• Title, Summary, Keyword: analytic solution

### An Analysis of the Optimal Control of Air-Conditioning System with Slab Thermal Storage by the Gradient Method Algorithm (구배법 알고리즘에 의한 슬래브축열의 최적제어 해석)

• Jung, Jae-Hoon
• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.20 no.8
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• pp.534-540
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• 2008
• In this paper, the optimal bang-bang control problem of an air-conditioning system with slab thermal storage was formulated by gradient method. Furthermore, the numeric solution obtained by gradient method algorithm was compared with the analytic solution obtained on the basis of maximum principle. The control variable is changed uncontinuously at the start time of thermal storage operation in an analytic solution. On the other hand, it is showed as a continuous solution in a numeric solution. The numeric solution reproduces the analytic solution when a tolerance for convergence is applied severely. It is conceivable that gradient method is effective in the analysis of the optimal bang-bang control of the large-scale system like an air-conditioning system with slab thermal storage.

### Analytic Solution to Mild Slope Equation for Transformation of Waves Propagating over an Axi-symmetric Pit (축대칭 함몰지형 위를 진행하는 파의 변형에 관한 완경사 방정식의 해석 해)

• Jung, Tae-Hwa;Suh, Kyung-Duck
• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.4
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• pp.308-320
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• 2006
• An analytic solution to the mild-slope equation is derived for waves propagating over an axi-symmetric pit. The water depth inside the pit varies in proportion to a power of radial distance from the pit center. The governing equation is transformed into ordinary differential equations by using separation of variables, and the coefficients of the equations are transformed into explicit forms by using Hunt's (1979) approximate solution. Finally, by using the Frobenius series, the analytic solution is derived. Due to the feature of Hunt's equation, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth water. The validity of the analytic solution is demonstrated by comparison with numerical solutions. The analytic solution is also used to examine the effects of pit geometry and relative depth on wave transformation.

### Analytic Solution of Wave Propagating over Depressive Seabed (함몰지형 위를 통과하는 파의 변형에 관한 해석해)

• Kim, Soo-Young;Lee, Seung-Oh;Jung, Tae-Hwa
• The Journal of the Korea Contents Association
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• v.12 no.3
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• pp.434-441
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• 2012
• An analytic solution to the extended mild-slope equation was derived for waves propagating over an axi-symmetric pit. The water depth inside the pit was in proportion to a power of radial distance from the center of pit. The equation was transformed into the ordinary differential equation using the method of separation of variables. The coefficients of differential terms were expressed as an explicit form composing of the phase and group velocities. The bottom curvature and the square of bottom slope terms, which were added to the extended mild-slope equation, were expressed as power series. Finally, using the Frobenius series, the analytic solution to the extended mild-slope equation was derived. The present analytic solution was validated by comparing with the numerical solution obtained from FEM.

### Plane strain bending of a bimetallic sheet at large strains

• Alexandrov, Sergei E.;Kien, Nguyen D.;Manh, Dinh V.;Grechnikov, Fedor V.
• Structural Engineering and Mechanics
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• v.58 no.4
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• pp.641-659
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• 2016
• This paper deals with the pure bending of incompressible elastic perfectly plastic two-layer sheets under plane strain conditions at large strains. Each layer is classified by its yield stress, shear modulus of elasticity and its initial percentage thickness in relation to the whole sheet. The solution found is semi-analytic. In particular, a numerical technique is only necessary to solve transcendental equations. The general solution is cumbersome because different analytic expressions for the radial and circumferential stresses should be adopted in different regions of the whole sheet. In particular, there are several alternative ways a plastic region (or plastic regions) can propagate. However, for any given set of material and process parameters the solution to the problem consists of a sequence of rather simple analytic expressions connected by transcendental equations. The general solution is illustrated by a simple example.

### Analysis of the Bird-cage Receiver Coil of a MRI System Employing a Equivalent Circuit Model Based on a Transmission Matrix (전송행렬 기반 등가 회로 모델을 이용한 자기공명영상 장치용 새장형 수신 코일 해석)

• Kim, Hyun Deok
• Journal of Korea Multimedia Society
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• v.20 no.7
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• pp.1024-1029
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• 2017
• A novel analytic solution has been derived for the bird-cage receiver coil of a magnetic resonance imaging (MRI) system, which is widely used in 3-dimensional medical imaging, by transforming the coil into an equivalent circuit model by using a transmission matrix-based circuit analysis. The bird-cage coil composed of N legs is divided into a cell for which input impedance is to be analyzed and the remaining N-1 cells, and then a transmission matrix corresponding to the N-1 cells is converted into a circuit to transform the 3-dimensional bird-cage coil into the 2-dimensional equivalent circuit model, which is suitable to derive the analytic solution for the input impedance. The proposed method derives directly the analytic solution for the input impedance at an arbitrary point of the coil unlike the conventional analytic solution of a bird-cage coil, so that it can be used not only for resonance frequency calculations but also for various coil characteristics analyses. Since the analytic solution agreed well with the results of computational simulations, it can be useful for the impedance matching of a coil and the analysis and the design of a multi-tune bird-cage coil.

### Performance Prediction Analysis for the PDA Filter (해석적 방법에 의한 PDAF의 성능예측 분석)

• 김국민;송택렬
• Journal of Institute of Control, Robotics and Systems
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• v.9 no.7
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• pp.563-568
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• 2003
• In this paper, We propose a target tracking filter which utilizes the PDA for data association in a clutter environment and also propose an analytic solution for ideal filter covariance which accounts for all the possible events in the PDA. Monte Carlo simulation for the proposed filter in a clutter environment indicates that the proposed analytic solution forms the true error covariance of the PDA Filter.

### Analytic Solution to the Spatial Propagation of the Flexible Structures (유연한 구조물의 공간전파에 관한 해석적 해법)

• Seok, Jin-Yeong;Jeong, Eun-Tae;Kim, Yu-Dan
• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.12
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• pp.2040-2047
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• 2001
• In this paper, a singularity problem of the state transition matrix is investigated in the spatial propagation when the spatial matrix differential equation is constructed via time finite element analysis. A parametric study shows that the degree of singularity of the state transition matrix depends on the degree of flexibility of the structures. As an alternative to avoid the numerical problems due to the singularity, an analytic solution fur spatial propagation of the flexible structures is proposed. In the proposed method, the spatial properties of the structure are analytically expressed by a combination of transcendental functions. The analytic solution serves fast and accurate results by eliminating the possibility of the error accumulation caused by the boundary condition. Several numerical examples are shown to validate the effectiveness of the proposed methods.

### Two-dimensional Analytic Solution of the Magnetic Field for the Ferrites of DC Magnetron Sputtering Device (DC 마그네트론 스퍼터링 장치의 영구자석에 의한 자기장의 2차원 해석적 해)

• Yu Dong-Hun;Kwon Deuk-Chul;Lee Jong-Kyu;Yoon Nam-Sik;Kim Jung-Hyung;Shin Yong-Hyeon
• The Transactions of the Korean Institute of Electrical Engineers C
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• v.54 no.7
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• pp.326-331
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• 2005
• We obtain analytical expressions the magnetic field of ferrites for DC magnetron sputtering device, which has been widely used for vacuum thin film deposition, and suggested the equation on maximum radius of the magnetic field by analytic solution. Also, the analytic results are compared with some calculations using magnetization elements of right-angled hexahedron.

### On the Optimal Solution Transportation Problem by Analytic Hierarchy Process (계층화 분석 과정에 의한 최적운송 수단에 관한 연구)

• Chung, Soon-Suk
• Proceedings of the Safety Management and Science Conference
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• pp.345-360
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• 2008
• The analytic hierarchy process is known as a useful tool for the group decision making methods. This tool has been area such as investment, R&D management, manufacturing, production and marketing. Typically, transportation problems have addressed by mathematical programming. In this paper, an optimal solution of transportation problem was determined by the analytic hierarchy process.

### Mass Transfer of Aerosol onto Spherical Collector at Low Knudsen Number (저 누드센 영역에서 구형 포집체상의 에어로졸 물질 전달)

• Jung, Chang-Hoon
• Journal of Korean Society for Atmospheric Environment
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• v.21 no.5
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• pp.547-555
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• 2005
• In this study, an analytical expression for aerosol mass transfer at spherical collector in the low Knudsen number region was obtained. Happel's zero shear stress cell model was extended in the low Knudsen number region and the result was compared with numerical solution results. The zero vorticity model based on the Kuwabara's cell model was also extended in the low Knudsen number region and compared with Happel's results. The results showed that both analytic and numerical solution agree very well with each other in low Knudsen number region. Happel's zero shear stress model also agrees with Kuwabara's zero vorticity model without significant loss of accuracy. The obtained solution converges to the original solution of Lee et al. (1999) when Knudsen number approaches to zero. Subsequently, this study derived most general type of analytic solution for aerosol mass transfer of spherical collector including the finite Knudsen number region.