• Nuclear Engineering and Technology
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• 제53권2호
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• pp.399-413
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• 2021

The solution of the time-dependent neutron diffusion equation can be approximated using quasi-static methods that factorise the neutronic flux as the product of a time dependent function times a shape function that depends both on space and time. A generalization of this technique is the updated modal method. This strategy assumes that the neutron flux can be decomposed into a sum of amplitudes multiplied by some shape functions. These functions, known as modes, come from the solution of the eigenvalue problems associated with the static neutron diffusion equation that are being updated along the transient. In previous works, the time step used to update the modes is set to a fixed value and this implies the need of using small time-steps to obtain accurate results and, consequently, a high computational cost. In this work, we propose the use of an adaptive control time-step that reduces automatically the time-step when the algorithm detects large errors and increases this value when it is not necessary to use small steps. Several strategies to compute the modes updating time step are proposed and their performance is tested for different transients in benchmark reactors with rectangular and hexagonal geometry.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.615-640
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• 2022

In this paper, we investigate a time-dependent double obstacle problem associated with the model of European call option pricing with transaction costs. We prove the existence and uniqueness of a W^2,1_p,loc solution to the problem. We then characterize the behavior of the free boundaries in terms of continuity and values of limit points.

• Bulletin of the Korean Chemical Society
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• 제33권3호
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• pp.993-996
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• 2012

We investigated fluorescence and fluorescence excitation of diphenylsilane (DPS) in a solution and molecular beams in combination with the aid of the DFT method. When the molecule was photoexcited at 250 nm in a cyclohexane solution, normal and excimer fluorescences were observed in the ranges of 260-320 and 330-450 nm, respectively. The fluorescence excitation spectrum indicates that the channel leading to the intramolecular excimer formation is not efficient in comparison with the normal fluorescence. Vibrationally resolved fluorescence excitation spectra were measured for the DPS molecules cooled in pulsed supersonic expansion of He in the range 262.2-271.7 nm, in which we can see several electronic excitation spectra exhibiting the electronic band origins. We found that the simulated absorption spectrum based on the time-dependent densityfunctional theory calculations accords well with the absorption spectrum.

• Computers and Concrete
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• 제27권3호
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• pp.269-282
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• 2021

A dynamic analytical solution for a simply supported, rectangular functionally graded plate with a porous middle layer under time-dependent load based on a refined third-order shear deformation theory with a cubic variation of in-plane displacements according to the thickness and linear/quadratic transverse displacement is presented. The solution achieved in the trigonometric series form and rests on the Green's function method. Two porosity types and their influence on material properties, and mechanical behavior are considered. The network of pores is assumed to be empty or filled with low-pressure air, and the material properties are calculated using the power-law distribution idealization. Numerical calculations have been carried out to demonstrate the accuracy of the kinematic model for the dynamic problem, the effect of porosity, thickness of porous layers, power-law index, and type of loading on the dynamic response of an imperfect functionally graded material plate.

• 에너지공학
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• 제15권4호
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• pp.250-255
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• 2006

원자력 분야에서 중성자 수송계산을 위해 개발되어 널리 사용되는 방향차분법을 시간 종속 복사 열전달식의 해를 구하는데 적용하였다. 광자의 방향별 밀도를 자체수반형 2계 편미분방정식으로 나타내어 해의 안정성을 높였고 매질의 온도방정식의 비선형성은 다단계 선형화법을 사용하여 근사하였다. 본 연구에서 개발된 해법을 전형적인 Marshak wave 문제에 적용하였고 계산 결과를 기존의 Monte Carlo의 계산결과와 비교하여 그 우월성을 보였다.

• Nuclear Engineering and Technology
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• 제55권12호
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• pp.4491-4503
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• 2023

This study aimed to verify and validate the transient simulation capability of the hybrid code system RAST-F for fast reactor analysis. For this purpose, control rod (CR) drop experiments involving eight separate CRs and six CR groups in the China Experimental Fast Reactor (CEFR) start-up tests were utilized to simulate the CR drop transient. The RAST-F numerical solution, including the neutron population, time-dependent reactivity, and CR worth, was compared against the measurement values obtained from two out-of-core detectors. Moreover, the time-dependent reactivity and CR worth from RAST-F were verified against the results obtained by the Monte Carlo code Serpent using continuous energy nuclear data. A code-to-code comparison between Serpent and RAST-F showed good agreement in terms of time-dependent reactivity and CR worth. The discrepancy was less than 160 pcm for reactivity and less than 110 pcm for CR worth. RAST-F solution was almost identical to the measurement data in terms of neutron population and reactivity. All the calculated CR worth results agreed with experimental results within two standard deviations of experimental uncertainty for all CRs and CR groups. This work demonstrates that the RAST-F code system can be a potential tool for analyzing time-dependent phenomena in fast reactors.

• 대한토목학회논문집
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• 제12권4호
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• pp.33-47
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• 1992

본 논문에서는 케이블로 지지된 프리스트레스트 콘크리트(PC) 뼈대의 시공중의 각 단계를 고려하고 콘크리트와 PC 강재, 케이블 재료의 시간의존적 특성 및 재료의 비선형성과 케이블의 색 및 구조물의 처짐에 의한 기하학적 비선형성도 고려하는 해석방법을 제시했다. 구조물의 비선형거동을 해석하기 위한 운동방정식은 Updated Lagrangian 방식을 이용하여 유도하고 시간의존적인 거동올 해석하기 위해서 시간영역을 시간단계로 나누어 순차적으로 적분했다. 시공중의 각 단계를 표현하기 위해 계속적인 구조계의 변화를 고려했다. 본 논문에서 제시한 해석방법에 근거하여 컴퓨터 프로그램 CFRAME을 개발하고 예제들을 통하여 해석방법의 정당성을 보였다.

• International Journal of Aeronautical and Space Sciences
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• 제4권2호
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• pp.17-25
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• 2003

Simple methods are developed to predict temperatures of a satellite box during launch stage. The box is mounted on outer surface of satellite and directly exposed to space thermal environment for the time period from fairing jettison to separation. These simple methods are to solve a 1st order ordinary differential equation (ODE) which is simplified from the governing equation after applying several assumptions. The existence of analytical solution for the 1st order ODE is determined depending on treatment of time-dependent molecular heating term. Even for the case that the analytical solution is not available due to the time dependent term, the 1st order ODE can be solved by relatively simple numerical techniques. The temperature difference between two different approaches (analytical and numerical solutions) is relatively small (Jess than $1^{\circ}C$ along the time line) when they are applied to STSAT-I launch scenario. The present methods can be generally used as tools to quickly check whether a satellite box is safe against space environment during the launch stage for the case that the detailed thermal analysis is not available.

• 한국과학교육학회지
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• 제16권3호
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• pp.295-302
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• 1996

The purpose of this study was to investigate the effects of training and use of worked-example on chemical problem-solving learning. Schema acquisition and rule automation are the basic components of skilled problem-solving, which are dependent on appropriately focused attention and sufficient cognitive resources. Training and use of worked-example facilitate schema acquisition and rule automation, so improve problem-solving learning. The subjects of this study were 60 high school students. The average age was 17 years old. Then, they were randomly assigned to each groups and the chemical reaction problems used as experimental materials. The independent variables of this study were training and use of worked-examples and dependent variables were time for solution and the number of error. The results of this study were as follows; 1. The worked-example groups spent significantly less time on solution for acquisition problems than the conventional problem groups. 2. The long-acquisition groups spent significantly less time on solution for acquisition problems than the short-acquisition groups. 3. The modified worked-example groups did not spend significantly less time on solution for acquisition problems than the worked-example groups.

• 충청수학회지
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• 제31권3호
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• pp.287-308
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• 2018

This paper deals with blow-up phenomena for an initial boundary value problem of a quasilinear parabolic equation with time-dependent coefficient in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and differential inequality technique, we establish some conditions on time-dependent coefficient and nonlinear functions for which the solution u(x, t) exists globally or blows up at some finite time $t^*$. Moreover, some upper and lower bounds for $t^*$ are derived in higher dimensional spaces. Some examples are presented to illustrate applications of our results.