• 호남수학학술지
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• 제43권4호
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• pp.667-678
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• 2021

Blow-up phenomena for a nonlocal reaction-diffusion system with time-dependent coefficients are investigated under null Dirichlet boundary conditions. Using Kaplan's method with the comparison principle, we establish new blow-up criteria and obtain the upper bounds for the blow-up time of the solution under suitable measure sense in the whole-dimensional space.

• 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.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2008년도 추계학술대회 논문집
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• pp.1096-1101
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• 2008

Concrete is shown the time dependent behavior after placing. The time dependent behavior of normal strength concrete that is used usually in present, were already examined closely lots of parameters by several investigators. however, high strength concrete is that the material characteristics are not definite and the experimental data are lacking. So, The goal of this study is to propose the material characteristics models, and to develop the routine of the time dependent behavior above 60 MPa. The thermal conductivity, the specific heat, the moisture diffusion coefficient, and the surface coefficient are proposed the suitable models through the parametric study. The structural element is used the 8-node solid element. The matrix equation is developed considering the transient heat transfer and moisture diffusion theory. The application of the time dependent behavior is used the finite differential method.

• Korean Chemical Engineering Research
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• 제57권5호
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• pp.652-665
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• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• 한국구조물진단유지관리공학회 논문집
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• 제19권5호
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• pp.83-91
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• 2015

콘크리트 표면의 상태에 따라 염화물은 증가 또는 감소하게 되며 이는 철근부식 및 내구수명에 매우 중요한 인자가 된다. 콘크리트의 내구성 저하를 방지하기 위해 표면함침과 같이 많은 표면강화 기술이 개발되었으나 이중 콘크리트 구조와 확산계수의 시간의존성을 고려한 염화물 해석방법은 매우 제한적이다. 본 논문에서는 표면 강화된 이중구조 콘크리트에 대해 시간의존성 확산계수를 도입하여 염화물 해석기법을 제안하였으며, 역해석을 통하여 기존의 실험결과와 비교하였다. 2년간 비말대, 해수중, 조석대 상태에 노출된 표면 함침된 콘크리트 시편에 대해 표면염화물량과 확산계수를 도출하고 Life-365에서 제안한 확산계수 식과 비교 분석하였다. 시간의존성을 고려한 결과 비말대 시편의 오차는 0.28에서 0.20 수준으로, 조석대 시편은 0.29에서 0.11 수준으로, 해수중에서는 0.54에서 0.40 수준으로 오차가 감소함을 알 수 있었다. 또한 Life365에서 사용되는 확산계수식을 사용할 경우, 과다한 확산계수로 인해 상대오차가 커지고 높은 침투깊이(e)와 낮은 확산계수비($D_1/D_2$)를 필요로 함을 알 수 있다.

• 한국세라믹학회지
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• 제29권1호
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• pp.65-73
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• 1992

The effect of grain size on the time-dependent piezoelectrice degradation of a poled PZT of MPB composition Pb0.988Sr0.012 (Zr0.52Ti0.48)O3 with 2.4 mol% of Nb2O5 was studied, and the degradation mechanism was discussed. Changes in the internal bias field and the internal stress both responsible for the time-dependent degradation of poled PZT were examined by the polarization reveral technique, XRD and Vickers indentation, respectively. The piezoelectric degradation increased with increasing time and grain size, and the internal bias field due to space charge diffusion decreased with increasing grain size of poled PZT. The internal bias field, however, was almost insensitive to the degradation time regardless of the grain size. On the other hand, both the x-ray diffraction peak intensity ratio of (002) to (200) and the fracture behavior including the crack propagation support that the ferroelectric domain rearrangement of larger grain size showed rapid relaxation of the internal stress compared with smaller one, which is thought the origin of the larger piezoelectric degradation in the former. In conclusion, the contribution of space charge diffusion on the piezoelectric degradation of PZT is strongly dependent on both the grain size and the composition. Thus, the relaxation of internal stress due to the ferroelectric domain rearrangement as well as the amount and time-dependence of the internal bias field due to space charge diffusion should be considered simultaneously in the degradation mechanism of PZT.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.747-752
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• 1994

Ussing's flux ratio theorem (1978) reflects a reciprocal relationship behavior between the unidirectional fluxes in asymmetric steady diffusion-convection in a membrane slab. This surprising result has led to many subsequent studies in a wide range of applications, in particular involving linear models of time dependent problems in biology and physiology. Ussing's theorem and its extensions are inherently linear in character. It is of considerable interest to ask to what extent these results apply, if at all, in situations involving, for example, nonlinear reaction. A physiologically interesting situation has been considered by Weisiger et at. (1989, 1991, 1992) and by McNabb et al. (1990, 1991) who studied the role of albumin in the transport of ligands across aqueous diffusion barriers in a liver membrane slab. The results are that there exist reciprocal relationships between unidirectional fluxes in the steady state, although albumin is chemically interacting in a nonlinear way of the diffusion processes. However, the results do not hold in general at early times. Since this type of study first started, it has been speculated about when and how the Ussing's flux ratio theorem fails in a general diffusion-convection-reaction system. In this paper we discuss the validity of Ussing-type theorems in time-dependent situations, and consider the limiting time behavior of a general nonlinear diffusion system with interaction.

• 한국건설순환자원학회논문집
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• 제4권3호
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• pp.259-268
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• 2016

염해에 노출된 콘크리트 구조물의 내구수명 평가는 크게 결정론적 방법과 확률론적 방법으로 분류할 수 있으며, 다양한 설계인자에 따라 내구수명은 크게 변화한다. 본 연구에서는 시간의존성 확산계수 및 내부영향인자(기본확산계수, 임계염화물량, 시간지수)를 고려하여 변화하는 내구적 파괴확률과 이에 따른 내구수명을 도출하였다. 임계 염화물량이 133.3% 증가할 때, 내구수명은 결정론적 방법에서 134.0~145.4%의 증가비를 나타내었으며, 확률론적 방법에서는 149.2%~152.5% 증가비를 나타내었다. 시간지수가 200% 증가할 경우, 내구수명의 증가비율은 결정론적 방법에서 323.8%, 확률론적 방법에서 346.0%로 증가하였다. 시간의존성 확산계수를 사용하여 과다설계를 방지할 수 있는 합리적인 확률론적 내구설계를 수행할 수 있었으며, 혼화재료를 사용하여 시간지수를 증가시키는 것이 매우 효과적인 내구수명 연장방안임을 알 수 있었다.

• 콘크리트학회논문집
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• 제25권2호
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• pp.145-153
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• 2013

촉진 염화물 확산계수는 최근들어 염화물 거동 평가를 위하여 많이 사용되고 있다. 촉진 염화물 확산계수는 겉보기 확산계수와 마찬가지로 재령에 따라 감소하는데, 이 연구에서는 공극률을 이용하여 촉진확산계수의 감소를 구현하였다. DUCOM 프로그램을 이용하여 15 배합에 대한 공극률을 도출하였으며, 이를 회귀분석하여 재령 270일 동안 감소하는 염화물 확산계수를 모델링하였다. 또한 자유염화물과 구속염화물간의 관계인 비선형 구속능을 고려하여, 고성능 콘크리트내의 염화물 거동을 평가하였다. 기존의 실험자료인 180일간 염화물에 침지되어 있는 시편을 이용하여, 이 연구에서 제안한 기법의 검증을 수행하였다. 제안된 기법은 다양한 물-시멘트비 및 혼화재(고로슬래그 미분말 및 플라이애쉬)를 가진 고성능 콘크리트의 염화물 거동을 적절하게 평가하였다. 또한 혼화재료를 사용한 콘크리트의 경우, 확산계수의 시간의존성이 뚜렷하므로 염화물 거동 해석시 재령에 따른 염화물 확산계수의 감소를 반드시 구현해야 함을 알 수 있었다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집E
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• pp.456-462
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• 2001

Comprehensive numerical computations are made of a homogenous spin-up in a cylindrical cavity with a time-dependent rotation rate. Numerical solutions are acquired to the governing axisymmetric cylindrical Navier-Stokes equation. A rotation rate formula is ${\Omega}_f={\Omega}_i+{\Delta}{\Omega}(1-{\exp}(-t/t_c))$. If $t_c$ is large, it implies that a rotation change rate is small. The Ekman number, E, is set to $10^{-4}$ and the aspect ratio, R/H, fixed to I. For a linear spin-up(${\epsilon}<<$), the major contributor to spin-up in the interior is not viscous-diffusion term but inviscid term, especially Coriolis term, though $t_c$ is very large. The viscous-diffusion term only works near sidewall. But for spin-up from rest, when $t_c$ is very large, viscous-diffusion term affects interior area as well as sidewall, initially. So azimuthal velocity of interior for large $t_c$ appears faster than that of interior for relatively small $t_c$. However, the viscous-diffusion term of interior decreases as time increases. Instead, inviscid term appears in the interior.