• Title/Summary/Keyword: Semi-Analytic Method

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Negative Turbulent Magnetic 𝛽 Diffusivity effect in a Magnetically Forced System

  • Park, Kiwan;Cheoun, Myung-Ki
    • The Bulletin of The Korean Astronomical Society
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    • v.46 no.2
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    • pp.47.3-48
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    • 2021
  • We studied the large scale dynamo process in a system forced by helical magnetic field. The dynamo process is basically nonlinear, but can be linearized with 𝛼&𝛽 coefficients and large scale magnetic field $\bar{B}$. This is very useful to the investigation of solar (stellar) dynamo. A coupled semi-analytic equations based on statistical mechanics are used to investigate the exact evolution of 𝛼&𝛽. This equation set needs only magnetic helicity ${\bar{H}}_M({\equiv}{\langle}{\bar{A}}{\cdot}{\bar{B}}{\rangle},\;{\bar{B}}={\nabla}{\times}{\bar{A}})$ and magnetic energy ${\bar{E}}_M({\equiv}{\langle}{\bar{B}}^2{\rangle}/2)$. They are fundamental physics quantities that can be obtained from the dynamo simulation or observation without any artificial modification or assumption. 𝛼 effect is thought to be related to magnetic field amplification. However, in reality the averaged 𝛼 effect decreases very quickly without a significant contribution to ${\bar{B}}$ field amplification. Conversely, 𝛽 effect contributing to the magnetic diffusion maintains a negative value, which plays a key role in the amplification with Laplacian ∇2(= - k2) for the large scale regime. In addition, negative magnetic diffusion accounts for the attenuation of plasma kinetic energy EV(= 〈 U2 〉/2) (U: plasma velocity) when the system is saturated. The negative magnetic diffusion is from the interaction of advective term - U • ∇ B from magnetic induction equation and the helical velocity field. In more detail, when 'U' is divided into the poloidal component Upol and toroidal one Utor in the absence of reflection symmetry, they interact with - B • ∇ U and - U • ∇ B from ∇ × 〈 U × B 〉 leading to 𝛼 effect and (negative) 𝛽 effect, respectively. We discussed this process using the theoretical method and intuitive field structure model supported by the simulation result.

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Optimal Design of Generalized Process-storage Network Applicable To Polymer Processes (고분자 공정에 적용할 수 있는 일반화된 공정-저장조 망구조 최적설계)

  • Yi, Gyeongbeom;Lee, Euy-Soo
    • Korean Chemical Engineering Research
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    • v.45 no.3
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    • pp.249-257
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    • 2007
  • The periodic square wave (PSW) model was successfully applied to the optimal design of a batch-storage network. The network structure can cover any type of batch production, distribution and inventory system, including recycle streams. Here we extend the coverage of the PSW model to multitasking semi-continuous processes as well as pure continuous and batch processes. In previous solutions obtained using the PSW model, the feedstock composition and product yield were treated as known constants. This constraint is relaxed in the present work, which treats the feedstock composition and product yield as free variables to be optimized. This modification makes it possible to deal with the pooling problem commonly encountered in oil refinery processes. Despite the greater complexity that arises when the feedstock composition and product yield are free variables, the PSW model still gives analytic lot sizing equations. The ability of the proposed method to determine the optimal plant design is demonstrated through the example of a high density polyethylene (HDPE) plant. Based on the analytical optimality results, we propose a practical process optimality measure that can be used for any kind of process. This measure facilitates direct comparison of the performance of multiple processes, and hence is a useful tool for diagnosing the status of process systems. The result that the cost of a process is proportional to the square root of average flow rate is similar to the well-known six-tenths factor rule in plant design.

Practical Numerical Model for Wave Propagation and Fluid-Structure Interaction in Infinite Fluid (무한 유체 영역에서의 파전파 해석 및 유체-구조물 상호작용 해석을 위한 실용적 수치 모형)

  • Cho, Jeong-Rae;Han, Seong-Wook;Lee, Jin Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.34 no.6
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    • pp.427-435
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    • 2021
  • An analysis considering the fluid-structure interaction is required to strictly evaluate the seismic behavior of facilities such as, environmental facilities and dams, that store fluids. Specifically, in the case of an infinite domain in the upstream direction, such as a dam-reservoir system, this should be carefully considered. In this study, we proposed a practical numerical model for both wave propagation and fluid-structure interaction analyses of an infinite domain, for a system with a semi-infinite domain such as a dam-reservoir system. This method was applicable to the time domain, and enabled accurate boundary analysis. For an infinite fluid domain, a small number of mid-point integrated acoustic finite elements were applied instead of a general acoustic finite element, and a viscous boundary was imposed on the outermost boundary. The validity and accuracy of the proposed method were secured by comparing analytic solutions of a reservoir having infinite domain, with the parametric analysis results, for the number of elements and the size of the modeling region. Furthermore, the proposed method was compared with other fluid-structure interaction methods using additional mass.

Analysis of Elementary Teachers' Views on Barriers in Implementing Inquiry-based Instructions (초등학교 과학 탐구 수업 실행의 저해 요인에 대한 교사들의 인식 분석)

  • Cho, Hyun-Jun;Han, In-Kyoung;Kim, Hyo-Nam;Yang, Il-Ho
    • Journal of The Korean Association For Science Education
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    • v.28 no.8
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    • pp.901-921
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    • 2008
  • The purpose of this study was to investigate elementary teachers' views on the barriers in implementing inquiry-based instruction in science education. For this, semi-structured in-depth interviews were performed with 22 elementary school teachers who have served for more than five years in the Gyeonggi province. The interview questions were developed through triangulation of Seidman's phase to achieve reliability in the interview data, then interview questions were modified and completed through an analytic induction method in pre-interviews. In-depth interviews were performed individually and all the interviews were recorded. The data of teachers' views on the barriers were categorized and analyzed into external and internal factors of teachers. The study found that the external factors referred by teachers included the following; the lack of a unit time, lack of materials and equipments, too many students in a class, problems in science curriculum management, difficulty in the assessment of students' inquiry activities, the students' learning, lack of opportunities for teaching inquiry activities, harmfulness of accidents, and so on. Internal factors included the following; lack of preparation for inquiry activities, lack of self-confidence, lack of patience, and so on. The various barriers presented and their causes were analyzed in detail, and possible efforts in activating inquiry activities in elementary science education were suggested.