• Nuclear Engineering and Technology
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• v.14 no.2
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• pp.78-85
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• 1982

The steady-state rotation of plasma centrifuge is theoretically analyzed to understand the physics of rotating plasmas and its feasibility for isotope separation. The centrifuge system under consideration consists of an annular gap between coaxial cylindrical anode and cathode in the presence of an externally-applied axial magnetic field. A problem for coupled partial differential equations describing centrifuge fields is formulated on the basis of the magnetohydrodynamic equations. Two-dimensional solutions are found analytically in the form of Fourier-Bessel series. The current density and velocity distributions are discussed in terms of the Hartmann number and the geometrical parameter of the system. At typical conditions, rotational speeds of the plasma up to the order of 10$^4$m/sec are achievable, and increase either with increasing Hartmann number, or with increasing ratio of the axial length to the inner radius of the cylinder. In view of much higher speeds of rotation which can be achieved in plasma centrifuge, it is expected that its efficiency is superior to mechanically driven gas centrifuges.

• Journal of Korean Association for Spatial Structures
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• v.6 no.4 s.22
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• pp.81-92
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• 2006

This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon Poisson's ratio ( V ), results are shown for $0{\leq}v{\leq}0.5$, valid for isotropic materials.

• Journal of Biosystems Engineering
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• v.10 no.1
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• pp.24-38
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• 1985

경사진 밀폐 공간에서 마주 보는 두 벽면의 온도 차로 인하여 발생되는 자연 대류 현상은 여러 공학 분야에서 볼 수 있는 중요한 열전달 현상으로서, 최근 들어 평판형 태양열 집열기를 설계하려는 사람들에게 많은 관심의 대상이 되고 있다. 평판형 태양열 집열기의 경우 덮개판으로 부터의 대류 열손실을 감소시킴으로서 집열 효율을 높일 수 있을 뿐만 아니라 사용목적에 따라 소형 집열기를 제작할 수 있어 경제적으로 유리하게 될 것이다. 밀폐된 공간에서 최초에 정지 상태에 있는 얇은 유체층을 하부에서 가열시켜 주면 열팽창 현상이 일어나고, 이것에 의한 부력이 점도나 열전도도 등의 안정화 요인을 극복할 수 있을 정도로 커지면 System이 불안정하게 되어 자연 대류 현상이 수반되며 이 때문에 열전달율이 급격히 증가하게 된다. 이러한 현상의 지배 방정식은 연립 비선형 편미분 방정식으로 특수한 경계 조건외에는 일반적으로 해석적 해를 구하기가 어렵기 때문에 실험적 연구가 많이 실시되어 왔고 이들 결과의 대부분은 전반적인 열전달 특성치만을 구하는데 집중되어 왔다. 본 연구에서는 수치 해석법의 하나인 유한 차분법을 도입하여 이차원으로 가정한 경사진 평판형 밀폐 공간에서의 자연 대류 현상의 지배 방정식을 유한 차분화시켜, $$2.74{\times}10^3\leq_-Gr\leq_-2.0{\times}10^6$$, Pr=0.73, $$15^{\circ}\leq_-a\leq_-150^{\circ}$$, 종횡비는 1, 2, 3, 5, 9에 대하여 정상 상태에서의 해를 구하면서 수치적으로 실험하였다. 본 연구에서 얻어진 결론을 요약하면 다음과 같다. (1) 해석적으로 구하기 어려운 경사진 밀폐 공간에서 자연대류현상의 지배 방정식을 유한 차분법으로 해결할 수 있으며, 대류항과 확산항을 따로 고려한 유한차분법이 효과적임을 확인하였다. (2) 저온과 고온 벽면에서의 온도를 각각 균일하게 놓고 단변으로 이루어진 벽면은 완전히 절연되어 있는 경우에 대하여 수치해를 구한결과, 이전의 해석적 및 실험적 결과와 일치하였으며, 시간의 경과에 따른 온도 및 유선의 변화를 현상학적으로 관찰할 수 있었다. (3) 평균 열전달 계수에 미치는 경사각의 효과를 살펴본 결과 종횡비가 1 인 경우 경사각이 $45^{\circ}$에서, 종횡비가 2, 3, 5, 9인 경우 경사각이 $60^{\circ}$에서 각각 평균 열전달 계수 최대치가 나타났다. (4) Ra수(Rayleigh number) 가 증가될수록, 경사각에 상관없이 평균 열전달 계수도 증가되었다. 한편 Ra수 및 경사각의 변화에 따라 종횡비가 증가될수록 평균 열전달 계수는 경사각이 $90^{\circ}$인 경우를 제외하고는 감소됨을 볼 수 있었다. 경사각이 $90^{\circ}$인 경우, 평균 열전달 계수는 종횡비가 2 인 곳에서 최대치를 얻을 수 있었으며, 종횡비가 계속 증가될수록 평균 열전달 계수는 점차 감소되어짐을 볼 수 있었다.

• Journal of the Korea institute for structural maintenance and inspection
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• v.9 no.4
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• pp.159-168
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• 2005

This study carries out a finite difference nonlinear analysis of anisotropic advanced composite plate structures with various layer sequences. In the numerical analysis of various mechanical problems involving complex partial differential equations, the finite difference method (FDM) developed in this study has an advantage over the finite element method in its ability to avoid mesh generation and numerical integration. Many studies in FDM have been made on clamped or simple boundary conditions using merely an energy approach. These approaches cannot be satisfied, however, with pivotal points along the free boundary. Therefore, this study addresses the nonlinear problem of anisotropic plates by adopting a finite difference modeling elimination of pivotal difference points in the case of a free boundary condition. Complex nonlinear behaviors of composite plate structures for various parameters, especially for layer sequences, are analyzed using the proposed approach.

• Korean Chemical Engineering Research
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• v.49 no.5
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• pp.560-564
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• 2011

The objective of this study is to propose a mathematical model for a pervaporation process for concentrating hydrogen peroxide. The process was developed by NASA, which consists of a shell and membrane tubes, where a liquid hydrogen peroxide solution flows in the shell, and a sweep gas flows in the tubes countercurrent to each other. The liquid retentate is concentrated as more water molecules permeate and evaporate through the membrane than hydrogen peroxide. For this process, a mathematical model has been developed in the form of a system of nonlinear partial differential algebraic equations based on a sorption-diffusion mechanism for permeation, an Arrhenius relationship for the temperature dependency of the permeate flux, and mass and momentum balances for the liquid concentrations and flows in the membrane module. The dynamic behavior of the concentration of hydrogen peroxide in the retentate side has been simulated by solving a simplified version of the proposed model, and the result is compared with the experimental data reported in the NASA patent.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.12
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• pp.641-655
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• 2007

Parameterization has been one of very important research subjects in several application areas including computer graphics. In the parameterization research, the problem of mapping 3D polygonal model to 2D plane has been studied frequently, but the previous methods often fail to handle complicated shapes of polygonal surfaces effectively as well as entail distortion between the 3D and 2D spaces. Several attempts have been made especially to reduce such distortion, but they often suffer from the problem when an arbitrary rectangular surface region on 3D model is locally parameterized. In this paper, we propose a new local parameterization scheme based on the projection level set method. This technique generates a series of equi-distanced curves on the surface region of interest, which are then used to generate effective local parameterization information. In this paper, we explain the new technique in detail and show its effectiveness by demonstrating experimental results.

• Journal of The Korean Society of Agricultural Engineers
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• v.58 no.1
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• pp.81-90
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• 2016

The Agricultural Systems Application Platform (ASAP) provides bottom-up modelling and simulation environment for agricultural engineer. The purpose of this study is to expand usability of the ASAP to the second order partial differential equations: elliptic equations, parabolic equations, and hyperbolic equations. The ASAP is a general-purpose simulation tool which express natural phenomenon with capsulized independent components to simplify implementation and maintenance. To use the ASAP in continuous problems, it is necessary to solve partial differential equations. This study shows usage of the ASAP in elliptic problem, parabolic problem, and hyperbolic problem, and solves of static heat problem, heat transfer problem, and wave problem as examples. The example problems are solved with the ASAP and Finite Difference method (FDM) for verification. The ASAP shows identical results to FDM. These applications are useful to simulate the engineering problem including equilibrium, diffusion and wave problem.

• The Journal of the Korea Contents Association
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• v.20 no.7
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• pp.212-222
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• 2020

The purpose of this study is to understand the current status and trends of the research studies published by the Society for Industrial and Applied Mathematics which is a leader in the field of industrial mathematics around the world. To perform this purpose, titles and abstracts were collected from 6,255 research articles between 2016 and 2019, and the R program was used to analyze the topic modeling model with LDA techniques and a regression model. As the results of analyses, first, a variety of studies have been studied in the fields of industrial mathematics, such as algebra, discrete mathematics, geometry, topological mathematics, probability and statistics. Second, it was found that the ascending research subjects were fluid mechanics, graph theory, and stochastic differential equations, and the descending research subjects were computational theory and classical geometry. The results of the study, based on the understanding of the overall flows and changes of the intellectual structure in the fields of industrial mathematics, are expected to provide researchers in the field with implications of the future direction of research and how to build an industrial mathematics curriculum that reflects the zeitgeist in the field of education.

• Fire Science and Engineering
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• v.26 no.3
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• pp.79-84
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• 2012

In this study thermal characteristics of heat-responsive element considering conduction, convection and rate of change of element using Response Time Index (RTI) applied to sensitivity test of sprinkler head at home and aborad are theoretically investigated. Analytic solution of temperature distributions with radial direction and time is obtained form energy transport equations, non-homogeneous 2th order partial differential equation, applying to constant wall temperature and symmetric condition in order to analyze thermal characteristics of heat-responsive element for circular cylindrical geometry. Base on the results, the analytic method of this study is fundamental data to practical use for sensitivity test of sprinkler head and design of heat-responsive element.

• Journal of Radiation Protection and Research
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• v.28 no.2
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• pp.97-108
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• 2003

A three-dimensional wind field model based on the variational technique has been developed for estimating the overall wind patterns over a complex terrain. The three-dimensional elliptic partial differential equations on Cartesian and terrain-following coordinates have been established to obtain the Lagrangian multiplier and the adjusted wind velocity. The simulations were performed to evaluate the variations of the velocity vectors on the hemisphere, half-cylinder, and saddle type obstacles. Also, the wind field model in the terrain-following coordinate has been applied for evaluating the characteristics of wind patterns according to the variations of Gauss precision moduli on the hemispheric topography. The results showed that the horizontal and vertical wind components were strongly governed by the selection of the values of Gauss precision moduli.