• 한국진공학회지
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• 제21권3호
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• pp.130-135
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• 2012

드리프트-확산 근사식을 이용한 1차원 유체 방정식으로부터 선형적 안정성 이론을 전개하여 Tosend 방전에서 전자 확산이 불안정성에 미치는 영향을 관찰하였다. 본 연구에서 관찰된 바에 따르면 Townsend 불안정성은 전자 확산과 공간 전하에 의해 형성된 전기장의 효과가 결합되어 발생하며, 공간전하에 의한 효과가 작은 영역, 즉 방전 전류가 낮은 영역에서는 전자 확산 효과가 커질수록 불안정이 더 빨리 진행된다는 것이 발견되었다.

• Transactions on Electrical and Electronic Materials
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• 제2권1호
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• pp.7-11
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• 2001

We measured the electron transport coefficients, the electron drift velocity, W, and the longitudinal diffusion coefficient, $D_{L}$, over the E/N range from 0.03 to 100 Td and gas pressure range from 0.133 to 122 kPa in the 0.526% and 5.05% $C_{3}F_{8}$-Ar mixtures by the double shutter drift tube with variable drift distance. And we calculated these electron transport coefficients by using multi-term approximation of Boltzmann equation analysis. We determined the electron collision cross sections set for $C_{3}F_{8}$ molecule by the comparison of measurement and calculation. Our special attention in the present study was focused upon the inelastic collision cross sections of the $C_{3}F_{8}$ molecule.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.1-14
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• 2008

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and $Gr\ddot{u}nwald$-Letnikov(G-L) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1996년도 춘계학술발표회논문집(1)
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• pp.34-39
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• 1996

A consistent general order nodal method for solving the 3-D neutron diffusion equation in (x-y-z) geometry has ben derived by using a weighted integral technique and expanding the spatial variables by the Legendre orthogonal series function. The equation set derived can be converted into any order nodal schemes. It forms a compact system for general order of nodal moments. The method utilizes the analytic solutions of the transverse-integrated quasi -one dimensional equations and a consistent expansion for the spatial variables so that it renders the use of an approximation for the transverse leakages no necessary. Thus, we can expect extremely accurate solutions and the solution would converge exactly when the mesh width is decreased or the approximation order is increased since the equation set is consistent mathematically.

• Journal of Photoscience
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• 제11권1호
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• pp.11-17
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• 2004

Fluorescence quenching of l,4-bis [2-(2-methylphenyl) ethenyl]-benzene (Bis-MSB) by carbon tetrachloride in five different solvents namely hexane, cyclohexane, toluene, benzene and dioxane has been carried out at room temperature with a view to understand the quenching mechanisms. The Stern-Volmer plot has been found to be non-linear with a positive deviation for all the solvents studied. In order to interpret these results we have invoked the Ground state complex and Sphere of action static quenching models. Using these models various rate parameters have been determined. The magnitudes of these parameters imply that sphere of action static quenching model agrees well with the experimental results. Hence the positive deviation in the Stem-Volmer plots is attributed to the static and dynamic quenching. Further, with the use of Finite Sink approximation model, it was possible to check whether these bimolecular reactions as diffusion limited and to estimate independently distance parameter R' and mutual diffusion coefficient D. Finally an effort has been made to correlate the values of R'and D with the values of the encounter distance R and the mutual diffusion coefficient D determined using the Edwardis empirical relation and Stokes-Einstein relation.

• Nuclear Engineering and Technology
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• 제48권1호
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• pp.43-54
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• 2016

In the present paper, development of the three-dimensional (3D) computational code based on Galerkin finite element method (GFEM) for solving the multigroup forward/adjoint diffusion equation in both rectangular and hexagonal geometries is reported. Linear approximation of shape functions in the GFEM with unstructured tetrahedron elements is used in the calculation. Both criticality and fixed source calculations may be performed using the developed GFEM-3D computational code. An acceptable level of accuracy at a low computational cost is the main advantage of applying the unstructured tetrahedron elements. The unstructured tetrahedron elements generated with Gambit software are used in the GFEM-3D computational code through a developed interface. The forward/adjoint multiplication factor, forward/adjoint flux distribution, and power distribution in the reactor core are calculated using the power iteration method. Criticality calculations are benchmarked against the valid solution of the neutron diffusion equation for International Atomic Energy Agency (IAEA)-3D and Water-Water Energetic Reactor (VVER)-1000 reactor cores. In addition, validation of the calculations against the $P_1$ approximation of the transport theory is investigated in relation to the liquid metal fast breeder reactor benchmark problem. The neutron fixed source calculations are benchmarked through a comparison with the results obtained from similar computational codes. Finally, an analysis of the sensitivity of calculations to the number of elements is performed.

• Computers and Concrete
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• 제23권2호
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• pp.145-153
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• 2019

Adaptive schemes are constructed in this paper for modeling the effective chloride diffusion coefficient of cement-based materials (paste and concrete). Based on the polarization approximations for the effective conductivity of isotropic multicomponent materials, we develop some fitting procedures to include more information about the materials, to improve the accuracy of the scheme. The variable reference parameter of the approximation involves a few free scalars, which are determined through the available numerical or experimental values of the macroscopic chloride diffusion coefficient of cement paste or concrete at some volume proportions of the component materials. The various factors that affect the chloride diffusivity of cement-based material (porous material structure, uncertainty of value of the chloride diffusion coefficient in water-saturated pore spaces, etc.) may be accounted to make the predictions more accurate. Illustrations of applications are provided in a number of examples to show the usefulness of the approach.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1995년도 춘계학술대회논문집
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• pp.155-161
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• 1995

Superplastic forming/diffusion bonding(SPF/DB) processes are analyzed using a rigid visco-plastic finite element method. The optimum pressure-time relationship for a target strain rate and thickness distributions were predicted using two-node line element based on membrane approximation for plane strain shapes. Material behavior during SPF/DB of the integral structures with complicated shapes are investigated. The tying condition is employed for the analysis inter-sheet contact problems. A movement of rib structure is successfully prodicted during the forming.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.517-529
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• 2009

In this paper, a singularly perturbed reaction-convection-diffusion problem with two parameters is considered. A parameter-uniform error bound for the numerical derivative is derived. The numerical method considered here is a standard finite difference scheme on piecewise-uniform Shishkin mesh, which is fitted to both boundary and initial layers. Numerical results are provided to illustrate the theoretical results.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.83-92
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• 2021

This paper studies approximate solutions for a class of nonlinear diffusion population models. Our methods are to use the fundamental solution of heat equations to construct integral forms of the models and the well-known Banach compression map theorem to prove the existence of positive solutions of integral equations. Non-steady-state local approximate solutions for suitable harvest functions are obtained by utilizing the approximation theorem of multivariate continuous functions.