometric and structural optimization, and adoption of efficient interface circuits. In this paper, the performance of Stepped Piezoelectric Energy Harvester (SPEH) under harmonic base excitation is studied analytically, numerically and experimentally. The motivation is to compare the energy harvesting performance of CPEH and SPEHs with the same characteristics (resonant frequency). The results of this study challenge the notion of achieving higher voltage and power output through incorporation of geometric discontinuities such as step sections in the harvester beams. A CPEH consists of substrate material with a patch of piezoelectric material bonded over it and a tip mass at the free end to tune the resonant frequency. A SPEH is designed by introducing a step section near the root of substrate beam to induce higher dynamic strain for maximizing the electrical output. The incorporation of step section reduces the stiffness and consequently, a lower tip mass is used with SPEH to match the resonant frequency to that of CPEH. Moreover, the electromechanical coupling coefficient, forcing function and damping are significantly influenced because of the inclusion of step section, which consequently affects harvester's output. Three different configurations of SPEHs characterized by the same resonant frequency as that of CPEH are designed and analyzed using linear electromechanical model and their performances are compared. The variation of strain on the harvester beams is obtained using finite element analysis. The prototypes of CPEH and SPEHs are fabricated and experimentally tested. It is shown that the power output from SPEHs is lower than the CPEH. When the prototypes with resonant frequencies in the range of 56-56.5 Hz are tested at 1 m/s2, three SPEHs generate power output of 482 μW, 424 μW and 228 μW when compared with 674 μW from CPEH. It is concluded that the advantage of increasing dynamic strain using step section is negated by increase in damping and decrease in forcing function. However, SPEHs show slightly better performance in terms of specific power and thus making them suitable for practical scenarios where the ratio of power to system mass is critical.

Output Characteristics of a Pulsed Ti:sapphire Laser Oscillator Pumped Longitudinally by Second Harmonic Wave of Nd:YAG Laser and a Ti:sapphire Laser Amplifier Operated along the Single Path of the Oscillator Beam (Nd:YAG 레이저의 제 2조화파로 종여기하는 펄스형 Ti:sapphire 레이저 발진기와 이를 이용한 단일경로 형태의 Ti:sapphire 증폭기의 출력특성)

  • Kim, Kyung-Nam;Jo, Jae-Heung;Lim, Gwon;Cha, Byung-Heon
    • Korean Journal of Optics and Photonics
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    • v.18 no.1
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    • pp.66-73
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    • 2007
  • The various output characteristics of a pulsed Ti:sapphire laser oscillator with a plane-parallel resonator, pumped longitudinally by the second harmonic wave of a Nd:YAG laser, and the output of a Ti:sapphire laser amplifier operated along the single path of the oscillator beam were investigated and analyzed. In the case of the oscillator, we measured the spectrum, the pulse buildup time, the temporal duration time of the pulse, and the output energy according to the variation of the pumping energy, resonator length, and the reflectance of the output coupler. And, in the case of the amplifier, we investigated and analyzed the output energy of the amplifier as a function of the time difference between the two pump beams of the oscillator and the amplifier, the pumping energy of the oscillator, and the pumping energy of the amplifier When pump energies of both the oscillator and the amplifier were 18 mJ/pulse, we could find that the output energy of the amplifier increased linearly and gradually up to the time difference of 35 ns. Finally, we determined that the slope efficiencies of the oscillator and the amplifier were 23.5 % and 11.6 %, respectively.

Design and Fabrication of a X-band Voltage Control Dielectric Resonator Oscillator with The Low Phase Noise (낮은 위상잡음을 갖는 X-band 전압제어 유전체 공진형 발진기의 설계 및 제작)

  • 박창현;최병하
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.41 no.5
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    • pp.69-76
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    • 2004
  • In this paper, a VCDRO (Voltage Control Dielectric Resonator Oscillator) with low phase noise for X-band application has been designed and fabricated. A low noise and low flicker noise MESFET and a high Q dielectric resonator were selected to obtain good phase noise Performance. Also, a varactor diode having high Q, qualify factor was used to reduce the loading effects and a big Gamma of diode was chosen for linearity of frequency over voltage tuning range. The fabricated circuits was simulated with circuit design tools, ADS to provide the optimum performances. As the measured results of fabricated oscillator, the output power was 5.8 ㏈m at center frequency 12.05㎓ and harmonic suppression -30㏈c, phase noise -114 ㏈c at 100 KHz offset frequency, respectively, and the frequency tuning range as the function of valtage applied to varactor diode was 15.2 MHz and its power variation with frequency was 0.2 ㏈. This oscillator could be available to a local oscillator in X-band.

Comparison of Newton's and Euler's Algorithm in a Compound Pendulum (복합진자 모형의 뉴튼.오일러 알고리즘 비교)

  • Hah, Chong-Ku
    • Korean Journal of Applied Biomechanics
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    • v.16 no.3
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    • pp.1-7
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    • 2006
  • The Primary type of swinging motion in human movement is that which is characteristic of a pendulum. The two types of pendulums are identified as simple and compound. A simple pendulum consist of a small body suspended by a relatively long cord. Its total mass is contained within the bob. The cord is not considered to have mass. A compound pendulum, on the other hand, is any pendulum such as the human body swinging by hands from a horizontal bar. Therefore a compound pendulum depicts important motions that are harmonic, periodic, and oscillatory. In this paper one discusses and compares two algorithms of Newton's method(F = m a) and Euler's method (M = $I{\times}{\alpha}$) in compound pendulum. Through exercise model such as human body with weight(m = 50 kg), body length(L = 1.5m), and center of gravity ($L_c$ = 0.4119L) from proximal end swinging by hands from a horizontal bar, one finds kinematic variables(angle displacement / velocity / acceleration), and simulates kinematic variables by changing body lengths and body mass. BSP by Clauser et al.(1969) & Chandler et al.(1975) is used to find moment of inertia of the compound pendulum. The radius of gyration about center of gravity (CoG) is $k_c\;=\;K_c{\times}L$ (단, k= radius of gyration, K= radius of gyration /segment length), and then moment of inertia about center of gravity(CoG) becomes $I_c\;=\;m\;k_c^2$. Finally, moment of inertia about Z-axis by parallel theorem becomes $I_o\;=\;I_c\;+\;m\;k^2$. The two-order ordinary differential equations of models are solved by ND function of numeric analysis method in Mathematica5.1. The results are as follows; First, The complexity of Newton's method is much more complex than that of Euler's method Second, one could be find kinematic variables according to changing body lengths(L = 1.3 / 1.7 m) and periods are increased by body length increment(L = 1.3 / 1.5 / 1.7 m). Third, one could be find that periods are not changing by means of changing mass(m = 50 / 55 / 60 kg). Conclusively, one is intended to meditate the possibility of applying a compound pendulum to sports(balling, golf, gymnastics and so on) necessary swinging motions. Further improvements to the study could be to apply Euler's method to real motions and one would be able to develop the simulator.