• Title/Summary/Keyword: Elliptic Equation

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Theoretical Investigations and measuring Techniques of Geometrical Factor influencing Sensitive Electronic Devices (감도전자장치에 영향을 주는 기하학적 인수의 이론적 연구와 측정)

  • S. K. Lee
    • 전기의세계
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    • v.14 no.1
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    • pp.5-12
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    • 1965
  • In the designs of the sensitive electronic devices such as phase sensitive detector, X-ray diffractometer, and neutron diffractometers, we must take into account the geometrical factors in a coil systems and extraneous stray fields. Input wave forms in such a sensitive electronic devices are often altered by the influence of these factors. Since the magnitude of the stray fields is generally very small, this affection may be removed by applying a good shielding but it is not ease to remove the affection from a geometrical factor. This affection must be however calculated by the theoretical methods and analytical solution in the equation of these factors. The fundamental purpose of this paper lie in the theoretical calculations and practical measurements of the geometrical factor in the coil systems, finite solenoid, and four point prove. In the heoretical calculations, the geometrical factors in the coil systems were calculated by applying the elliptic functions and in the contact points were calculated by applying the elliptic functions and in the contact points were calculated by applying the eigen functions and the infinite series. The measurements were carried out by using the sensitive electronic device made from author's design, as shown in the Fig. 9. The result of this work has verified the essential correctness of theoretical investigations and measuring techniques of geometrical factors on the design of sensitive electronic devices. It also has several advantages such that: (1) all the data obtained may give effective data to designer to work on the field of sensitive electronic devices or microelectronic devices, (2) it has evidently explained the characteristics of electrical investigations and physical definition, and has removed the conventional error of geometrical factors in the coil systems and contact points.

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Security Analysis of ElGamal-Type Signature Scheme Using Integer Decomposition (정수의 분해를 이용한 ElGamal형 서명기법의 안전성 분석)

  • 이익권;김동렬
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.14 no.2
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    • pp.15-22
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    • 2004
  • For an ElGamal-type signature scheme using a generate g of order q, it has been well-known that the message nonce should be chosen randomly in the interval (0, q-1) for each message to be signed. In (2), H. Kuwakado and H. Tanaka proposed a polynomial time algorithm that gives the private key of the signer if two signatures with message nonces 0<$k_1$, $k_2$$\leq$Ο(equation omitted) are available. Recently, R. Gallant, R. Lambert, and S. Vanstone suggested a method to improve the efficiency of elliptic curve crytosystem using integer decomposition. In this paper, by applying the integer decomposition method to the algorithm proposed by Kuwakado and Tanaka, we extend the algorithm to work in the case when |$k_1$ |,|$k_2$, |$\leq$Ο(equation mitted) and improve the efficiency and completeness of the algorithm.

COMPUTATION OF TURBULENT NATURAL CONVECTION IN A RECTANGULAR CAVITY WITH THE FINITE-VOLUME BASED LATTICE BOLTZMANN METHOD (유한체적법을 기초한 레티스 볼쯔만 방법을 사용하여 직사각형 공동에서의 난류 자연대류 해석)

  • Choi, Seok-Ki;Kim, Seong-O
    • Journal of computational fluids engineering
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    • v.16 no.4
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    • pp.39-46
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    • 2011
  • A numerical study of a turbulent natural convection in an enclosure with the lattice Boltzmann method (LBM) is presented. The primary emphasis of the present study is placed on investigation of accuracy and numerical stability of the LBM for the turbulent natural convection flow. A HYBRID method in which the thermal equation is solved by the conventional Reynolds averaged Navier-Stokes equation method while the conservation of mass and momentum equations are resolved by the LBM is employed in the present study. The elliptic-relaxation model is employed for the turbulence model and the turbulent heat fluxes are treated by the algebraic flux model. All the governing equations are discretized on a cell-centered, non-uniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with the deferred correction way to ensure accuracy and stability of solutions. The present LBM is applied to the prediction of a turbulent natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for the validation of turbulence models and those by the conventional finite-volume method. It is shown that the LBM with the present HYBRID thermal model predicts the mean velocity components and turbulent quantities which are as good as those by the conventional finite-volume method. It is also found that the accuracy and stability of the solution is significantly affected by the treatment of the convection term, especially near the wall.

An Experimental Study on the Turbulent Flow of a 45$^{\circ}C$ Free Cross Jet (450自由衝突 噴射 의 亂流流動 에 관한 實驗的 硏究)

  • 노병준;김장권
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.8 no.5
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    • pp.442-449
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    • 1984
  • Turbulent jet flow has been studied in many ways; a plane jet, a rectangular jet, an annular jet, a round jet, a wall jet, a parallel jet, a valve jet, a cross jet, a slit jet and etc. In this report, a 45.deg. cross jet flow was tried by using two same dimensioned nozzels(dia..phi.20)which were set up at the exit of the subsonic wind tunnel. Each jet flows to the direction of 22.5.deg. to the axis of downstream of the mixed flow. The centerline of each jet meets at the distance of 217.3mm and their mixing flow could be imagined to develop beyond that distance, so the measurement was effectuated at X/X$_{0}$=1.2-1.5. The section of the mixed flow a elliptic circle which is formed by the 22.5.deg. inclined flows to the X direction. This experimental study aimed at the investigation of the turbulent mixing process of two jets; the mean velocities, the turbulent shear stresses, the correlation coefficients, and the momentum were respectively measured. The mean velocity distribution profiles of the down-stream component measured in the Y direction coincide well with the empirical equation of Gortler and those measured in the Z direction agree with the equation of H. Schlichting. Other mean velocities V over bar and W over bar components were randomly distributed. The higher values with same order of the intensity of turbulence were largely distributed at the central part of the flow. The momentum was decreased up to 70% by the shock losses and the development of intense turbulences, but it kept its value constantly beyond X/d=14. Two-channel hot-wire anemometer systems (model 1050 series), X-type hot-wire made of tungsten (dia. .phi.e.mu.m, long 3mm, model 0252 T5), a computer(model HP 9845B0, and a plotter (model HP 9872C) were used for the experiments and the analyses.s.

Wave Transformation Due to Energy Dissipation Region (에너지 감쇠영역으로 인한 파랑변형)

  • 윤종태
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.11 no.3
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    • pp.135-140
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    • 1999
  • To simulate the wave transformation by an energy dissipation region, a numerical model is suggested by discretizing the elliptic mild-slope equation. Generalized conjugate gradient method is used as solution algorithm to apply parabolic approximation to open boundary condition. To demonstrate the applicabil-ity of the numerical procedure suggested, the wave scattering by a circular damping region is examined. The feature of reflection in front of the damping region is captured clearly by the numerical solution. The effect of the size of dissipation coefficient is examined for a rectangular damping region. The recovery of wave height by diffraction occurs very slowly with distance behind the damping region.

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A Numerical Study on the Heat Transfer Characteristics in an Internally Finned Circular Tube Flow (내부핀이 부착된 원형관유동에서의 열전달특성에 관한 수치적연구)

  • Pak, H.Y.;Park, K.W.;Choi, M.S.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.8 no.2
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    • pp.267-278
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    • 1996
  • Steady, laminar, forced convection flow and heat transfer in the entrance region of an internally finned circular duct with a finite thermal conductivity has been analyzed numerically. The problem under investigation is a three-dimensional boundary layer problem, and is solved by employing a marching-type procedure which involves solution of a series of 2-dimensional elliptic problems in the cross-stream plane. Two types of inlet hydrodynamic conditions are considered : (a) uniform velocity flow and (b) fully developed flow. From the above inlet conditions, the effects of the fin height(h), fin number(N) and conductivity ratio($k_r$) on the flow and thermal characteristics are investigated. The numerical results show that the height and number of fins, and ratio of the solid to fluid thermal conductivity have pronounced effect on the solution. Considering pressure drop, optimized dimensionless fin height is 0.4.

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Numerical Simulation of Developing Turbulent Flow in a Circular Pipe of 180° Bend (원형 단면을 갖는 180° 굽은 곡관내 발달하는 난류유동에 관한 수치해석)

  • Myong Hyon-Kook
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.30 no.10 s.253
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    • pp.966-972
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    • 2006
  • A numerical simulation is performed fur developing turbulent flow in a strongly curved 180 deg pipe and its downstream tangent by a new solution code(PowerCFD) which adopts an unstructured cell-centered method. The governing equations are discretized as the full elliptic from of the equations of motion. Three typical two-equation turbulence models of low-Reynolds-number form are used to approximate the turbulent stress field. Solutions fur both streamwise and circumferential velocity components are compared with the experimental data by Azzola et at.(1986). The ${\kappa}-{\omega}$ model by Wilcox(1988) is found to give better prediction performance than the other two. Predicted secondary velocities and streamwise velocity component contours at sequential longitudinal stations are also presented in order to enable a detailed description of the complete flow. It is also found that, in the bend both mean streamwise and secondary velocities never achieve a fully-developed state and the code is capable of producing very well the complex nature of steady flow in a strongly curved pipe.

Simulation of Natural Gas and Pulverized Coal Combustion using 93-PCGC-2 (93-PCGC-2을 이용한 천연가스 연소와 미분탄 연소 모사)

  • 조석연;서경원;이진욱
    • Proceedings of the Korea Society for Energy Engineering kosee Conference
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    • 1995.11a
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    • pp.50-55
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    • 1995
  • 향상되어진 93-PCGC-2는 기존의 PCGC-2와 같이 미분탄 연소를 포함하는 다양한 반응성흐름과 비반응성 흐름을 설명하기 위해 2차원 정상상태 모델로 제시되어 졌다. 93-PCGC-2는 실린더형의 축 대칭계에 응용되어질 수 있고, 난류(Turbulence)는 유체역학식과 연소기구 양쪽을 위해 고려되어졌으며, 불연속 세로좌표 방법(Discrete Ordinates Method)을 이용하여 기체, 벽 및 입자들로부터의 복사열(Radiation)을 모사하였다. 입자상은 입자 무리들의 평균 경로들을 따라 해석하는 Lagrangian계의 해석법으로 모델화되어졌다. 석탄의 팽윤(Swelling)과 촤의 반응성에 관한 부모델과 더불어 새롭게 일반화된 석탄 탈휘발화 부모델 (FG-DVC)도 첨가되어졌다. 비균일 반응기구는 확산과 화학반응 둘 모두를 고려하였다. 주요 기상반응은 국부 순간 평형을 가정하여 모델화하였다. 그래서 반응속도는 혼합의 난류속도에 의해 제한되어진다. Thermal NOx과 Fuel NOx의 유한속도 화학론(Finite Rate Chemstry)에 대한 부모델은 화학반응속도론와 난류성의 통계치를 통합하여 만들어져 있다. 기상은 반복적인 line-by-line기교에 의해 풀려지는 elliptic partial differential equation으로 묘사되어진다. 수치적인 안정을 고려하기 위해 under-relaxation이 이용되어졌다. 이렇게 코드화된 93-PCGC-2는 연소를 위해 모사되어졌다. 또한 더 나아가 이 수치모델의 활용범위는 미분탄의 가스화에도 활용되어질 것으로 기대되어진다.

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Approximate natural vibration analysis of rectangular plates with openings using assumed mode method

  • Cho, Dae Seung;Vladimir, Nikola;Choi, Tae Muk
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.5 no.3
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    • pp.478-491
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    • 2013
  • Natural vibration analysis of plates with openings of different shape represents an important issue in naval architecture and ocean engineering applications. In this paper, a procedure for vibration analysis of plates with openings and arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. The presented solution represents an extension of a procedure for natural vibration analysis of rectangular plates without openings, which has been recently presented in the literature. The effect of an opening is taken into account in an intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with rectangular, elliptic, circular as well as oval openings with various plate thicknesses and different combinations of boundary conditions. The results are compared with those obtained by the finite element method (FEM) as well as those available in the relevant literature, and very good agreement is achieved.

Variation of Surface Crack Shape in Pressure Vessel Materials (압력용기 소재에서의 표면균열의 형상변화)

  • 허용학;이주진;이해무
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.14 no.3
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    • pp.617-623
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    • 1990
  • Cracks present in pressure vessels have been reported to be mostly semi-elliptic surface cracks. The fatigue crack growth rates(FCGR) of surface cracks in the pressure vessel materials, API5A-K55 and SPV 500, used in this study were showed to be different depending on the direction of propagation of the surface crack. An equation for the prediction of the shape change of the surface crack was obtained by combining the Paris' relations for each direction of surface crack extension and agreed well with the experimental data. And also FGGR in both materials were evaluated and prediction of the shape change of surface crack were made using averaged stress intensity factor.