• Honam Mathematical Journal
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• v.43 no.4
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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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• v.53 no.2
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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.

• Proceedings of the KSR Conference
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• 2008.11b
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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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• v.57 no.5
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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.

• Journal of the Korea institute for structural maintenance and inspection
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• v.19 no.5
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• pp.83-91
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• 2015

With varying conditions of concrete surface, induced chloride contents are changed and this is a key parameter for steel corrosion and service life in RC (Reinforced Concrete) structures. Many surface enhancement techniques using impregnation have been developed, however the evaluation techniques for chloride behavior through doubly layered media and time-dependent diffusion are rarely proposed. This paper presents an analysis technique considering double-layer concrete and time-dependent diffusion behavior, and the results are compared with those from the previous test results through reverse analysis. The chloride profiles from the surface-impregnated concrete exposed to atmospheric, tidal, submerged zone for 2 years are adopted. Furthermore surface chloride contents and diffusion coefficients are obtained, and are compared with those from Life365. Through consideration of time effect, the relative error decreases from 0.28 to 0.20 in atmospheric, 0.29 to 0.11 in tidal, and 0.54 to 0.40 in submerged zone, respectively, which shows more reasonable results. Utilizing the diffusion coefficients from Life365, relative errors increases and it needs deeper penetration depth (e) and lower diffusion coefficient ratio ($D_1/D_2$) due to higher diffusion coefficient.

• Journal of the Korean Ceramic Society
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• v.29 no.1
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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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• 1994.10a
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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.

• Journal of the Korean Recycled Construction Resources Institute
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• v.4 no.3
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• pp.259-268
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• 2016

The service life evaluation in RC(Reinforced Concrete) structure exposed to chloride attack can be classified into deterministic and probabilistic method, and it significantly varies with design parameters. The present work derives PDF (Probability of Durability Failure) and the related service life considering time-dependent diffusion coefficient and internal parameters such as reference diffusion coefficient, critical chloride content, and time-exponent. When critical chloride content increases to 133.3%, the changing ratios of service life are 134.0~145.4% for deterministic method and 149.2%~152.5% for probabilistic method, respectively. In the case of increasing time-exponent to 200%, they increase to 323.8% for deterministic method and 346.0% for probabilistic method. Through adopting time-diffusion coefficient for probabilistic method, reasonable service life evaluation can be achieved, and it is also verified that increasing time-exponent through mineral admixture is very effective to extension of service life in RC structure.

• Journal of the Korea Concrete Institute
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• v.25 no.2
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• pp.145-153
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• 2013

Recently, accelerated chloride diffusion coefficients are used for an evaluation of chloride behavior. Similar as apparent diffusion coefficients, accelerated diffusion coefficients decrease with time. In this study, decrease in diffusion coefficient with time is simulated with porosity. Utilizing DUCOM-program, porosities from 15 mix proportions are obtained and diffusion coefficients are modelled with regression analysis of porosity for 270 days. Considering non-linear binding capacity which means the relation between free and bound chloride ion, chloride behavior in high performance concrete is evaluated. Through utilizing the previous test results for concrete under chlorides for 180 days, the applicability of the proposed technique is verified. The proposed technique is evaluated to reasonably predict the chloride behavior in concrete with various w/c (water to cement) ratios and mineral admixtures (GGBFS and FA). It is also shown that decrease in chloride diffusion should be considered for chloride prediction in concrete with mineral admixture since it has very clear decrease in diffusivity with time.

• Proceedings of the KSME Conference
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• 2001.06e
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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.