• Title/Summary/Keyword: Theoretical equation

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Derivation of the refractive index profile equation of K-Na ion-exchange waveguide by a rapid thermal method (급열법에 의한 K-Na 이온교환 도파로의 굴절율 분포식산출)

  • 강승민
    • Proceedings of the Optical Society of Korea Conference
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    • 1990.02a
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    • pp.237-241
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    • 1990
  • A detailed theoretical and experimental study of k-na exchange in soda lime silicate glasses by RTP is presented. Concentration profiles i.e. index profiles are given by complementary error function added Gaussian function. The estimated diffusion coefficient is 1.54${\mu}{\textrm}{m}$2/min.

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Analysis Of Induction Motor Direct Control Using VI Space Vector (VI 공간벡터와 관련한 유도전동기 Direct Control 분석)

  • 오성업
    • Proceedings of the KIPE Conference
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    • 2000.07a
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    • pp.207-210
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    • 2000
  • In this paper a theoretical formulation of the direct control relating the action exerted by the inverter space vectors on the stator flux and the torque of Induction motor is analyzed. From the equation the scheme of the inverter switching is proposed and influence of the stator flux and the electromagnetic torque in each switching pattern is also analyzed.

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Prediction Equation of Compulsory Replacement Depth of Silty Layer in Sihwa Region (시화지역 실트질 지반에서 강제치환심도 예측식 산정)

  • Park, Young;Lim, Heui-Dae
    • Journal of the Korean Geotechnical Society
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    • v.27 no.9
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    • pp.55-66
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    • 2011
  • The compulsory replacement method for soft ground treatment is simple but excellent in economic feasibility. However, the accurate replacement depth is not easy to properly predicted since an theoretical algorithm has not presently been established so far. In this research a prediction equation is proposed in a new form based on the liquid limit and natural moisture content rather than on the bearing capacity of the soft soil layer. The equation is based on the monitoring as well as the confirmatory boring at the site. In addition, the equation has been derived from the data obtained from the analysis of the characteristics of silt/clay of Sihwa region. The final prediction equation has been drawn by applying the regression analysis method.

Characteristics of Insulation Resistance of Cable according to Temperature Rise and Over-Current for Process of the Melting Furnace (용해로의 공정상 온도상승 및 과전류에 따른 케이블의 절연저항 특성)

  • Suk Bong Ko;Doo-Hyun Kim;Sung-Chul Kim
    • Journal of the Korean Society of Safety
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    • v.39 no.2
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    • pp.22-27
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    • 2024
  • The purpose of this study is to explore the trend in insulation resistance values according to temperature and overcurrent by conducting an investigation on the actual condition and experiments on the electrical wiring during the melting furnace process. In addition, the Arrhenius equation is used to determine whether temperatures in the furnace operating process can be applied to the actual field. In the investigation of the actual condition, the insulation resistance started to decrease seven years after replacement, even though cables in oil pump A were replaced in 2010. Both the experimental and theoretical values of the insulation resistance obtained using the Arrhenius equation decreased with an increase in temperature. Errors in insulation resistance (MΩ) values between tests and the Arrhenius equation ranged from ±2 to ±10, demonstrating a high similarity. Results revealed that when the insulation resistance cannot be measured in a manufacturing workplace (quarterly analysis), it can be estimated by partially applying the Arrhenius equation.

Dynamics of Resonant Energy Transfer in OH Vibrations of Liquid Water

  • Yang, Mi-No
    • Bulletin of the Korean Chemical Society
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    • v.33 no.3
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    • pp.885-892
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    • 2012
  • Energy transfer dynamics of excited vibrational energy of OH stretching bonds in liquid water is theoretically studied. With time-dependent vibrational Hamiltonian obtained from a mixed quantum/classical calculation, we construct a master equation describing the energy transfer dynamics. Survival probability predicted by the master equation is compared with numerically exact one and we found that incoherent picture of energy transfer is reasonably valid for long-time population dynamics. Within the incoherent picture, we assess the validity of independent pair approximation (IPA) often introduced in the theoretical models utilized in the analysis of experimental data. Our results support that the IPA is almost perfectly valid as applied for the vibrational energy transfer in liquid water. However, proper incorporation of radial and orientational correlations between two OH bonds is found to be critical for a theory to be quantitatively valid. Consequently, it is suggested that the Forster model should be generalized by including the effects of the pair correlations in order to be applied for vibrational energy transfer in liquid water.

A SCHWARZ METHOD FOR FOURTH-ORDER SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEM WITH DISCONTINUOUS SOURCE TERM

  • CHANDR, M.;SHANTHI, V.
    • Journal of applied mathematics & informatics
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    • v.34 no.5_6
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    • pp.495-508
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    • 2016
  • A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter ε multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.

NUMERICAL SIMULATION OF THE RIESZ FRACTIONAL DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM

  • Zhang, H.;Liu, F.
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.1-14
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    • 2008
  • In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and $Gr\ddot{u}nwald$-Letnikov(G-L) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

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Effect of the Vibration Modes on the Radiation Sound for Plate (강판의 진동모드를 고려한 방사음 예측에 관한 연구)

  • Kim Chang-Nam;Byun Young-Su;Kim Jeong-Man;Kim Ue-Kan
    • Journal of Advanced Marine Engineering and Technology
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    • v.30 no.1
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    • pp.73-80
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    • 2006
  • In order to compute the radiated sound from a vibrating structure, the Rayleigh's integral equation has to be derived from the Helmholtz equation using Green's function. Generally, the surface velocity in the Rayleigh's integral equation uses the root mean square(rms) velocity. The calculation value is too large, because it's not considered cancelation. On the other hand. using the complex velocity, the sound pressure is calculated too small, because it considers that sound is perfectly canceled out. Therefore, this thesis proposes a correction factor(CF) which considers vibration modes and the method by which to calculate the radiating sound pressure. The theoretical results are compared with the experimental values, and the proposed method can be verified with confluence.

Calculation of the air ratio in the case of firing gaseous fuels containing incombustibles

  • Cho, Kil-Won;Kunwoo Han;Park, Heung-Soo;Lee, Yong-Kuk;Lee, Kun-Hong
    • Proceedings of the Korea Society for Energy Engineering kosee Conference
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    • 1998.05a
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    • pp.43-48
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    • 1998
  • A short-cut equation for the calculation of the air ratio in the case of firing gases containing incombustibles has been derived on the basis of mass balances. The new equation requires the oxygen concentration and the amount of carbon dioxide in the combustion gas, theoretical oxygen and air requirements, and the content of incombustibles other than carbon dioxide in the fuel for the air ratio calculation. By using the equation, a theoretically correct calculation of the air ratio has been enabled.

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