• Nuclear Engineering and Technology
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• v.29 no.4
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• pp.320-326
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• 1997

The nuclide transport in the one-dimensional porous medium is considered as a first step in developing a decay chain transport in multidimensional inhomogeneous media. A method of solving conventional advection-dispersion equation with decay chain of arbitrary length by using the method of characteristics (MOC) is introduced. In specific cases where the advection are dominant rather than dispersion, the method is known to be useful : one of the most distinctive advantages in applying the model is that the MU minimizes the numerical dispersion, which is distinguished in such common numerical schemes as finite element method and finite difference method. The suggested model is considered to be effective through several illustrations for the case that decay chain of arbitrary length is involved during transport which is difficult to solve by standard numerical solutions if the medium becomes more complicated.

• Nuclear Engineering and Technology
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• v.26 no.2
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• pp.277-284
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• 1994

Much attention has been given to predict the near-field mass transfer of a single radioactive species from a waste solid into surrounding porous medium. But only limited considerations have been given to predict the coupled mass transfer of species with a radioactive decay chain. In this study we present an analysis assuming that the members of a decay chain dissolve congruently with a solubility-limited matrix. We give general, non-recursive analytic solutions for the transport of a radioactive decay chain in a finite porous medium when nuclides are released congruently with the matrix. As an illustration we consider the decay chain $^{234}$ Ulongrightarrow$^{230}$ Thlongrightarrow$^{226}$ Ra from spent fuel. These solutions may be useful and potentially important in performance assessment of radioactive waste repositories.

• Nuclear Engineering and Technology
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• v.26 no.4
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• pp.453-460
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• 1994

The migration equation is modified for a three-member decay chain in the fracture and porous matrix Analytical solutions are obtained by utilizing Laplace transform the initial conditions of Delta function and Bateman equation. The concentrations for each nuclide of Np$^{237}$ -U$^{233}$ -Th$^{229}$ and U$^{234}$ -Th$^{230}$ -Ra$^{226}$ chains selected from the 4n＋1 and 4n＋2 chains are plotted by utilizing analytical solutions in the fracture. Retardation coefficient of the nuclides are obtained using those of the granite. The results indicate that the daughter nuclides such as U$^{233}$ , Th$^{229}$ , Th$^{230}$ and Ra$^{226}$ become important at the far field from the repository though there is very small initial inventory in the waste solid or spent fuel, for they are produced by the mother nuclides decayed in the fracture and porous matrix.

• Nuclear Engineering and Technology
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• v.34 no.3
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• pp.218-231
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• 2002

Using a three-dimensional numerical code, B3R developed for nuclide transport of an arbitrary length of decay chain in the buffer between the canister and adjacent rock in a high- level radioactive waste repository by adopting a finite difference method utilizing the control- volume scheme, some illustrative calculations have been done. A linear sorption isotherm, nuclide transport due to diffusion in the buffer and the rock matrix, and advection and dispersion along thin rigid parallel fractures existing in a saturated porous rock matrix as well as diffusion through the fracture wall into the matrix is assumed. In such kind of repository, buffer and rock matrix are known to be important physico-chemical harriers in nuclide retardation. To show effects of buffer and rock matrix on nuclide transport in HLW repository and also to demonstrate usefulness of B3R, several cases of breakthrough curves as well as three- dimensional plots of concentration isopleths associated with these two barriers are introduced for a typical case of decay chain of $^{234}$ Ulongrightarrow$^{230}$ Thlongrightarrow$^{226}$ Ra, which is the most important chain as far as the human environment is concerned.

• Journal of the Korean Mathematical Society
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• v.38 no.4
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• pp.723-761
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• 2001

The objects of this paper are to formulated a model for the transport of a chain of radioactive waste products in a fractured porous medium, to devise an effective and efficient numerical method for approximating the solution of the model, and to demonstrated the convergence of the numerical method. The formulation begins from a model in an unfractured (single porosity) medium, passes through a double porosity model in a fractured medium, and ends with a modified single porosity model that takes the relevant time scales of the flow and the nuclear decay.

• Nuclear Engineering and Technology
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• v.25 no.4
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• pp.539-547
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• 1993

A stochastic approach using continuous time Markov process is presented to model the one-dimensional nuclide transport in fractured rock media as a further extension for previous works［1-3］. Nuclide transport of decay chain of arbitrary length in the single planar fractured rock media in the vicinity of the radioactive waste repository is modeled using a continuous time Markov process. While most of analytical solutions for nuclide transport of decay chain deal with the limited length of decay chain, do not consider the case of having rock matrix diffusion, and have very complicated solution form, the present model offers rather a simplified solution in the form of expectance and its variance resulted from a stochastic modeling. As another deterministic way, even numerical models of decay chain transport, in most cases, show very complicated procedure to get the solution and large discrepancy for the exact solution as opposed to the stochastic model developed in this study. To demonstrate the use of the present model and to verify the model by comparing with the deterministic model, a specific illustration was made for the transport of a chain of three member in single fractured rock medium with constant groundwater flow rate in the fracture, which ignores the rock matrix diffusion and shows good capability to model the fractured media around the repository.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.20 no.2
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• pp.171-183
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• 2022

The parent and daughter nuclides in a radioactive decay chain arrive at secular equilibrium once they have a large half-life difference. The characteristics of this equilibrium state can be used to estimate the production time of nuclear materials. In this study, a mathematical model and algorithm that can be applied to radio-chronometry using the radioactive equilibrium relationship were investigated, reviewed, and implemented. A Bateman equation that can analyze the decay of radioactive materials over time was used for the mathematical model. To obtain a differential-based solution of the Bateman equation, an algebraic numerical solution approach and two different matrix exponential functions (Moral and Levy) were implemented. The obtained result was compared with those of commonly used algorithms, such as the Chebyshev rational approximation method and WISE Uranium. The experimental analysis confirmed the similarity of the results. However, the Moral method led to an increasing calculation uncertainty once there was a branching decay, so this aspect must be improved. The time period corresponding to the production of nuclear materials or nuclear activity can be estimated using the proposed algorithm when uranium or its daughter nuclides are included in the target materials for nuclear forensics.

• The korean journal of orthodontics
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• v.54 no.3
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• pp.153-159
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• 2024

Objective: This study aimed to assess the effects of commonly consumed hot drinks on the force decay of orthodontic elastomeric chains. Methods: This in vitro experimental study evaluated 375 pieces of elastomeric chains with six rings placed on a jig. Four rings were stretched by 23.5 mm corresponding to the approximate distance between the canine and the second premolar. Fifteen pieces served as reference samples at time zero, and 360 pieces were randomized into four groups: control, hot water, hot tea, and hot coffee. Each group was further divided into six subgroups (n = 15) according to the different exposure periods. The specimens in the experimental groups were exposed to the respective solutions at 65.5℃ four times per day for 90 seconds at 5-second intervals. The control group was exposed to artificial saliva at 37℃. The force decay of the samples was measured at 1, 2, 7, 14, 21, and 28 days using a universal testing machine. Data were analyzed using repeated-measures analysis of variance. Results: Maximum force decay occurred on day 1 in all groups. The minimum force was recorded in the control group, followed by the tea, coffee, and hot water groups on day 1. At the other time points, the minimum force was observed in the tea group, followed by the control, coffee, and hot water groups. Conclusions: Patients can consume hot drinks without concern about any adverse effect on force decay of the orthodontic elastomeric chains.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.12
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• pp.2230-2234
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• 2010

This paper deals with the change of surface potential decay, surface resistivity, contact angle and XPS of ultraviolet-treated PET films. From the experimental results on the surface potential decay of UV degraded-samples, it was found that the accumulation of charge is decreased and the surface potential decay time is shortened. Also, from the result of XPS, it was found that the changes affected by the surface degradation of PET film were caused by the generation of carboxyl groups through the chain decomposition and recombination with oxygen molecules in the air.

• Nuclear Engineering and Technology
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• v.31 no.4
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• pp.432-443
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• 1999

Using a two-dimensional numerical model, nuclide transport in the buffer between the canister and adjacent rock in a high-level radioactive waste repository is dealt with. Calculations are made for a typical case with a three-member decay chain, $^{234}$ U longrightarrow $^{230}$ Th longrightarrow $^{226}$ Ra. The solution method used here is based on a physically exact formulation by a control volume method directly integrating the governing equation over each control volume.